FIELD

[01 ] The present invention relates to an optical beam-forming apparatus arranged for forming an optical suitable for use in manipulating cold atoms or molecules, and/or in cooling atoms or molecules, e.g. such as to form cold atoms or molecules. In particular, though not exclusively, the invention relates to optical beam-forming apparatus for use in magneto-optical traps (MOTs), such as 2-dimensional (2D) or 3-dimensional (3D) MOTs.

BACKGROUND

[02] The temperature of a gas depends upon the speeds of the particles forming the gas. This relationship underpins the concept of laser cooling of gasses. Mechanical forces between a laser beam and the moving atoms in a gas are used to slow the atoms in a gas and thereby produce very low gas temperatures. Gas temperatures achievable by laser cooling may be a few micro-Kelvins. This corresponds to atomic speeds ten around thousand times smaller than when the gas is at room temperature. An important property of laser-cooled gas is that gas atoms only weakly interact with each other. This makes it possible to observe low-temperature quantum effects. In the following, reference is made to atoms of a gas, and it is to be understood that the following also applied to molecules of a gas, as would be readily understood by the skilled person.

[03] The technique of laser cooling exploits the condition in which the frequency of a laser beam is set close to resonance with an energy difference between two energy levels within the atoms of the gas. This allows transitions of the quantum states of atoms of gas being cooled. An atom of gas moving in the +x direction with a velocity v _x is caused to interact with a counter- propagating laser beam of light having a frequency f which is close to resonance with one of the allowed quantum transitions of the atom: f = ω + δ, in which ω is the frequency of a photon required to achieve the quantum transition in the atom, and δ « ω is a small frequency detuning. As seen from the perspective (inertial frame) of the atom, the source of the laser light moves with a relative velocity (v _x ) towards the atom. Due to the Doppler effect, the frequency of the laser light (photon energy) is shifted to a frequency f in proportion to that relative velocity : f = f(1 +v c) ~ ω + δ + ω [v c].

[04] If the value of δ is selected so that δ = - ω [v c], where c is the speed of light in vacuum, then f = ω. Under these conditions the laser is in resonance with the an atomic transition of the atoms within the gas moving in the +x direction. Thus, when a gas atom absorbs a photon from the laser, it is excited to an excited quantum state for a short period of time and subsequently returns to the original un-excited quantum state by emitting a photon spontaneously in a random direction. [05] Each time this quantum transition cycle is repeated, a net change (Ap) in momentum of the atom occurs in the +x direction. This net change is equal to the momentum of the initially absorbed photon, which is given by: Ap = - h/λ, where h is Planck's constant and A is the wavelength of the laser light. The absorption of the photon, and therefore the momentum change, is always in the -x direction. However, importantly, the momentum change experienced by atom caused by the subsequent spontaneous photon emission averages-out to zero. This is because the direction of spontaneous photon emission is random. The slowing force imposed upon atoms by the cooling laser beam, is equal to the rate of change of momentum experienced by an atom. This is given by the momentum change per absorption-emission cycle, multiplied by the rate of such cycles. Accordingly, repeated photon absorption-emission cycles generate a net slowing force in the -x direction, which reduces the velocity of gas atoms in the +x direction.

[06] However, this Doppler cooling process begins to become ineffective when the detuning required for cooling becomes comparable to the natural line width (Af) of the atomic transition in question. As a consequence, the minimum thermal energy of the atom approximately equal to hAf. This means that the minimum temperature (7) will be about: 7 ~ hAf /k _B , where k _B is Boltzmann's constant.

[07] Laser cooling with a single laser beam is effective when the laser detuning (<5) is larger than the line width (Af) of the atomic transition. However as the atoms cooled down, the necessary detuning becomes comparable to the line width and atoms moving in the -x direction then experience an accelerating force which cancels the slowing force experienced by atoms moving in the +x direction. The increased speed of the former atoms reheats the latter atoms by inter-atomic collisions.

Optical Molasses

[08] One application of laser cooling is the so-called Optical molasses' technique. To achieve lower temperatures, two counter-propagating laser beams are directed upon the atoms to be cooled. A first laser imparts a frictional force F ₊ on an atom, whereas the counter-propagating second laser imparts a frictional force F. on the atom. In this situation, the atom experiences separate forces from each laser with a net force being:

[09] F _X = F ₊ + F.

[10] When the laser is tuned to the condition required for cooling, identified above, then F. » F ₊ for atoms moving in the +x direction at high temperatures/velocities, and F ₊ » F. for atoms moving in the -x direction at high temperatures/velocities. In this way, the two laser beams are able to cool atoms moving in opposite directions. As the atoms cool, and there velocities fall, the net force imposed on an atom by the two counter-propagating laser beams, is given by:

F _x = -β\ν _χ \ [1 1 ] This is a damping force (i.e. negative sign) which applies equally whatever the direction (+/-) of the velocity of the atom. The motion of the cold atoms is damped in both x-directions. As a result, an arrangement of two counter-propagating laser beams, described above, is commonly known as "optical molasses". This technique is often applied in three dimensions, using six laser beams. This makes the atoms slow but it does not completely reduce their velocity to zero. As a result, the atoms do not remain stationary and consequently are not trapped by this technique alone.

Magneto-optical Atomic &/or Molecular Cooling

[12] As described above, an optical molasses arrangement provided by two counter- propagating laser beams provides optical cooling only along the axis of laser beam counter- propagation (the x-direction [+/-]). To provide optical cooling along multiple orthogonal axes requires a pair of counter-propagating laser beams along each of the orthogonal axes in question (e.g. x-direction, y-direction, z-direction). This will enable atoms to be cooled/stopped in respect of multiple velocity components (x; y; z directions [+/-]).

[13] However even such two-dimensional or three-dimensional optical molasses does not have the ability to trap cooled atoms at the same location in space, and so is not effective in generating a concentration of cooled atomic gas. The addition of a magnetic field provides this means of concentration, when used in conjunction with the optical molasses described above. This combination is generally known as a magneto-optical trap (MOT) arrangement.

[14] A typical type of three-dimensional MOT comprises six laser beams consisting of three pairs of counter-propagating beams, arranged to converge at a location corresponding to the centre of a magnetic quadrupole field which creates an attractive potential for atomic states with , > 0. This achieves atomic cooling of all three velocity components within the magnetic trapping region where the cooling beams converge. Alternatively, a two-dimensional MOT may omit one of the three pairs of counter-propagating beams thereby achieving atomic cooling in two of the three orthogonal velocity components within the magnetic trapping region where the cooling beams converge, while simultaneously allowing cooled atoms to be ejected/pushed from the cooling region in a direction along the third of the three orthogonal velocity components.

[15] The magnetic quadrupole field is typically generated using two coils carrying currents flowing in opposite directions. The magnitude of the quadrupole magnetic field produced by these coils has a minimum value at its centre, where the magnetic fields from the two individual coils mutually cancel. Applying a magnetic quadrupole field of the simple form B(z) = (0, 0, b z) with b being the magnetic field gradient and z the spatial coordinate, leads to Zeeman-splitting of otherwise degenerate spin-state energy levels in an atom. For the ground spin state J = O the energy remains undisturbed (no angular momentum) while for the excited state J' = 1 the degeneracy is lifted by the non-zero value of the magnetic field at locations other than z = 0. [16] The energy of a magnetic sub-level in a magnetic field B is given by the magnetic interaction energy:

E = guJ _B M _j B

in which g _L is the Lande g-factor, and μ _Β is the Bohr magneton. Right-circular polarized light is able to drive atomic transitions between the split spin states when propagating in one direction along the z-axis, whereas left-circular polarized light is able to drive atomic transitions between the split spin states when propagating in the other (opposite) direction along the z-axis. This is due to the conservation of angular momentum. As a result, an atom bathes within two such counter-propagating laser beams (with opposite circular polarisation senses) will experience a net force pushing it towards the location z = 0 where the magnetic field is zero and where the Zeeman splitting ceases. At position z = 0, an atom feels no net force.

[17] Atomic states having , > 0 achieve their lowest energy when B is its smallest, whereas atomic states with , < 0 achieve their lowest energy when B is higher. Accordingly, the centre of a magnetic quadrupole field, where its minimum lies, is attractive for atomic states with , > 0, but repulsive for atomic states with , < 0. In this way, a magnetic field is used to compress a gas of cold atoms produced by the optical molasses effect, thereby increasing the density of the gas of cold atoms within the cooling region at the centre of the quadrupole field. This enables quantum effects such as Bose-Einstein condensation to be realised.

[18] Accordingly, laser cooling beams may be used in conjunction with magnetic traps to provide magneto-optical traps (MOTs), such as 2-dimensional (2D) MOTs which use laser beams counter-propagating in the x direction [+/-] and the y direction [+/-], but not the z direction, or 3-dimensional (3D) MOTs which use laser beams counter-propagating in the x direction [+/-] and the y direction [+/-], and the z direction [+/-].

[19] However, the optical apparatus employed to prepare, direct and control the multiple laser beams in 2D-MOTs and 3D-MOTs is large, expensive and typically bespoke or peculiar to the experimentalist who has created the MOT in question. There is no standardisation in this new technical field. Indeed, constructing such optical apparatus requires expert specialist knowledge which may be difficult or expensive (or both) to obtain. These difficulties are a large barrier to building MOTs and other similar optical apparatus for working with cold atoms or molecules.

[20] The invention aims to address these matters.

SUMMARY

[21 ] According to the present invention there is provided an apparatus and method as set forth in the appended claims. Other features of the invention will be apparent from the dependent claims, and the description which follows.

[22] A first aspect of the invention provides an optical beam-forming apparatus arranged for forming an optical beam for manipulating cold atoms or cold molecules, the apparatus comprising a first optical expander arranged to receive a laser beam and to expand the cross- sectional area of the laser beam asymmetrically in a first dimension transverse to the laser beam thereby to provide a first expanded laser beam. The apparatus includes a second optical expander arranged to receive the first expanded laser beam and to expand the cross-sectional area of the first expanded laser beam asymmetrically in a second dimension which is transverse to the first dimension, and to output the result as a second expanded laser beam in a direction which is transverse to both the first dimension and the second dimension thereby to provide an output laser beam having a cross-sectional area expanded in two transverse dimensions of the output laser beam. The term 'expand' may be understood to mean, for example, to increase the cross-sectional area of the laser beam whilst substantially providing collimation in/of the expanded laser beam (e.g. in at least one dimension thereof transverse to the beam axis), optionally with a small degree of convergence (e.g. in at least one dimension thereof transverse to the beam axis) such as towards a notional focal point or the like. However, the disclosures herein are not limited to this interpretation of the term 'expand', unless otherwise indicted. The term 'cold atom' and the term 'cold molecule' may be understood to mean, for example, an atom or molecule, respectively, which has a kinetic energy (E) sufficiently small that the equivalent thermal temperature (7) of the atom or molecule (i.e. according to: E=(3/2)kT, where k is Boltzmann's constant) has a value which is less than 1 (one) Kelvin. However, the disclosures herein are not limited to this interpretation of the term 'cold atom' and the term 'cold molecule', unless otherwise indicted. The optical beam forming apparatus may be configured to manipulate (e.g. as part of a cooling process or otherwise) atoms or molecules in or for a 'cold atom apparatus'. A 'cold atom apparatus' may be understood to mean an apparatus configured to produce Bose-Einstein condensation in a gas of cold atoms or cold molecules. However, the disclosures herein are not limited to this interpretation of the term 'cold atom apparatus', unless otherwise indicted. The second optical expander may present a substantially planar optical output face which is substantially coplanar with the plane containing both the first dimension and the second dimension. For example, the optical output face may be rectangular in shape (e.g. square or elongated rectangular). The optical output face may be oblique (but not perpendicular) or substantially perpendicular to the output direction of the second expanded laser beam.

[23] The first optical beam expander may be arranged to over-expand the incoming beam before it outputs the first expanded laser beam such that the cross-sectional area of the first expanded laser beam has a width dimension (e.g. a direction perpendicular to the second dimension, such as perpendicular to the longitudinal axis of the second optical expander) exceeding the corresponding width dimension of the clear aperture of the optical input area/face of the second optical expander. Desirably, both width dimensions of the over-expanded input beam (i.e. those which are mutually perpendicular and both also perpendicular to the second dimension) may each exceed the corresponding width dimensions of the clear aperture of the optical input area/face of the second optical expander. The cross-sectional area of the first expanded laser beam may be over-expanded to fully fill the clear aperture of the optical input area/face of the second optical expander receiving it. Consequently, due to the over-expansion, the second expanded laser beam may provide a fully-supplied output laser beam having substantially no intensity 'nulls' or gaps within its beam cross-section. Put another way, the cross-section beam intensity may be made free of 'gaps' or 'holes' at which the local light intensity of the beam is negligible or too small to be of practical use.

[24] The optical beam-forming apparatus may include a chassis comprising a first chassis part bearing the first optical expander and the second optical expander, and a second chassis part bearing an optical reflector in spaced opposition to the second optical expander and in optical communication therewith for returning to the second optical expander the output laser beam received at the optical reflector from the second optical expander. The optical reflector may be arranged to retro-reflect the output laser beam back to the second optical expander. It may comprise a plane mirror or an array of reflecting (retro-reflecting) prisms. This permits re-cycling of the light of the output laser beam for re-use (e.g. in cooling/manipulating atoms/molecules) in the space between the optical reflector and the second optical expander.

[25] The first chassis part is preferably spaced from the second chassis part by a spacing adapted for receiving an optically transparent vacuum chamber permitting the aforesaid optical communication through the vacuum chamber between the second optical expander and the optical reflector. The vacuum chamber may accommodate the cooling/manipulating atoms/molecules in the space between the optical reflectory) and the second optical expander.

[26] The chassis may further comprise a third chassis part bearing an aforesaid first optical expander and an aforesaid second optical expander, and a fourth chassis part bearing an optical reflector in spaced opposition to the second optical expander of the third chassis part and in optical communication therewith for returning to the second optical expander of the third chassis part the output laser beam received at that optical reflector from the second optical expander of the third chassis part. The optical reflectors may be arranged to retro-reflect the output laser beam back and forth to each other via the second optical expander. They may comprise a plane mirror or an array of reflecting (retro-reflecting) prisms. This permits multiple re-cycling of the light of the output laser beam for multiple re-use (e.g. in cooling/manipulating atoms/molecules) in the space between the optical reflectors e.g. with the second optical expander between them.

[27] The third chassis part is preferably spaced from the fourth chassis part by a spacing adapted for receiving the aforesaid optically transparent vacuum chamber permitting the aforesaid optical communication through the vacuum chamber between the second optical expander of the third chassis part and the optical reflector of the fourth chassis part. [28] The chassis may further comprise a translation stage including an optical collimator unit arranged for receiving an end of an optical fibre and for collimating laser light output from the optical fibre into a collimated laser beam directed along an optical axis parallel to a longitudinal axis of the chassis between the second optical expander and the optical reflector, wherein the translation stage is arranged to adjustably position the optical axis relative to the longitudinal axis.

[29] Desirably, the first optical expander includes a laser line-generator (Powell) lens to receive the laser beam and therewith to form a diverging laser line beam.

[30] Desirably, the first optical expander includes a converging lens in optical communication with the laser line-generator (Powell) lens and arranged to receive the laser line beam and to therewith to form a converging laser line beam shaped to converge towards a focal point.

[31 ] Desirably, in the optical beam-forming apparatus the first optical expander, and/or the laser line-generator (Powell) lens, and/or the converging lens, are fixed in position (e.g. rigidly fixed) relative to each other and may be mounted upon a common mounting plate, a/the chassis or a common frame. The fixed state of optical components described above, obviates the need for mechanisms for adjusting the axial position (e.g. along the optical axis) or angular position (e.g. orientation/rotation about the optical axis) of the optical component in question, thereby saving space and allowing a compact design.

[32] Desirably, the first optical expander includes a telescope in optical communication with the laser line-generator (Powell) lens and arranged to receive the laser beam and to expand the cross-sectional area of the laser beam in two dimensions transverse to the laser beam, and to output the result to the laser line-generator (Powell) lens.

[33] Desirably, the telescope is a Galilean telescope. A particular advantage of using a Galilean telescope is that it has a shorter focal length than other types of telescope, such as a Keplerian telescope. This allows for a more compact and space-efficient arrangement.

[34] Desirably, the optical beam-forming apparatus includes a folded optics unit arranged to receive the first expanded laser beam and to reverse the direction of the first expanded laser beam thereby to redirect the first expanded laser beam towards the second optical expander for input thereto. The folding of the optical axis permits a very significant saving in the space/volume occupied by the optical beam forming apparatus. This allows for a very compact unit/apparatus/assembly. The folded optics unit may be arranged to fold or turn the optical path of the first expanded laser beam by substantially 180 degrees. The folded optics unit may be arranged to transversely displace the beam axis of the first expanded laser beam output by it towards the second optical expander, relative to the beam axis of the first expanded laser beam received by it from the first optical expander. Accordingly, using the folded optics unit, the optical axis of the first optical expander may be laterally displaced relative to the optical axis of the second optical expander, but the two may remain in optical communication via the folded optics unit. The second optical expander may be disposed 'under' or Over' the first optical expander with the folded optics unit disposed to one side of both of them. The folded optics unit may comprise optically reflective surfaces disposed and oriented to achieve such optical folding of the beam path of the first expanded laser beam. The reflective surfaces may comprise plane mirrors, reflecting prisms (e.g. 180 degree reflector prisms, or pairs of roof prisms) or the like.

[35] The optical beam-forming apparatus may include a mounting plate or frame, wherein the first optical expander and the second optical expander are disposed on opposite sides of the mounting plate or frame and the folded optics unit is arranged to redirect the first expanded laser beam firstly in a direction transverse to the mounting plate or frame and subsequently in a direction substantially parallel to the mounting plate or frame towards the second optical expander. The first optical expander and/or the second optical expander (preferably both) may be fixed (e.g. rigidly fixed) in relative position upon the mounting plate or frame. The fixed state of these optical components, obviates the need for mechanisms for adjusting the axial position (e.g. along the optical axis) or angular position (e.g. orientation/rotation about the optical axis) of the optical component in question, thereby saving space and allowing a compact design.

[36] Desirably, the second optical expander comprises a plurality of optical reflectors spaced in succession along a transmission axis for separately reflecting a respective proportion of the first expanded laser beam in a direction transverse to the transmission axis which is said direction transverse to both the first dimension and the second dimension, thereby to provide said output laser beam formed as a spatial succession of separate said respective proportions of the first expanded laser beam reflected concurrently therefrom. At least one of, and preferably each of, the optical reflectors presents an elongated reflective surface area towards the transmission axis wherein the long axis of the elongate surface is transverse (e.g. perpendicular to the transmission axis. Preferably, the long axis of the elongate surface is substantially parallel to (e.g. or at least extends in a direction with a projection along) the first dimension along which the first expanded beam is expanded. This allows the reflective surface(s) to be sympathetic to the first dimension of beam expansion, for efficiently accommodating that expansion. Preferably, the area of each of the reflective surfaces is sufficiently large and appropriately positioned to each accommodate the full cross-sectional area of the first expanded laser beam when input thereto. This avoids certain optical losses. The cross-sectional area of the combined reflective surfaces of the second optical beam expander, when viewed down the optical output axis thereof (i.e. the direction of the output laser beam) is preferably substantially rectangular. This helps maximise the useable area of the output least beam for manipulating/cooling atoms or molecules. When two or more such beams overlap, in use in a 2D-MOT or a 3D-MOT for example, the rectangular area of each allows a greater overall volume of useable light intensity where overlap occurs - that is to say, overlap is easier to achieve with more efficiency.

[37] Desirably, the plurality of optical reflectors comprises a plurality of optical beam splitters arranged in succession along the transmission axis for receiving the first expanded laser beam, wherein each optical beam splitter is arranged to reflect a proportion of the first expanded laser beam in said direction transverse to the transmission axis, and to transmit a proportion of the first expanded laser beam along the transmission axis, wherein one or more of the plurality of optical beam splitters is arranged for receiving the proportion of the first expanded laser beam transmitted to it by a preceding said optical beam splitter.

[38] Desirably, the first optical expander is arranged to define a focal point such that the first expanded laser beam and the output laser beam are each caused to converge towards the focal point. The convergence may be such as to substantially provide/maintain collimation in/of the expanded laser beam one of the two beam dimensions transverse to the beam axis, with a small degree of convergence in the other dimension transverse to the beam axis. The convergence may be towards a notional/distant focal point or the like, without actually reaching/achieving focus. A particular advantage of this arrangement is that the slight convergence has the effect of compensating for optical losses (scattering, absorption etc.) suffered by the output laser beam upon passage through sample atoms/molecules, and/or by reflection from an aforementioned optical reflector, and/or transmission through filters in its path.

[39] By slightly converging the laser beam, a greater degree of light intensity may be achieved by the beam even when the amount of light available in the beam is diminished by such losses. The convergence may be such as to provide a small degree of convergence in both of the two dimensions transverse to the beam axis. The convergence may define a convergence angle of the laser beam which is less than 5 degrees relative to the laser central beam axis, or more preferably less than 4 degrees, or yet more preferably less than 3 degrees, or less than 2 degrees. The first optical expander may be configured to impose a convergence upon the first expanded laser beam according to a focal length thereof. The focal length of the first optical beam expander may be a value of between 0.5m and 2m from the optical output end and of first optical expander (e.g. the final/output optical element e.g. lens, thereof). This focal length may preferably be between 0.75m and 1 .5m, or may more preferably be between 0.8m and 1 .2m, such as about 1 .0m.

[40] The optical beam-forming apparatus may include an optical collimator for receiving an output end of an optical fibre and for collimating a laser beam input to the optical collimator from the optical fibre. The optical beam-forming apparatus may include a circular polarising filter disposed in optical communication with the second optical expander for receiving light of the laser beam (e.g. the output laser beam) and transmitting a circularly polarised light output (e.g. the output laser beam). The circular polariser may be attached, bonded or laminated to the output surface of the second beam expander, or may be separate from it. Right-circular polarized light is able to drive atomic transitions between the split spin states of an atom/molecule split by an applied magnetic field when propagating in one direction along the axis of the output laser beam, whereas left-circular polarized light is able to drive atomic transitions between the split spin states when propagating in the other (opposite) direction. As a result, an atom/molecule bathed within the output laser beam (propagating in one direction) will experience a net force pushing it towards the location where the magnetic field is zero and where the Zeeman splitting ceases. Accordingly, the output laser beam may be used in conjunction with a magnetic field to provide a magneto-optical trap (MOT), such as 2- dimensional (2D) MOTs which may use such output laser beams counter-propagating in the x direction [+/-] and the y direction [+/-], but not the z direction, or 3-dimensional (3D) MOTs which may use such output laser beams counter-propagating in the x direction [+/-] and the y direction [+/-], and the z direction [+/-].

[41 ] In a second aspect, the invention provides an magneto-optical trap (MOT) comprising an optical beam-forming apparatus described above. The expansion in the first dimension and/or in the second dimension may result in the output laser beam having a cross-sectional area that is expanded in a direction transverse to the atom/molecule beam axis. The magneto-optical trap may be configured to form/provide a beam of cold atoms or cold molecules directed along an axis thereof (i.e. an axis of the MOT). The first dimension may be transverse to the axis, or alternatively the second dimension may be transverse to the axis, or alternatively both the first dimension and the second dimension may be transverse to the axis. For example, one of the first and second dimensions may be perpendicular to the axis while the other is parallel, or both of the first and second dimensions may be oblique, diagonal or otherwise transverse to that axis. The optical beam-forming apparatus may preferably be configured to form an optical beam for cooling atoms or molecules in a magneto-optical trap (MOT) which is arranged to provide a beam of cold atoms or cold molecules. The magneto-optical trap may be configured to provide a beam of cold atoms or cold molecules extending along an axis thereof (i.e. an axis of the MOT), and the first dimension may be transverse to that axis (i.e. of the MOT). Alternatively, both are transverse to that axis. For example, one of the first and second dimensions may be perpendicular to the axis, with the other parallel, or both of the first and second dimensions may be oblique, diagonal or otherwise transverse to that axis.

[42] Desirably, in an aspect, the invention may provide an apparatus comprising a first said optical beam-forming apparatus to provide a first output laser beam, and a second said optical beam-forming apparatus disposed to provide a second output laser beam directed to intersect the first output laser beam in a direction transverse to the first output laser beam.

[43] The optical beam-forming apparatus may include an optical reflector for reflecting (e.g. retro-reflecting) a said output laser beam from the second optical expander. The second optical expander may be arranged to output circularly polarised light, and the apparatus may include a quarter-wave plate disposed between the optical reflector and the second optical expander, wherein the quarter-wave plate is disposed to receive the output laser beam both before and after reflection thereof by the optical reflector. The provision of a reflector, such as a retro- reflector, permits an output laser beam to be re-used after it has traversed a sample of atoms/molecules being cooled or otherwise manipulated, by simply re-directing it back through the sample. The reflector may be a plane mirror. It may be disposed in the chassis so as to oppose the second beam expander in optical communication across a space within the chassis adapted for receiving a sample of atoms/molecules for manipulation/cooling - such as a vacuum chamber possessing optically transmissive or transparent walls.

[44] Provision of a quarter wave-plate before the reflector (e.g. immediately before it, or attached to it, allows incoming circularly polarised light of the output laser beam to be transformed into linearly polarised light for reflection at the reflector. After reflection, the reflected output laser beam (linearly polarised) passes back through the quarter wave-plate and is transformed back into circularly polarised light having the correct 'handedness' (i.e. right- circular or left-circular) of circular polarisation for manipulating/cooling the atoms/molecules of the sample into which it is re-directed by the reflector. Otherwise, of the output laser beam is reflected by the reflector while still circularly polarised, it may chance to different handedness' of circular polarisation upon reflection, which is inappropriate for use in cooling/manipulating the sample of atoms/molecules into which it is directed by the reflector, in use. Desirably, when such reflectors (e.g. retro-reflectors) are used the first optical expander preferably is arranged to define a focal point such that the first expanded laser beam and the output laser beam are each caused to converge towards the focal point. This allows the light intensity of the reflected (e.g. retro-reflected) laser beam to be maintained or boosted by the convergence.

[45] The optical beam-forming apparatus may comprise a first optical beam-forming apparatus as described above to provide a first output laser beam, and a second optical beam-forming apparatus as described above and disposed to provide a second output laser beam directed intersect the first output laser beam in a direction transverse to the first output laser beam.

[46] The second optical beam-forming apparatus may comprise a second circular polarising filter disposed in optical communication with the second optical expander of the second optical beam-forming apparatus, for receiving the second output laser beam and transmitting a circularly polarised second output laser beam.

[47] The second optical beam-forming apparatus may comprise a second optical reflector for reflecting (e.g. retro-reflecting) a said output laser beam from the second optical expander of the second optical beam forming apparatus. The second optical expander of the second optical beam forming apparatus may be arranged to output circularly polarised light, and the apparatus may include a second quarter-wave plate which may be disposed between the second optical reflector and the second optical expander, wherein the second quarter-wave plate is disposed to receive the output laser beam from the second optical expander of the second optical beam- forming apparatus both before and after reflection thereof by the second optical reflector.

[48] The chassis may comprise a laser input aperture disposed for receiving an optical push- beam into the chassis in a direction transverse to both the first output laser beam and the second output laser beam. Preferably, the laser input aperture is opposed by a cold-atom output port of the chassis for receiving cold atoms/molecules cooled by the first and second output laser beams pushed therethrough by the optical push-beam.

[49] The optical beam-forming apparatus may include a push-beam alignment stage disposed at the laser input aperture comprising a push-beam output optical part mounted thereto and adjustable in position relative to the push-beam alignment stage in two dimensions transverse to the output optical axis of the push-beam output optical part.

[50] The optical beam-forming apparatus may be combined with a vacuum chamber (e.g. of a magneto-optical trap) comprising a transmission window disposed in a wall of the vacuum chamber via which the circular polarising filter is in optical communication with the vacuum chamber. The transmission window may be opposed by the optically reflective surface disposed at an opposite side of the vacuum chamber. A quarter-wave plate may be disposed at that opposite side of the vacuum chamber between the optically reflective surface and the transmission window. The quarter-wave plate may be disposed to receive the output laser beam both before and after reflection thereof by the optically reflective surface.

[51 ] Desirably, the second said optical beam-forming apparatus comprises a second circular polarising filter disposed in optical communication with the second optical expander of the second said optical beam-forming apparatus, for receiving the second output laser beam and transmitting a circularly polarised second output laser beam.

[52] Desirably, the vacuum chamber may comprise a second transmission window disposed in a wall of the vacuum chamber via which the second circular polarising filter is in optical communication with the vacuum chamber. The second transmission window may be opposed by a second optically reflective surface disposed at an opposite side of the vacuum chamber. A second quarter-wave plate may be disposed at said second opposite side of the vacuum chamber between the second optically reflective surface and the second transmission window.

[53] Desirably, the vacuum chamber comprises a third optical window disposed in a wall of the vacuum chamber for receiving an optical push-beam into the vacuum chamber in a direction transverse to both the first output laser beam and the second output laser beam, wherein the third optical window is opposed by a cold-atom output port of the vacuum chamber for receiving cold atoms cooled by the first and second output laser beams pushed therethrough by the optical push-beam.

[54] The optical beam-forming apparatus may include a push-beam alignment stage disposed at the third optical window comprising a push-beam output optical part mounted thereto and adjustable in position relative to the push-beam alignment stage in two dimensions transverse to the output optical axis of the push-beam output optical part.

[55] Desirably, the optical beam-forming apparatus includes three said optical beam formers including a first said optical beam-forming apparatus to provide a first output laser beam, and a second said optical beam-forming apparatus disposed to provide a second output laser beam directed intersect the first output laser beam in a direction transverse to the first output laser beam, a third said optical beam-forming apparatus to provide a third output laser beam directed intersect the first output laser beam and the second output laser beam in a direction transverse to both the first output laser beam and the second output laser beam. In this way, a configuration for a 3D MOT may be provided. The 3D MOT may include a fourth laser beam configured and arranged to provide a push beam for manipulating cold atoms or cold molecules to force them in a direction along an axis of the 3D MOT which is transverse (e.g. perpendicular) to the first and second output laser beams or to all three of the first, second and third output laser beams.

[56] In another aspect, the invention provides a magneto-optical trap (MOT) comprising an optical beam-forming apparatus as described above, and including a magnetic field apparatus for providing a magnetic field arranged to concentrate gas atoms or molecules cooled or manipulated using the optical beam-forming apparatus.

[57] In yet another aspect, the invention provides a magneto-optical trap (MOT) comprising an optical beam-forming apparatus as described above, and including a magnetic field apparatus for providing a magnetic field within the chassis (or within a vacuum chamber received within the chassis) to concentrate gas atoms or molecules cooled or manipulated by the optical beam- forming apparatus. The magnetic field apparatus may be housed within the chassis, or the chassis may be arranged to house the magnetic field apparatus. The invention may provide a cold atom apparatus comprising a magneto-optical trap (MOT) as described above, for example a 2D MOT or a 3D MOT. In yet another aspect, the invention may provide a 3D MOT configured to produce Bose-Einstein condensation in a gas of atoms or molecules. The 3D MOT may comprise one, two or three or more of he optical beam forming apparatus as described above, or may comprise a MOT or a 2D MOT as described above.

[58] In a further aspect, the invention provides a method of forming an optical beam for manipulating cold atoms or cold molecules, comprising receiving a laser beam and expanding the cross-sectional area of the laser beam asymmetrically in a first dimension transverse to the laser beam thereby to provide a first expanded laser beam, receiving the first expanded laser beam and expanding the cross-sectional area of the first expanded laser beam asymmetrically in a second dimension which is transverse to the first dimension, and outputting the result as a second expanded laser beam in a direction which is transverse to both the first dimension and the second dimension thereby to provide an output laser beam having a cross-sectional area expanded in two transverse dimensions of the output laser beam.

[59] Desirably, the method includes expanding the laser beam into a diverging laser line beam.

[60] Desirably, the method includes receiving the laser line beam and to therewith forming a converging laser line beam shaped to converge towards a focal point.

[61 ] Desirably, the method includes providing a telescope to receive the laser beam and therewith expanding the cross-sectional area of the laser beam in two dimensions transverse to the laser beam, and forming the laser line beam therewith.

[62] Desirably, the method includes receiving the first expanded laser beam and reversing the direction of the first expanded laser beam thereby to redirect the first expanded laser beam forming the second expanded laser beam therewith.

[63] Desirably, the method includes providing a plurality of optical reflectors spaced in succession along a transmission axis and therewith separately reflecting a respective proportion of the first expanded laser beam in a direction transverse to the transmission axis which is said direction transverse to both the first dimension and the second dimension, thereby providing said output laser beam formed as a spatial succession of separate said respective proportions of the first expanded laser beam reflected concurrently therefrom.

[64] Desirably, the plurality of optical reflectors comprises a plurality of optical beam splitters arranged in succession along the transmission axis for receiving the first expanded laser beam, wherein the method includes reflecting by each beam-splitter a proportion of the first expanded laser beam in said direction transverse to the transmission axis, and transmitting a proportion of the first expanded laser beam along the transmission axis, at one or more of the plurality of optical beam splitters receiving the proportion of the first expanded laser beam transmitted to it by a preceding said optical beam splitter.

[65] Desirably, the method includes imposing a convergence upon the first expanded laser beam and the output laser beam such that they are each caused to converge towards a focal point.

[66] Desirably, the method includes imposing a circular polarisation upon the second expanded thereby transmitting a circularly polarised output laser beam.

[67] In a yet further aspect, the invention provides a method of cooling atoms or molecules in a magneto-optical trap (MOT), the method comprising cooling atoms or molecules within the optical trap using at least one optical beam formed as described above. The magneto-optical trap may be configured to provide a beam of cold atoms or cold molecules directed along an axis the magneto-optical trap, and said expansion in said first dimension and/or in said second dimension results in said output laser beam having a cross-sectional area that is expanded in a direction transverse to said axis.

[68] Desirably, the method of cooling atoms or molecules in a magneto-optical trap includes providing a first said output laser beam, and a second said output laser beam directed intersect the first output laser beam in a direction transverse to the first output laser beam.

[69] Desirably, the method of cooling atoms or molecules in a magneto-optical trap includes directing a said output laser beam to an optically reflective surface via a quarter-wave plate disposed to receive said output laser beam both before and after reflection thereof by the optically reflective surface.

[70] Desirably, the method of cooling atoms or molecules in a magneto-optical trap includes directing a said second output laser beam to a second optically reflective surface via a second quarter-wave plate disposed to receive said second output laser beam both before and after reflection thereof by the second optically reflective surface.

[71 ] Desirably, the method of cooling atoms or molecules in a magneto-optical trap includes providing an optical push-beam in a direction transverse to both the first output laser beam and the second output laser beam, cooling atoms or molecules using the first and second output laser beams and pushing the cooled atoms using the optical push-beam. [72] Desirably, the method of cooling atoms or molecules in a magneto-optical trap includes providing a first output laser beam, and a second output laser beam directed intersect the first output laser beam in a direction transverse to the first output laser beam, and a third output laser beam directed intersect the first output laser beam and the second output laser beam in a direction transverse to both the first output laser beam and the second output laser beam.

[73] In an additional aspect, the invention provides a method of magneto-optical trapping (MOT) comprising providing an output laser beam by the method of forming an optical cooling beam in a magneto-optical trap as described above, and providing a magnetic field arranged to provide a concentration of gas atoms or molecules cooled or manipulated using the optical beam-forming apparatus.

[74] In a further additional aspect, the invention provides a method of magneto-optical trapping (MOT) comprising the method of cooling atoms or molecules in a magneto-optical trap as described above, and providing a magnetic field within the optical trap arranged to provide a concentration of gas atoms or molecules cooled or manipulated using the optical beam-forming apparatus. In yet a further aspect, the invention provides a method for forming Bose-Einstein condensation in a gas of atoms or molecules, the method comprising the method of magneto- optical trapping described above.

[75] The invention may provide a beamformer (which may form the second optical expander disclosed herein), for forming a beam of light, comprising a stack of prisms, each of the prisms being monolithic and having orthogonal faces and at least one oblique face oblique to the orthogonal faces, each prism being adjacent to at least one other prism in the stack; and reflective layers, each reflective layer being disposed between oblique faces of adjacent prisms, each pair of adjacent prisms having a respective reflective layer disposed therebetween, the reflective layers having different reflectivities. At least one of the prisms may be a rhomboid prism and at least one of the prisms may be a triangular or trapezoidal prism. The prisms may include plural rhomboid prisms and at least one of the prisms is a triangular or trapezoidal prism. Each prism may have a non-oblique face with an anti-reflection coating thereon. Each prism may have a non-oblique face without an anti-reflection coating thereon. Accordingly, the invention, in its first aspect, may comprise a second optical expander in the form of a beamformer described above.

[76] The invention may provide a process for forming a beamformer (which may form the second optical expander disclosed herein) comprising forming a stack of transparent sheets having reflective coatings, each transparent sheet being bonded to at least one other transparent sheet, the reflective coatings having different reflectivities; and carving the stack to define an array of prisms, each prism having been carved from a respective one of the transparent sheets, each of the prisms being monolithic and having at least one oblique face, each prism being bonded to at least one other prism in the array. The carving may include polishing to form flat faces of the prisms. The carving may also involve dicing the stack prior to the polishing to form plural stacklets, the polishing converting the stacklets to prisms. Preferably, at least one of the prisms is a rhomboid prism and at least one of the prisms is a triangular or trapezoidal prism. The prisms may include plural rhomboid prisms and at least one of the prisms may be a triangular or trapezoidal prism. The process may further comprise applying anti- reflection coatings to at least one non-oblique face of each of the prisms. The process may further comprise applying anti-reflection coatings to exactly one face of each of the prisms. Accordingly, process of forming a beamformer described above, may provide a second optical expander of the invention in its first aspect or as described above.

BRIEF DESCRIPTION OF DRAWINGS

[77] For a better understanding of the invention, and to show how embodiments of the same may be carried into effect, reference will now be made, by way of example only, to the accompanying diagrammatic drawings in which:

[78] Figure 1A, 1 B, 1 C and 1 D show different views of a vacuum chamber of a magneto- optical trap for receiving samples of atoms for trapping and cooling. The vacuum chamber is shown surrounded by four magnetic pole pieces for providing a quadruple magnetic field, upon which are mounted upper and lower chassis pieces of optical beamforming apparatus (other parts of which are not shown);

[79] Figure 2 shows a plan view of an optical beamforming apparatus adapted to be mounted upon the upper and lower chassis pieces of figures 1 A, 1 B, 1 C and 1 D;

[80] Figure 3 shows a plan view of an optical beamforming apparatus shown in figure 2;

[81 ] Figure 4 schematically illustrates the optical beam splitting and beam expanding function of an embodiment of the second optical expander within the optical beamforming apparatus of figures 2 and 3;

[82] Figure 5 schematically illustrates the beam expanding operation of the first optical expander within the optical beamforming apparatus of figures 2 and 3;

[83] Figure 6 schematically illustrates the beam expanding operation of the second optical expander within the optical beamforming apparatus of figures 2, 3 and 5 when acting upon the output of the first optical expander following an optical folding;

[84] Figure 7 schematically illustrates the optical beam splitting and beam expanding function of an embodiment of the second optical expander within the optical beamforming apparatus of figures 2, 3, 5 and 6;

[85] Figures 8A, 8B, 8C and 8D illustrate the embodiment of the second optical expander of Figure 7 in more detail in which figure 8A schematically demonstrates optical expanding function also illustrated in figure 7, figure 8B shows a side view, figure 8C shows a perspective view and figure 8D shows a cross-sectional view defined by axis A-A' indicated in figure 8C; [86] Figures 9A, 9B and 9C illustrate perspective views of the topsides and underside of the mounting plate (in isolation) forming a part of the beamforming apparatus of figure 2 and figure 3;

[87] Figures 10A, 10B and 10C illustrate perspective views of the topsides and underside of the beamforming apparatus of figure 2 and figure 3, incorporating the mounting plate of figures 9A, 9B and 9C;

[88] Figures 1 1 A and 1 1 B illustrate opposite perspective views of a chassis bearing an optical beamforming apparatus of figures 10A, 10B and 10C, in optical communication with an optical reflector disposed in spaced opposition thereto at opposite sides of the chassis;

[89] Figures 1 1 C to 1 1 E schematically illustrate a cross-sectional view of an alternative arrangement of an optical beamforming apparatus within a chassis in optical communication with optical reflectors disposed in spaced opposition thereto at both sides of the chassis;

[90] Figure 12 illustrates a translation stage adapted for connection to an end of the chassis of figures 1 1A and 1 1 B for positioning an optical push-beam for transmission through the chassis;

[91 ] Figures 13A and 13B illustrate the translation stage of figure 12 mounted upon an end of the chassis of figures 1 1 A and 1 1 B with an output optical unit for outputting a push-beam, which is coupled to, and adjustably positionable by, the translation stage;

[92] Figures 14A and 14B illustrate the assembly shown in figures 13A and 13B bearing a second optical beamforming apparatus of figures 10A, 10B and 10C, in optical communication with a second optical reflector disposed in spaced opposition thereto at opposite sides of the chassis;

[93] Figures 15A and 15B show opposite end views of the assembly shown in figures 14A and 14B;

[94] Figures 16A and 16B show two views, from opposite sides, of a three-dimensional magneto-optical trap (3D-MOT) incorporating the assembly illustrated in figures 14A and 14B;

[95] Figure 17 schematically illustrates the assembly of figures 14A, 14B 15A and 15B employed as a cold atom source in combination with an optical source for providing laser light used for cooling atoms or molecules and pushing cooled/cold atoms using the laser light provided, the cold atoms then being output to a user application, such as an atomic trap in the manner indicated in figures 16A and 16B;

[96] Figure 18 shows a cross-sectional view of an output laser beam of the optical beam forming apparatus of Figure 2, that is to say, a view looking down the axis of the output laser beam towards the optical beam forming apparatus. Beam intensity profiles are shown along the first and second dimensions (transverse) of the beam; [97] FIGURE 19 illustrates an embodiment of the second optical expander ('beamformer') as a combined perspective illustration of an 8-prism beamformer in the process of its manufacture and during its use in optical beam splitting and beam expanding as a beamformer;

[98] FIGURE 20 is a schematic illustration of an embodiment of the second optical expander ('beamformer') as a 5-prism beamformer in the process of its manufacture and during its use as a beamformer;

[99] FIGURE 21 is a flow chart of a process for making and using a beamformer;

[100] FIGURE 22 is a flow diagram showing dicing of a stack of FIG. 19 for forming beamformers in accordance with the process of FIG. 21 ;

[101 ] FIGURE 23 is a perspective illustration of a beamformer stacklet resulting from the dicing represented in FIG. 22;

[102] FIGURE 24 is a perspective view of an embodiment of a first optical expander (602) and a second optical expander (604) collectively defining a two-stage beamformer;

[103] FIGURE 25 is a schematic view of a beamformer/beamsplitter with front and rear triangular prisms;

[104] FIGURE 26 presents a comparison of three beamformers with reflective coatings at different angles so that their output beams transmit in different directions;

[105] FIGURE 27 is an isometric view of vacuum system having the beamformers of FIG. 26 mounted thereon;

[106] FIGURES. 28A and 28B are elevational and plan views of the vacuum system of FIG. 27 (with certain elements omitted from each for clarity);

[107] FIGURES 29A and 29B are isometric views of an optical beam-forming system in which lens elements provide a first optical expander and are mounted on/over a second optical expander ('beamformer'), with 29B showing a beam path through the lens elements;

[108] FIGURE 30 is a flow chart of a process for making a MOT cell;

[109] FIGURE 31 is an image of an MOT cell;

[1 10] FIGURE 32 is a set of images relating to a rubidium (Rb) source capsule for the MOT cell of FIG. 31 ;

[1 1 1 ] FIGURE 33 is a dual-perspective view of an alternative Rb dispenser;

[1 12] FIGURE 34 is an image of an integrated system showing a laser path for entire system;

[1 13] FIGURE 35 is a cutaway of a suspended-cell enclosure;

[1 14] FIGURE 36 is a suspended cell showing suspension members with electrical heating elements; [1 15] FIGURE 37 is a side cross sectional view of a suspended hollow cell showing geometry of an interior etched and polished chamber.

DESCRIPTION OF EMBODIMENTS

[1 16] There now follows a description of one or more embodiments of the invention useful for understanding the general inventive concept, but not intended to be limiting of the scope of the invention. In the drawings like items are assigned like reference numerals.

[1 17] Referring to figures 1A 1 B, there are shown two perspective views of two parts of a chassis for an optical beam forming apparatus for use in a 2D-MOT. The chassis parts comprise a top chassis part (30) and a bottom chassis part (31). Figure 1A shows a side perspective view and Figure 1 B shows a top perspective view of the two chassis parts in situ upon a magnetic trap assembly (101) comprising four pole pieces (39) of a quadruple magnetic trap structure and a transparent-walled vacuum chamber (300). The magnetic pole pieces and the two chassis parts are each disposed surrounding the vacuum chamber (300) in such a way as to reveal four optically transparent windows (303) of the vacuum chamber which are adapted for placing the inner volume of the vacuum chamber in optical communication with optical cooling beams of the optical beamforming apparatus (not shown) mounted upon the top and bottom chassis parts (30, 31 ). In this way, the chassis parts allow the optical beamforming apparatus, discussed in more detail below, to be mounted upon pre-existing quadrupole magnetic pole pieces of a magnetic trap apparatus in such a way as to encapsulate the vacuum chamber within the chassis so as to place the optical beamforming apparatus in the necessary optical communication with the inner volume of the vacuum chamber. Accordingly, when sample atoms are received into the vacuum chamber and trapped therein by the magnetic quadruple field formed by the four quadruple pole pieces (39), optical cooling beams from the beamforming apparatus (discussed below) are able to cool and/or manipulate those atoms by a process of magneto-optical trapping as described above.

[1 18] Figure 1 C and Figure 1 D show a side perspective view and a top view of the four magnetic pole pieces (39) and the vacuum chamber (300) with the two chassis parts absent, for clarity. The vacuum chamber (300) comprises four windows formed of optically transparent material, such as glass, each joint at a long edge of the window to a neighbouring window by a column piece (302) which sealingly holds (to vacuum standards, preferably to ultra-high vacuum standards) the two window edges at a 90° relative orientation. The result is for windows held together by for respective column pieces (302) to define an elongated chamber of square cross- section and rectangular on each side.

[1 19] An entrance cover is disposed at the entrance end of the vacuum chamber and sealingly holds (to vacuum standards) each of the four end edges of the four windows of the vacuum chamber, at an atom input end of the chamber, while the other four end edges of the four windows of the vacuum chamber are sealingly connected (to vacuum standards) to the rest of the magnetic trap apparatus (101) at an atom output end of the chamber. This apparatus is also illustrated in figures 16A and 16B, discussed below. The atom input end of the chamber possesses an input aperture (301) with its centre arranged in register with the central longitudinal axis of the vacuum chamber. This longitudinal axis is in optical communication with the chassis of the optical beamforming apparatus via the four windows (303).

[120] Each magnetic pole piece (39) comprises a right circular cylindrical rod embedded within the curved external surface of which is embedded an elongate strip of magnetic material. One elongate side of the strip of magnetic material (39N) is magnetised to define a North magnetic pole, whereas the opposite elongate side (39S) of the strip of magnetic material is magnetised to define a South magnetic Pole. Each of the first and second elongate sides of the respective strips of magnetic material is disposed in parallel with the cylindrical axis of the right circular rod within which it is embedded, and mutually parallel with each other. These two elongate sides of the respective strips are also disposed to face the longitudinal axis of the vacuum chamber such that a straight line (imaginary/notional) joins the two. Similarly, each one of the four magnetic pole pieces is opposed by one other of the four magnetic pole pieces such that the longitudinal axis of the vacuum chamber bisects a straight line (imaginary/notional) joining the two opposing pole pieces. Each pole piece of the four magnetic pole pieces is disposed to reside at a respective one of the four vertices of a square damage and to receive the square cross- sectional shape of the vacuum chamber within it. Each magnetic pole piece is arranged adjacent to, and extending in parallel with, a respective one of the four column pieces (302) of the vacuum chamber. Accordingly, the combined magnetic field produced by the magnetised material of the four magnetic pole pieces, which defines a quadrupole field suitable for trapping atoms upon the longitudinal axis of the vacuum chamber, in the manner described above. This provides a magnetic field apparatus.

[121 ] The top and bottom chassis parts (30, 31) each comprise four circular openings arranged at a respective one of the four vertices of a square (imaginary/notional) matching the dimensions of the square array of the four magnetic pole pieces. Accordingly, each one of the four magnetic pole pieces is receivable into a respective one of the four openings of both the bottom chassis part and the top chassis part, concurrently, so that the bottom chassis part on the top chassis part can be concurrently mounted upon the four magnetic pole pieces, as shown in Figure 1 A and Figure 1 B thereby to concurrently position the top and bottom chassis parts in register with the vacuum chamber and its longitudinal axis.

[122] Each of the four circular openings of the top chassis part are closed-ended, meaning that they terminate within the body of the top chassis part thereby providing an internal "stop" or "buffer" against which a terminal end of an inserted magnetic pole piece may abut when fully inserted into the top chassis part. Conversely, each of the four circular openings of the bottom chassis part are through-openings allowing the shaft of each magnetic pole piece to pass through fully permitting the bottom chassis part to slide down the four magnetic pole pieces, collectively, as the chassis is mounted upon those pole pieces, as shown in Figure 1 A.

[123] Both the top chassis part on the bottom chassis part define a square central through- opening, dimensions to admit the square cross-section of the vacuum chamber (300). Accordingly, the top chassis part of the bottom chassis part permit the beamforming apparatus to be mounted upon the magnetic field apparatus (101) by slidingly mounting the chassis onto the four magnetic pole pieces of the magnetic field apparatus to surround and encase the vacuum chamber of the magnetic field apparatus in such a way which places the beamforming apparatus of the chassis in the required orientation and position for the desired optical communication necessary to perform optical cooling (optical molasses) of atoms trapped within the vacuum chamber (300) by the quadruple field of the magnetic field apparatus.

[124] Figures 2 and 3 shows a plan view (Figure 2) and a side cross-sectional view (Figure 3) of an additional component part of the chassis of Figure 1A and Figure 1 B.

[125] The chassis component (1) defines optical beamforming apparatus including a chassis plate (2) upon which are mounted, been successive optical communication, the following optical components. An optical fibre output collimator unit (3) is disposed at an input edge of the chassis plate so as to present, at the input edge, and optical input port (3A) for receiving the output end of an optical fibre and for disposing the output end of the optical fibre in optical communication with collimation optics (a lens train, not shown) located within the optical collimator unit. The optical collimator unit functions to collimate received laser radiation input thereto via the optical input port (3A) and to output a collimated laser beam at the optical output port (3B) of the collimator unit. The optical collimator unit (3) defines an optical axis along which the optical axes of subsequent lenses are coincident/collinear. A first of the subsequent lenses is a converging lens (4) arranged to receive the collimated laser beam output by the optical collimator unit (3) and to output a divergent laser beam for input to a subsequent converging lens (5) which defines, together with the diverging lens (4) a Galilean telescope. The converging effect of the converging lens (5) of the Galilean telescope is to a laser beam which is an expanded form of the input laser beam received by the diverging lens (4) of the Galilean telescope. The expanded laser beam is expanded in both dimensions transverse to the axis of the laser beam received by the Galilean telescope, substantially equally so as to magnify the beam width.

[126] A laser line-generator (Powell) lens (6) is arranged to receive the expanded laser beam output by the Galilean telescope. The laser line-generator lens has its optical axis arranged collinearly with the optical axis of the Galilean telescope.

[127] The laser line-generator lens is arranged to expand the laser beam, from the Galilean telescope, in a first dimension transverse to the laser beam to provide a first expanded laser beam. The first expanded laser beam is a diverging fan of light the transverse dimension of which is a thick line or strip of light. Subsequent to the laser-line generator lens, and in coaxial alignment optically, is a collimator lens in the form of a cylindrical lens (7). The collimator lens is a converging lens arranged to apply a convergence only in the plane containing the diverging fan of laser light output by the laser-line generator lens. In other words, the radius of curvature of a curved optical surface of the collimator lens for imposing optical convergence, lies always within the plane containing the fan of laser light output by the laser line-generator lens. This means that convergence is not applied in a direction transverse to the plane containing the fan of laser light. Notably the laser-line generator lens is arranged upon the chassis plate (2) such that plane of the fan of light produced by it is substantially parallel plane of the chassis plate (2).

[128] The function of the collimator lens is to receive the diverging fan of light from the laser- line generator lens and to collimate that diverging fan of light into either a collimated laser beam or preferably into a slightly converging laser beam. The collimated laser beam output by the collimating lens (7) defines a strip of light having intensity l ₀ extending in a first dimension W1, as a schematically illustrated in Figure 5. The thickness of the strip is defined by the diameter of the expanded laser beam output by the Galilean telescope, and the length of the strip is defined by the fan angle provided by the laser line-generator lens (6) and the distance between the laser-line generator lens and the subsequent collimator lens (7).

[129] A V-shaped groove (1 1 , 12) is formed on the upper surface of the chassis plate (2) and has disposed within it the optical collimator unit (3), the diverging and converging lenses (4, 5) of the Galilean telescope and the laser line-generating lens (Powell) piece (6) in that order along the axis of the groove. The V-groove is a linear and right-angular groove with the right-angled vertex at the base of the groove disposed to the equidistant from the peripheral edges of the groove the upper surface of the chassis plate (2). The two converging walls of the V-groove are smooth and abut against outer cylindrically curved surfaces of the collimator unit (3), the lenses of the Galilean telescope (4, 5) and the laser line-generator lens (6).

[130] The length of the V-groove exceeds the length of the Galilean telescope and the length of the laser line-generator lens combined, thereby permitting axial position of the Galilean telescope to be adjusted relative to the position of the laser light-generating lens, and relative to the position of the collimator unit (3) as may be desired to optimise the optical performance of the optical beam-forming apparatus. Notably, the separation between the diverging lens (4) and the converging lens (5) of the Galilean telescope may similarly be slightly adjusted along the axis of the V-groove so as to adjust the focus of the Galilean telescope. Similarly, the separation between the laser line-generating lens and the collimator lens (7) may be adjusted by slidingly adjusting the position of the laser line-generating lens within the V-groove, so as to adjust the width (W1) and intensity of the collimated laser line/strip output by the collimator lens. The collimator lens (7) is secured within a recess (10) formed within the upper surface of the chassis plate (2) so as to fix his position relative to other optical components of the optical beam-forming apparatus. [131 ] An edge of the chassis plate, which is opposite to the input edge of the chassis plate, defines a through-slot (9) within which is housed a right-angle prism (8) in a position permitting optical communication between the upper surface of the chassis plate and the underside of the chassis plate. The right-angle prism presents to reflective internal surfaces which converge internally at a right-angle. The hypotenuse surface of the right-angle prism is presented towards, and in optical communication with, the surface of the converging to lens (7) for receiving the collimated (or converging) line/strip beam. The hypotenuse surface is disposed to be substantially perpendicular to the optical axis of the lens train (4, 5, 6, 7) preceding it and perpendicular to the plane containing the first dimension (W1) of the expanded light output by that lens train.

[132] Light received by the right-angle prism from the converging lens (7), impinges upon a first internally reflective surface of the prism, is thereby directed to the second internally reflective surface of the prism whereupon it is reflected out of the right-angle prism through the hypotenuse surface in a direction across the underside of the chassis plate (2) which is parallel to, but the reverse of the direction in which the light was input to the right-angle prism.

[133] Referring to Figure 3 and Figure 6 together, the underside of the chassis plate bears a second optical expander unit (13) disposed thereupon in optical communication with the right- angle prism (8) for receiving the reversely-directed light output thereby. The second optical expander unit comprises a succession of optically transparent component parts each bearing a partially reflective and partially transmissive optical surface presented towards the right-angle was (8). The plurality of partially reflective/transmissive optical surfaces are arranged mutually spaced-apart in a linear succession along the underside of the chassis plate (2), each being in optical communication with another such that light transmitted by any preceding optical surface is received by the succeeding optical surface for reflection (and partial transmission as appropriate) by that succeeding optical surface. Each of the plurality of such reflective/transmissive optical surfaces are substantially planar, and are plane-parallel to each other.

[134] As a consequence of these properties, when a reverse-directed laser beam (laser line strip) is received by the second optical expander the unit (13) from the right-angled prism (8), each of the partially reflective/transmissive optical surfaces reflects some of the received light out of the second optical expander unit in a direction perpendicular to the plane of the chassis plate (2), and transmits the rest to the succeeding partially reflective/transmissive optical surface. Because the successive partially reflective/transmissive optical surfaces is spaced from the preceding such surface in a direction along the underside of the chassis plate, the corresponding reflected output from that successive surface also occurs at a position further along the underside of the chassis plate. Each one of the succession of such partially reflective/transmissive surfaces makes its own contribution to the light output by the second optical expander unit at a respective location spaced along the underside. Consequently, the collective optical output of the optical expander unit serves to expand the laser beam in a second dimension (W2) which is transverse to the first dimension, and to output the result as a second expanded laser beam (i.e. the initial input laser beam expanded in the second dimension) in a direction, away from the underside of the chassis plate (2), which is transverse to both the first dimension and the second dimension. A circular polarising filter (14) is positioned across the entirety of the optical output surface of the second optical expander unit (13) and is arranged to convert linearly polarised light output from the second optical expander unit into circularly polarised light for transmission into a vacuum chamber (300) through a transmission window (303) thereof.

[135] The second optical beam expander (13) may be arranged to provide the output laser beam as linearly polarised light. The partially reflective/transmissive surfaces may be arranged to preferentially reflect light polarised in one of the two orthogonal states of linear polarisation present in the first expanded laser beam, and to preferentially transmit light polarised in the other state of the two orthogonal states of linear polarisation. This may be achieved by the provision of an optical coating upon the partially transmissive/reflective surfaces, such as a dielectric coating (e.g. a multi-layered structure), designed to have a reflection characteristic which is polarisation-dependent so as to produce a reflection output which is linearly polarised. As would be readily apparent to the skilled person, the number, thickness and material of the individual layers in a multi-layer optical coating may be designed to achieve such a result. For example, one sub-layer or layers of the multi-layer structure may be designed to preferentially reflect one state of linear polarisation, and another sub-layer or layers of the multi-layer structure may be designed to preferentially transmit the other (orthogonal) state of linear polarisation. The effect of this is that the polarisation beam splitter acts as a linear polariser, by receiving the first expanded laser bean as substantially un-polarised light, and outputting the second expanded laser beam as linearly polarised light.

[136] The circular polarising filter (14) may then be a quarter-wave plate arranged to convert the linearly polarised light input to it from the second optical beam expander, into circularly polarised light as the output from the quarter-wave plate.

[137] The quarter-wave plate may be formed from a birefringent material, defining an optic axis. Passing linearly polarized light through a quarter-wave plate with its optic axis oriented at 45° to the polarization axis of incident linearly polarised, will convert the linearly polarised light in to circularly polarized light. In particular, linearly polarized light entering a quarter-wave plate can be resolved into two component waves: one parallel and one perpendicular to the optic axis of the wave-plate. The component wave with polarisation oriented parallel to the optic axis propagates more slowly than the component wave polarised perpendicular to the optic axis. At the output side of the wave-plate, the parallel-oriented component wave is delayed by a distance equal to substantially one quarter of a wavelength relative to the perpendicular- oriented component wave. The resulting combination of the two component waves, at the output side of the quarter wave-plate is a circularly polarised wave.

[138] Alternatively, in other embodiments, the light output from the second optical beam expander may be not linearly polarised (i.e. substantially unpolarised, e.g. a degree of linear polarisation which is negligible), and the circular polarising filter may comprise a linear polarising filter arranged to receive the output laser beam of the second optical expander, and to transmit/output a linearly polarised beam to immediately to a quarter wave-plate with its optic axis arranged to convert the received linearly polarised light into a circularly polarised light output, for use. In another alternative embodiment, the optical beam forming apparatus may comprise a circular polarising filter, which may be located before the second optical beam expander, or before the first optical beam expander, or between the two, along the optical path of the laser beam. The circular polarising filter may be in the form of one filter body/unit or in the form of a combination of a linear polarising filter and a quarter wave-plate acting together in optical communication, but optionally spatially separated. Either one of the linear polarising filter and a quarter wave-plate may be separately be located before the second optical beam expander, or before the first optical beam expander, or between the two, along the optical path of the laser beam.

[139] Figure 4 and Figure 7 each illustrates a respective one of two embodiments of the second optical beam expander. In a first embodiment, illustrated in Figure 4, the optical beam expander (13A) comprises a row of polarisation beam-splitter cubes (15A, 15B, 15C... etc.). It is to be understood that this is just one example of implementation, and other implementations of the second optical beam expander may be used, as is discussed below. However, the present example, employing polarisation beam splitter cubes, is useful for understanding the principles of the second optical beam former. In the present example, each polarisation beam-splitter cube contains a partially reflective surface (16A, 16B, 16C... etc.) each adapted to reflect a predetermined proportion (R) of light incident upon it internally, and to transmit the rest for input to the next polarisation beam-splitter cube within the row. Thus, for example, an incident laser beam (17) of intensity / ₀ , impinges upon an input surface of a first polarisation beam-splitter cube (15A) and is transmitted into the beam-splitter cube to the partially reflective surface (16A) having a surface reflectivity R-, disposed therein at an angle of 45° to the input surface. This partially reflective surface reflects an output beam (18) of intensity R-,l ₀ , from an output surface of the beam-splitting cube. Concurrently, a transmitted part of the incident laser beam, of intensity T-,l ₀ where R-,+Τ^Ι, transmits through the partially reflective surface of the first beamsplitter cube and impinges upon an input surface of the next polarisation beam-splitter cube (15B). This is transmitted into the next beam-splitter cube to its partially reflective surface (16B), which has a surface reflectivity R ₂ disposed therein at an angle of 45° to the input surface of the cube. This partially reflective surface reflects an output beam (19) of intensity R ₂ 7 o, from an output surface of that beam-splitting cube. Concurrently, a transmitted proportion of the incident laser beam, of intensity TiT ₂ lo, impinges upon an input surface of the further successive polarisation beam-splitter cube (15C) and is transmitted into the beam-splitter cube to its partially reflective surface (16C) having a surface reflectivity R ₃ disposed therein at an angle of 45° to the input surface. This partially reflective surface reflects an output beam (20) of intensity R3T1T2I0, from an output surface of that beam-splitting cube. By suitably designing the reflectivity of the partially reflective/transmissive surfaces in each successive beam-splitter cube, it is possible to provide a situation in which the intensity of each of the beams (18, 19, 20 ...) output by the successive beam-splitter cubes is substantially the same. That is to say:

R ₁ I ₀ = R ₂ T ₁ I ₀ = R ₃ T ₁ T ₂ lo ⁼ ... etc. for subsequent beam-splitter outputs.

[140] Consequently, the optical output from each optical beam splitter represents a component part of a greater optical beam defined by the succession of partial optical beams. Of course, in the above analysis, it has been assumed that the output surface of a preceding beam-splitter cube, and the input surface of the succeeding beam-splitter cube abutted against it, present negligible optical loss to laser light transmitted across that interface. In practice, the provision of such a loss-less optical interface (or at least negligibly lossy) may not be required, and the reflectivity is and transmissive it is of the partially reflecting surfaces (16A, 16B, 16C etc.) may be adjusted to account for that.

[141 ] By ensuring that the optical input face of the first, and subsequent, polarisation beamsplitter cubes is fully illuminated with input laser light (17) will make sure that substantially the whole of each of the partially reflecting surfaces within each of the succession of polarisation beam-splitter is also fully illuminated. Consequence is that there is substantially no gap between neighbouring output optical beams (18, 19, 20...) of the second optical beam expander. Consequently, the output intensity this tradition forces profile of the optical output beam from the second optical expander may possess no zero-intensity null-points such that the output optical beam presents a usable intensity (l _ou tput) of laser light across the whole of the second dimension (W2) in which it is expanded by the second optical beam expander.

[142] Referring to Figure 7, an alternative embodiment is schematically illustrated which implements the same principles as described above with reference to figure 4. Figures 8A, 8B, 8C and 8D schematically illustrate the second optical beam expander (13) of this embodiment.

[143] According to this alternative embodiment, the individual beam-splitter optical elements are not beam-splitter cubes, but are instead each an elongated transparent body (21) with six plane faces amongst which the two short end faces of the transparent body are each shaped as a parallelogram, while the remaining four long side faces which extend along the long axis of the transparent body are rectangular in shape. A succession of a plurality of such transparent bodies are arranged with a respective first one (22) of the four long side faces disposed nearest to, and in optical communication with, the right-angle prism (8) for receiving laser light therefrom, thereby placing a second one (22) of the four long side faces, opposite to the first long side face, in direct contact and optical communication with the first long side face of a successive transparent body. Each such contact interface between successive transparent bodies defines a partially reflective and partially transmissive surface for use in outputting a component part (18, 19, 20 etc.) of the output optical beam.

[144] The first optical beam expander may be arranged to over-expand the incoming beam before it outputs the first expanded laser beam (l ₀ ) such that the cross-sectional area of the first expanded laser beam fully fills the clear aperture of the optical input area/face of the second optical expander receiving it. Consequently, the second expanded laser beam may provide a fully-supplied output laser beam having substantially no intensity 'nulls' or gaps within its beam cross-section. Put another way, the cross-section beam intensity may be made free of 'gaps' or 'holes' at which the local light intensity of the beam is negligible or too small to be of practical use. Another example of this is shown in Figure 19 in which the second optical expander (1000) is an 8-prism beamformer and is illustrated during its use in beam expanding as a beamformer whereby an over-expanded input beam (1040) has a width dimension (in this case, in the direction perpendicular to the longitudinal axis of the beamformer) exceeding the corresponding width dimension of the optical input face (P1 1) of the beamformer (1000). This ensures that the final output beam is formed of eight adjacent sub-beams (B1 1 to B18) which are fully contiguous (no gaps) in the dimension along which the final output beam has been expanded (i.e. the longitudinal axis of the beamformer). The over-expanded beam (1040) may be even more over- expanded such that it fully covers the whole of the optical input face (P1 1) of the beamformer (1000). Both width dimensions of the over-expanded input beam (i.e. those which are mutually perpendicular and both also perpendicular to the longitudinal axis of the beamformer) could exceed the corresponding width dimensions of the optical input face (P1 1) of the beamformer (1000).

[145] Referring to figures 8A, 8B, 8C and 8D, the second optical beam expander is shown in side view (figure 8A and 8B), and in perspective view (Figure 8C). Figure 8D illustrate a cross- sectional view of the second optical beam expander of figure 8C is viewed across the axis AA'. This reveals the optically partially reflective surfaces (22) therein.

[146] A consequence of this alternative arrangement is that the interface between the faces of successive transparent optical bodies itself provides the reflective/transmissive surface for use in beam forming/output and avoids the presence of the potentially loss-inducing interface between successive cube beam splitters such as is present in the embodiment illustrated in figure 4. [147] Figures 9A, 9B and 9C illustrate perspective views of the chassis plate (2) described above with reference to figures 2 and 3, in the absence of any of the optical elements of the optical beamforming assembly. This illustrates the V-groove structure (1 1 , 12, 23) on the upper side of the chassis plate, the through slot (9) at an end edge of the chassis plate, and underside of the chassis plate in which a recess (26) is formed for receiving the second optical beam expander (13, 13A). These views also show an end part (23) of the V-groove on the other side of the chassis plate adapted for receiving the collimator unit (3) as shown in Figure 2 and Figure 3. Figures 10A, 10B and 10C also show these perspective views of the chassis plate with the optical elements of the optical beamforming apparatus in place.

[148] It is to be noted that this chassis plate forms an integral part of the chassis in conjunction with the upper chassis part (30) and the lower chassis part (31) of the optical beamforming apparatus shown partially in Figure 1A and Figure 1 B. In particular, chassis plate possesses through-openings at corners of the plate for receiving fastening members (screws or bolts) with which the chassis plate is adapted to be fixed to both the upper chassis part and the lower chassis part such that the length of the chassis plate (2) is dimensions to define the separation between the upper chassis part (30) and lower chassis part (31). The outer surface of each of the upper chassis part and lower chassis part presents for flat sides. Each one of the flat side of the upper chassis part is aligned to be substantially coplanar with a respective one of the flat sides of the lower chassis part. Openings are arranged in each of these flat side surfaces for receiving the fastening members from the chassis plate permitting the chassis plate to be fixed to the upper and lower chassis numbers thereby joining them together as a chassis assembly. Figures 1 1 A and 1 1 B illustrate the chassis so assembled.

[149] The beamforming apparatus of the present embodiment also includes a second chassis plate (34) disposed at a side of the chassis assembly opposite to that at which the first chassis plate (2) is disposed. The underside of the second chassis plate opposes the underside of the first chassis plate across the chassis assembly. Upon an upper side of the second chassis plate is mounted a mirror assembly (36) which opposes, and is in optical communication with, the second optical expander unit (13) via a through-opening (35) formed in the second chassis plate and positioned in register with the second optical expander unit. An end of the second chassis plate is firmly connected to an outer surface of the lower chassis part (31) to hold the second chassis plate (34) in position relative to the first chassis plate (2).

[150] Reference is now made again to Figure 1A and Figure 1 B which show the top and bottom chassis part mounted upon each one of four magnetic pole pieces (39) of a magnetic field apparatus (101 ), which passes through openings in the top and bottom chassis parts. These openings are shown in figures 1 1A and 1 1 B as four through-openings (38) at corners of the bottom chassis part (31), and as for openings (37) at the corners of the top chassis part (30). [151 ] Accordingly, the chassis of the optical beamforming apparatus illustrated in Figure 1 1A and Figure 1 1 B provides a first chassis plate (2) and a second chassis plate (34) disposed to oppose each other across a space internal to the chassis dimensioned and adapted for receiving a vacuum chamber (300) of a magnetic field apparatus (101), by mounting the chassis onto the four magnetic pole pieces (39) which provide the quadrupole field of the magnetic field apparatus. When surmounted, the second optical expander unit (13) is in optical communication with the mirror assembly (36) across the vacuum chamber via to opposite windows (303) of the vacuum chamber thereby permitting the output laser beam of the optical beamforming apparatus to traverse the vacuum chamber, to impinge upon the mirror assembly, and to be reflected by the mirror assembly back towards the second optical expander unit as a counter- propagating laser beam fully overlapping with, and propagating in the opposite direction to, the laser beam output from the second optical expander unit. This provides two opposing optical cooling beams able to provide optical cooling in the dimension corresponding to the axis of their propagation direction, by a process of optical molasses described above.

[152] The mirror assembly (36) comprises a quarter wave plate disposed over a plain reflecting surface. When circularly polarised light from the second optical beam expander unit (13) has reversed of the vacuum chamber (300) through a transmission windows (303) thereof, it is initially transmitted through the quarter wave plate of the mirror assembly whereby it is converted into linearly polarised light which is reflected by the plain reflecting surface of the mirror assembly. The act of reflection of the linearly polarised light imposes a 180° phase change in the reflected light. The reflected light is then transmitted through the quarter wave plate in a direction towards the vacuum chamber (300). Due to the 180° phase change in the reflected, linearly polarised light input into the quarter wave plate from the plain reflecting surface, the orientation/sense of circular polarisation of light reflected back into the vacuum chamber is opposite to the orientation/sense of circular polarisation of light input into the vacuum chamber from the second optical beam expander (13), via the quarter wave plate (14) disposed upon it. This means that the counter propagating optical cooling beams provided by the optical beamforming apparatus of the chassis are of the required opposite orientation/sense of circular polarisation required to optimise the optical cooling effect, upon atoms within the vacuum chamber (300), as described above.

[153] Figure 1 1 C schematically shows an alternative arrangement equally applicable to the apparatus illustrated in figures 1 1A and 1 1 B. The optical beam-forming apparatus includes a quarter-wave plate (14) disposed in optical communication with the second optical expander (13) for receiving light of the laser beam and transmitting a circularly polarised light output (loutput)- The quarter-wave plate may be attached, bonded or laminated to the output surface of the second beam expander, or may be separate from it.

[154] The optical reflector (36) is arranged for reflecting the output circularly polarised beam (loutput) from the second optical expander (13). It includes a quarter-wave plate (36A) and a plane mirror (36B). The quarter-wave plate is disposed upon, over or adjacent the plane mirror between the plane mirror and the second optical expander. The quarter-wave plate (36A) is disposed to receive the output circularly polarised beam (l _ou t _P ut) both before and after reflection thereof by the plane mirror (36B). This permits the output circularly polarised beam (l _ou t _P ut) to be re-used after it has traversed a sample of atoms/molecules being cooled or otherwise manipulated, by simply re-directing it back through the sample. The plane mirror is disposed in the chassis so as to oppose the second beam expander (13) in optical communication across a space within the chassis adapted for receiving a sample of atoms/molecules for manipulation/cooling, such as a vacuum chamber possessing optically transmissive or transparent walls.

[155] The quarter wave-plate (36A) disposed before the mirror reflector allows incoming circularly polarised light of the output laser beam to be transformed into linearly polarised light for reflection at the mirror reflector (36B). After reflection, the once-reflected output laser beam (linearly polarised) passes back through the quarter wave-plate and is transformed back into circularly polarised light (l _Ref i) having the correct 'handedness' circular polarisation (i.e. right- circular or left-circular) for manipulating/cooling the atoms/molecules of the sample into which it is re-directed by the reflector. After having traversed the sample chamber, the once-reflected output beam reaches the circular polariser filter (14) and the second optical expander (13), and is transmitted through the first and then partially transmitted through the partially reflective internal surface of the latter, to emerge as a beam of laser light (l _Re)2 ) from behind the second optical beam expander.

[156] The action of the quarter-wave plate (14) upon the circularly polarised light (l _Ref i) returned to it by the first plane mirror, is to convert it into linearly polarised light (l _Re t2) - A second plane mirror (36C) is disposed behind the second optical beam expander so as to face it, and to reflect back towards the second optical beam expander a reflected linearly polarised light (l _Re f3) , which is re-transmitted (partially) back through the partially reflective internal surface of the second optical beam expander (13), and then through the quarter-wave plate (14), to emerge as a beam of circularly polarised laser light (l _Ref4 ) from the front surface of thereof and into the sample chamber having the correct 'handedness' of circular polarisation (i.e. right-circular or left-circular) for manipulating/cooling the atoms/molecules of the sample. This beam of light then reaches the optical reflector (36) where it is reflected back towards the second optical expander (13) once more, as a beam of circularly polarised light (l _Re fs) . This beam of light is once more reflected back and forth between the first and second plane mirrors (36B, 36C) repeatedly until the intensity of the beam is diminished fully. This enables efficient use of the optical input beam of light (lo).

[157] Accordingly, optical beam-recycling may be implemented using one or two planar recycling mirrors. In this scheme, a planar mirror is placed behind the beamformer optic (i.e. the second optical expander). After the light has passed through the MOT cell, and has been retro- reflected by the opposing planar mirror (with ¼-wave plate), it returns to the beamformer. Since the beamformer surface has e.g. only approximately 10% reflectivity, this that about 90% of that returned light will pass straight through. This light is reflected by the planar mirror located behind the beamformer optic and re-enters the beamformer optic for onward transmission into the MOT cell for use there.

[158] Figure 1 1 D shows an alternative arrangement in which the second plane mirror (36C) is replaced by an array of 180-degree reflector prisms which present to the back surface of the second optical expander, two internal plane reflective surfaces each inclined at 45 degrees to the opposing flat surface of the second optical expander, and at 90 degrees to each other, in optical communication with the rear surface of the second optical expander via an optically transmissive/transparent hypotenuse face of the prism disposed plane-parallel to the rear surface of the second optical expander. The function of each 180-degree reflector prism is to internally retro-reflect linearly polarised light (\ _Re12 ) incident upon it using the two plane reflective surfaces of the prism. Each such prism of the array of prisms is immediately adjacent a neighbouring prism of the array leaving substantially no optical gaps between them. This presents a substantially continuous optically reflective surface towards the rear surface of the second optical expander, for retro-reflecting incident light.

[159] Thus, beam-recycling may be implemented using prisms placed behind the beamformer optic (i.e. the second optical expander). This arrangement provides the recycling mirror in the form of prisms (either 180-degree reflector prisms, or abutted pairs of roof prisms). This arrangement has the benefit that the alignment tolerance is less critical. The beams in this scheme are recycled into a different 'segment' of the beamformer optic, which helps to make the system more robust to 'dark spots' caused by any flaws that might be present in the beamformer.

[160] Figure 1 1 E shows another alternative arrangement in which the both the first plane mirror (36B) and the second plane mirror (36C) is replaced by a respective array (36E, 36D) of 180- degree reflector prisms as described above. Each of these prism arrays is disposed to present to one or the front surface and the back surface of the second optical expander, a substantially continuous optically reflective surface towards the rear surface of the second optical expander, for retro-reflecting incident light as described above. In alternative arrangements (not shown) only the first plane mirror (36B), and not the second plane mirror (36C), is replaced by a respective array (36E) of 180-degree reflector prisms as described above.

[161 ] In this way, beam-recycling may be implemented using an array of prisms both in front and behind the beamformer optic (i.e. the second optical expander). In this arrangement, a second prism array is also disposed in front of the beamformer optic as a retro-reflective mirror. Prisms have the benefit that they do not require one to employ a preceding ¼-wave plate (36A), since because of the double-reflection process they use to achieve retro-reflection, they intrinsically maintain the handedness of the circular polarisation on reflection (unlike a single- reflection plane mirror which reverses handedness). This can simplify construction as well as having the benefits described in above with respect to alignment and robustness.

[162] Figure 12 illustrates a perspective view of a translation stage (40) adapted for inclusion in preferred embodiments of the optical chassis of the beamforming apparatus of the present invention.

[163] The translation stage comprises a translation base part (41) possessing for fixture through-openings (45) for receiving 60 fixing members (e.g. bolts or screws) with which to fix the translation base part to the upper chassis part (30) of the optical beamforming apparatus. The translation base part is shaped as a ring defining a central through-aperture containing an annular coupling collar (42). The axis of the central through-aperture and the central axis of the annular coupling collar are arranged to be parallel to each other, and the coupling collar is arranged to be adjustably movable relative to the translation base part in the two-dimensional plane perpendicular to both central axes. The coupling collar is adapted for receiving an optical collimator unit (50, 51 : figure 13B) comprising an optical fibre input port (51) and an optical assembly (50) adapted for receiving laser light signal input to the optical fibre input port (from an optical fibre coupled thereto: not shown). The optical assembly comprises a lens train (not shown) for collimating the received laser light into a push-beam for use in moving atoms along the central longitudinal axis of the optical chassis when in use in a magneto-optical trap (MOT).

[164] The coupling collar (42) is coupled to the translation base part (41) via translation couplings/gears (not shown) controllably adjustable via two transverse translation micrometre control dials (43, 44) each adapted to allow the user to finely adjust the position of the central axis of the coupling collar relative to the central axis of the translation base part thereby to finely adjust the position of the transmission axis of a laser push-beam relative to the central longitudinal axis of the optical chassis when in use in a magneto-optical trap (MOT).

[165] Figures 13A and 13B show the chassis defining the optical beamforming apparatus of a preferred embodiment, with the translation stage (40) coupled to the chassis top part (30) thereby placing the optical axis of the optical collimator unit (50, 51) in register with, and in optical communication with, the through-opening (33) formed in the centre of the chassis top part (30). This permits a laser push-beam to be transmitted from the optical collimator unit through the chassis top part and into the inner space of the chassis between the first chassis plate (2) and the second chassis plate (34) so as to intersect the atom-cooling laser beams transmitted between the second optical expander unit (13) and the opposing mirror (36).

[166] Figures 14A and 14B shown two perspective views, from opposite ends, of a chassis providing a complete optical assembly for use in providing for optical cooling laser beams for implementing laser cooling by optical molasses in two dimensions, together with an optical push beam for moving called atoms out of the optical chassis in a third dimension (2D-MOT). The chassis assembly comprises a two pairs of chassis plates, in which each pair comprises a first chassis plate (2) opposed across the chassis by a second chassis plate (34). The first pair of chassis plates oppose one another across a chassis along a direction which is perpendicular to the direction across which the second pair of chassis plates oppose one another. The first and second pairs of chassis plates are identical and are each as described above.

[167] Figures 15A and 15B illustrate end views of the complete chassis assembly, in which Figure 15A shows the output end of the chassis assembly from which cooled atoms are pushed by a laser push-beam entering the chassis assembly via the through-opening (33) in the centre of the chassis top part (30). Figure 15B shows the input end of the chassis assembly in which the optical collimator assembly (51) for the laser push-beam is disposed.

[168] Referring to Figure 16A and 16B, there are shown two perspective views of one 3D-MOT apparatus. The 3D-MOT comprises the 2D-MOT apparatus incorporating the chassis assembly and apparatus 100 of figures 14A, 14B, 15A and 15B, which is mounted upon a translation stage 101 adapted and arranged to allow adjustment of the 2D-MOT in two dimensions transverse to the central atom/molecule output beam axis of the 2D-MOT relative to a corresponding atom/molecule input beam axis of the 3D-MOT.

[169] This permits the atom/molecule output beam of the 2D-MOT to be appropriately positioned to extend along the longitudinal axis of a transparent sample chamber (ultra-high vacuum, in use) 109 of the 3D-MOT.

[170] In this way, the vacuum chamber 300 of the 2D-MOT 100 is axially adjustably aligned in communication with the vacuum chamber 109 of the 3D-MOT, such that cold atoms or molecules prepared within the vacuum chamber of the 2D-MOT may pass directly as a beam of cold atoms or molecules from the vacuum chamber of the 2D-MOT into the vacuum chamber of the 3D-MOT. One, two or three separate optical beam forming apparatuses such as illustrated in any of Figure 2, Figure 3, Figure 6, or Figs 10A to 10C, may be used to provide optical output beams, as described above, for use individually or collectively in manipulating the cold atoms or molecules and/or for cooling them further to produce a Bose-Einstein condensate therein. For example, the three output laser beams (Fig.16B: 200, 350, 400) provided by the respective optical beam formers may be all mutually perpendicular and overlap within the vacuum chamber of the 3D-MOT. Reflectors (not shown) may be arranged at three sides of the vacuum chamber of the 3D-MOT so as to oppose a respective beam-forming apparatus and to retro-reflect a respective output laser beam therefrom. Each output laser beam may be retro-reflected to re- traverse the vacuum chamber e.g. to support the process of optical molasses described above.

[171 ] Anti-Helmholtz magnetic-field coils (not shown) may be positioned beside the vacuum chamber of the 3D-MOT to provide an appropriate magnetic field to assist in magneto-optically trapping and cooling the atoms or molecules supplied from the 2D-MOT 100. The translation stage is mounted upon one side of an interface plate 102 upon the opposite side of which is mounted an ion pump (103, 104), a blanking flange 105 configured to close an opening of the vacuum chamber not being used in the 3D-MOT, a pinch-off tube 106 configured to crush closed an outlet tube of the vacuum chamber to cold-weld it closed as a vacuum-tight seal, and an interface part 107 to form a mounting interface between a rail assembly and the rest of the 3D-MOT apparatus. Upon the underside of the interface part 107 is mounted a base part 108 of a rail assembly (108, 1 10) comprising a set of four straight, elongate mounting rails 1 10 attached rigidly thereto and arranged in parallel in a square array. They extend in parallel to the axis of the 3D-MOT and parallel to the longitudinal axis of the vacuum chamber 109. The base part 108 is rotatable relative to the interface part 107 around the longitudinal axis (the atom/molecule beam axis) of the 3D-MOT so as to allow the mounting rails to revolve in unison about that axis to permit adjustment of the position of apparatus mounted upon the mounting rails 1 10 (e.g. optical beam forming assemblies and/or reflectors therefor).

[172] Figure 17 schematically shows the assembly of figures 14A, 14B 15A and 15B employed as a cold atom source 100 in combination with an optical source unit 200 for providing a first laser light 202 (cooling beam optical power of about 75mW) used for cooling atoms or molecules and a second laser light 203 for pushing cooled/cold atoms or molecules using the laser light provided (push beam optical power of about 10mW). A third laser light 204 for use in the user application 206 in forming a push beam for pushing cooled/cold atoms or molecules (push beam optical power exceeding 50mW). The cold atoms or molecules 150 may be output from the cold atom source 100 at a rate exceeding 10 ⁹ atoms/molecules per second. The output cold atoms or molecules may then be input to a user application 206 of any desired description. One example of a user application is a 3D-MOT apparatus such as described above, for forming a Bose-Einstein condensate with the supplied cold atoms or molecules 150. An electrical power supply comes from the optical source and feeds electrical power to the cold atom source for use in heating an atomic/molecular sample (e.g. Rb, to a few 100 degrees Celsius) in order to sublime the sample to provide a vapour of atoms for cooling by the cold atom source 100. Typically 2 to 4 Amps may be supplied at less than 5 Volts. The optical source unit 200 also provides an electrical power transmission line 205 for providing power to the anti-Helmholtz coils (not shown) of the user application 206 (e.g. in a 3D-MOT). For example, 1 Amp of current at 5 Volts may be provided for this purpose.

[173] Figure 18 shows a cross-sectional view of an output laser beam of the optical beam forming apparatus of Figure 2, that is to say, a view looking down the axis of the output laset beam towards the optical beam forming apparatus. Beam intensity profiles are shown along the first and second dimensions (transverse) of the beam. It can be seen that the output laser beam is generally rectangular in cross-section and presents a wall of light. In the example shown, the cross-sectional dimensions of the wall of light are about 25mm by about 35mm. The output laser beam has a significant, non-zero light intensity over the whole of that cross-sectional area. Whereas the intensity distribution is not uniform in the example shown, a greater degree of uniformity may be achieved, if desired, by adjusting the reflectivity of the reflective surfaces within the second optical beam expander such as illustrated in Figures 4, Figure 7 or Figure 8A etc. in order to achieve a desired uniformity (or at least greater agreement/similarity) as between the intensity of the reflected light output by each such surface relative to the others.

[174] Similarly, the uniformity of the cross-sectional intensity distribution of the first expanded laser beam, produced by the first beam expander, may also impact upon the cross-sectional intensity distribution of the ultimate output laser beam and factors such as the performance of the optical components of the first optical beam expander may be adjusted as desired to improve intensity uniformity, if that is desired. In addition, the cross-sectional uniformity of the light intensity initially input to the optical beam forming apparatus will influence the intensity distribution of the ultimate output laser beam.

[175] A vertical slice of the output laser beam intensity profile is illustrated in the upper section of Figure 18 and corresponds to the intensity distribution along the vertical line passing from the bottom of the beam cross-section to the top at a constant horizontal position of about 21 mm, and a vertical position spanning from 0mm to 26mm. of the output laser beam intensity profile is illustrated in the upper section of Figure 18 and corresponds to the intensity distribution along the horizontal line passing from the left hand side of the beam cross-section to the right at a constant vertical position of about 12.5mm, and a horizontal position spanning from 0mm to 40mm. A series of twelve intensity peaks can be seen which correspond to the peaks in reflected intensity from a second beam expander comprising twelve successive reflecting surfaces 22 (see Figs. 8A to 8D). A drop in output intensity is seen between successive intensity peaks and this arises at the region of the second optical beam expander where the bottom edge or one reflecting surface 22 coincides with the upper edge of the succeeding reflective surface as viewed down the output axis of the output laser beam. Here, greater optical losses may occur, but these optical losses are not so significant as to prevent a useful intensity of light to be present in the output laser beam at the location of an intensity minimum, albeit less than that at the peak of the intensity peaks either side. Overall, the reduction in intensity at the troughs between peaks amounts to only about 5% of the overall output intensity of the beam and is not significant. The width and depth of these troughs may be reduced by adjusting the extent of the reflective regions 22 so that the region where the bottom edge or one reflecting surface 22 . overlaps, or projects over, with the upper edge of the succeeding reflective surface as viewed down the output axis of the output laser beam. This means that light from two neighbouring reflecting surfaces may be combined at the overlap region so as to boost output intensity there.

[176] It is important to note that it is not essential that the cross-sectional intensity distribution of the output laser beam is uniform in order to be able to manipulate cold atoms or molecules (e.g. in a 2D-MOT, or other MOT cooling process). This is because the optical processes (e.g. optical molasses) underpinning the manipulation induce optical forces upon an atom/molecule that saturate in value above a certain light intensity threshold, and no significant improvements in performance are achieved by employing a higher output lase beam intensity at a given location of a manipulated atom/molecule. This, it is quite sufficient that, if one wishes to provide greater uniformity performance (optical forces) of the output laser beam for manipulating cold atoms/molecules, then preferably one merely requires that there is an intensity of light across the laser beam that is at or above a threshold intensity level.

[177] The present invention provides for forming a beamformer (e.g. the second optical expander), such as described above, from a stack of transparent sheets, each of which can have a partially or completely reflective coating, e.g., on a rear face. The beamformer is carved, e.g., by dicing and polishing, from the stack of sheets. The resulting beamformer includes a stack of beamsplitters. Each beamsplitter of the beamformer stack is carved from a respective sheet of the stack of sheets. Each beamsplitter is a monolithic prism with a reflective coating. The prisms can be rhomboid in shape except that a front beamsplitter can have its front face polished so that the front prism becomes a triangular or trapezoidal prism. Likewise, the back of the beamformer may be cut square to enable a second output beam or tapped beam orthogonal to the primary expanded output beam. The innovative beamformers can be used on nearly any optical cell, nested optical cell, channel cell, or windowed vacuum chamber or other device requiring coupling of a large area beam with minimal wasted volume.

[178] The present invention provides for millimeter-range beamsplitters. Herein, "millimeter range" may refer to beamsplitters with a minimum dimension within a range of 0.1 millimeters to 10 millimeters, or 100 microns to a centimeter. Some embodiments are most applicable to a narrower range of 0.3 millimeters (300 microns) to 3 millimeters. Typically, the minimum dimension is the distance between the front and back faces of a beamsplitter.

[179] For example, in FIG. 19, at time period T1 1 , a beamformer 1000 is to be carved out of a stack 1020 of eight transparent monolithic sheets S1 1 -S18 so that beamformer 1000 ends up as an array of a like number of eight monolithic prisms P1 1 -P18, with each prism having been carved out of a respective one of the monolithic sheets S1 1 -S18.

[180] As shown at time T12, an input beam 1040 enters beamformer 1000 at a front-face of prism P1 1 and exits as an output beam 1060 constituted by eight component beams B1 1 -B18, each of which is orthogonal to input beam 1040. Each of component beams B1 1 -B18 results from a reflection by a reflective coating oriented 45° relative to both input beam 1040 and the corresponding component output beam. This 45° angle results from the 45° tilt of sheets S1 1 - S18 relative to the planned beam direction. In other embodiments, this tilt can differ from 45°.

[181 ] Due to this 45° tilt, prisms P1 1 -P18 are, at least initially, rhomboid prisms. However, front prism P1 1 is polished to define a front face that is orthogonal to the planned direction of transmission for input beam 1040. Accordingly, front prism P1 1 is a triangular prism; in an alternative embodiment, the front prism can be a trapezoidal prism. In an alternative embodiment, the last prism can be triangular or trapezoidal as well. [182] A second beamformer 2000, shown in Fig. 20 is carved from a stack 2020 of transparent sheets S21 -S25. As a result, beamformer 2000 has a front trapezoidal prism P21 and rhomboid prisms P22-P25. As indicated in FIG. 20, each sheet S21 -S25 has a reflective coating R21 -R25. Accordingly, each prism P21 -P25 has a reflective coating Q21 -Q25.

[183] The reflectivities are 20%, 25%, 33%, 50%, and 100%, respectively for coatings R21 -R25 and respectively for coatings Q21 -Q25. These values, which correspond to the fractional values 1/5, 1/4, 1/3, 1/2, and 1/1 , are selected so that the light of input beam 104 is evenly distributed among output beam components B21 -B25. More generally, for an N-prism beam former, the reflectivity associated with the front prism can be about 1/N, with successive reflectivities increasing as 1/(N+1 -/) for the fth prism. As described further below, in some embodiments, some lower percentages appear twice in succession in a stack to reduce the number of different reflectivities required and, thus, to save manufacturing costs. They may also all be lowered by some factor to enable the beamformer to only reflect a fraction of the total power, allowing the remainder to pass straight through for other purposes.

[184] Beamformer 2000 is designed to convert an input beam 2040 to an output beam 2060 with a 5x elongated cross section. A similar transformation of beam cross section could be accomplished using an array of cube beamsplitters. Each cube beamsplitter includes two triangular right isosceles prisms bonded together with a reflective layer at the interface. A beamformer could then assembled by bonding the resulting beamsplitting cubes together. Thus there are two monolithic prisms per cube beamsplitter; therefore, a beamformer made by assembling cube beamsplitters would have twice as many monolithic elements as a stacked beamformer carved from plates. This means that a cube-based beamformer would have about twice as many interfaces between monolithic elements that might negatively impact the transmission characteristics of the beamformer.

[185] In terms of manufacturability, the present invention offers many advantages including small component counts and ease of forming a beamformer from sheets than from triangular prisms. Furthermore, although FIG. 20 indicates only one beamformer is carved from a stack, it is clear from FIG. 19 that many beamformers can be carved out of a stack of sheets, provided the sheet dimensions are relatively large. Finally, compared to fabricating beamformers from arrays of cubes, it is relatively simple to scale down to millimetre dimensions and below when manufacture is based on stacks of sheets. In summary, the present invention offers numerous advantages over at least one alternative that also uses beamsplitters.

[186] A process 300 for making and using a beamformer is flow charted in FIG. 21 . At 31 1 , transparent sheets are formed or otherwise obtained. Herein, "transparent" regards visible, infrared, and/or ultraviolet light within a frequency range of interest. The sheets may be purchased, manufactured, or grown (e.g., using photolithographic techniques), for example. The sheets may be thick or thin, depending, for example, on the desired dimensions of the beamsplitters that collectively constitutes the beamformer.

[187] Herein, a "sheet" is defined as an object with two parallel faces separated by edges of smaller cross sectional area than the area of the faces. For example, the faces have areas of several square centimetres, while the edges can be between 100 microns and half a centimetre thick and have a total area less than one-square centimetre.

[188] At 312, the faces of the sheets are polished to ensure flatness and parallelism of the sheets. Advantageously, both faces may be polished at once in a parallel polishing operation. If flatness is otherwise assured or obtained, this polishing may be omitted. Commercially, achieving parallel plates is significantly easier than achieving 90° and 45° polishing making fabrication of the beamformer constituent components vastly easier than their cube counterparts. Further sequential stackup error of triangular prisms is more likely to lead to an output beam that is not comprised of parallel beam sections, while sequential stackup error of very parallel plates comprising a the proposed beamformer will be very parallel to each other yielding superior output beam specifications with less effort or expense, regardless of the output angle.

[189] At 313, reflective coatings are applied to the sheets. One face of each sheet is coated. Due to symmetries of the sheets, the face to be coated can be selected arbitrarily. However, once coated, the coated face is referred to herein as the "rear" face and the opposing face is the "front" face. The reflective coatings can have different reflectivities, as explained above with reference to FIG. 20. Further, while homogenous glass or crystal is often chosen, birefringent materials may also be used wherein the orientation of their fast and slow axis may be used to adjust polarization before, and/or after each reflection. Further, a birefringent and or piezoelectric substrate formed into beamformers may be used with electrodes such as ITO and a voltage potential modulation to modulate the birefrengent properties thereby modulating the path length and or polarization in each segment.

[190] At 314, the polished and coated sheets are stacked. The flatness of the sheets ensures good optical connections between adjacent sheets. The sheets are preferably tilted, e.g., at 45° or other oblique angle relative to a base or other reference that will turn out to have been parallel to an input beam path for the beamformer being manufactured. In some embodiments, the sheets are not tilted, or are tilted at an angle other than 45°. The sheets are then bonded, with each rear faces being bonded to the front faces of other sheets with exceptions for sheets at the front (top) and rear (bottom) of the stack.

[191 ] At 315, the stack of sheets is obliquely (e.g., at a 45° angle to the faces) diced to form plural stacks (aka, "stacklets") of monolithic beamsplitters. It is an economic advantage of the invention that one stack of sheets can be used for manufacturing plural beamformers. To this end, stack 1020 (shown in FIGS. 19 and 22) can be diced as indicated at 400, in FIG. 22. This dicing yields stacklets of monolithic beamsplitters, such as stacklet 500, shown in FIG. 23. Where the stack was tilted prior to bonding, the dicing can be parallel to the stack base; where the stack was not tilted prior to bonding, some other approach can be taken to implement the oblique dicing.

[192] At 316, each stacklet is polished to its final form. Polishing input and output faces improves transmission characteristics into and out of the beamformer. Polishing other exposed faces of the beamformer reduces opportunities for light scatter or leaks by maintaining a constant angle for internal reflections. Note that a front face 502 of a rhomboid input prism 504 of stacklet 500 (FG. 23) is polished so that the front face of the beamformer (1000, FIG. 19) is orthogonal to the input beam direction to optimize transmission into the beamformer. Thus, the rhomboid front prism 504 of stacklet 500 becomes a triangular or trapezoidal front prism of the beamformer. Note that all stacklets diced from a stack of sheets may economically be polished in parallel.

[193] At 317, anti-reflection (AR) coatings can be applied to the input and output faces of the beamformer to improve transmission characteristics into and out of the beamformer. These coatings may be omitted, e.g., to save costs and manufacturing complexity, if the transmission characteristics are not critical. This completes manufacture of the beamformer. Non transmitting faces may be black or absorptive coated to reduce undesired light scatter and reflections. Non- transmitting faces may also be high-reflectivity coated to maximize light out of the output face, especially in configurations where the output beam may be retroreflected back into the beamformer, thus increasing the effective output power of the beamformer by at least 50%. Note the input faces of plural beamformers may be AR coated in a single operation; likewise, the output faces of plural beamformers may be AR coated in a single operation to leverage economies of scale.

[194] At 321 , in input beam is transmitted into the non-rhomboid front face of the beamformer. At 322, the input beam is split at each reflector (except the last, which reflects the entire incident beam) and reflected to yield component output beams that are output from the beamformer. The component output beams collectively constitute the output beam for the beamformer. For example, component beams B1 1 -B18 constitute output beam 1060 in FIG. 19.

[195] Multistage beamformers can be made by ganging simple beamformers. For example, a multistage beamformer 600 is shown in FIG. 24 including a first stage beamformer 602 and a second stage beamformer 604. First stage beamformer 602 can convert an input beam with a circular cross section to a beam with an elongated cross section. The beam with the elongated cross section can be input to the second-stage beamformer 604, which expands the beam cross section in the direction orthogonal to that of the original elongation. Alternatively, if the reflectivities of a first beamformer are lowered by some factor and the last reflector is not 100% then the light leaving the last reflector may launch into another optical or another beamformer allowing a single beam to be split and formed by two beamformers in the same or different directions. For example a first beamformer whose output beam is at +30 degrees from normal to the large face of the beamformer may be followed by a second beamformer whose output beam is at -30 degrees from normal or 60 degrees from the first beam allowing these beams to cross at some distance from the plane of both beamformers to form part of an optical trap or lattice. Other angles and orientations are also possible.

[196] As shown in FIG. 25, a beamformer 700 includes an array of four monolithic prisms. A front beamsplitter 710 is a triangular prism with an anti-reflective (AR) coating 71 1 on its non- oblique front face 712 and a 20% reflectivity coating 713 on its oblique rear face 714. Beamsplitter 720 is adjacent to front beamsplitter 710 and is a rhomboid prism with a 25% reflectivity coating 723 on it oblique rear face 724. Beamsplitter 730 is adjacent beamsplitter 720 and is a rhomboid prism with a 33% reflectivity coating 723 on its oblique rear face 734. A fourth prism 740 is adjacent beamsplitter 730; prism 704 is a triangular prism and has an AR coating 743 on its non-oblique rear face 744. The right-angled rear face 744 can facilitate coupling to other optical elements, e.g., one may wish to daisy chain beamformers or tap out the end as a second output beam.

[197] The reflectivities of coatings 713, 723, and 733 are chosen so that half of the light of an input beam 750 transmits through beamformer 700 to yield a through beam 751 in addition to the reflected output beam 752 (which is constituted by component output beams for beamsplitters 710, 720, and 730. Different reflectivities can be chosen to change the ratio of light in the through beam to the light in the reflected output beam. However, no completely (100%) reflective coatings are applied to rear prism faces unless there is to be no through beam. An AR coating 753 is applied to the output (bottom) face 754 of beamformer 700. The remaining faces of beamformer 700, i.e., the faces through which light is not to be transmitted, e.g., top face 755, can have an anti-transmissive or black coating 756 to mitigate light leaks.

[198] FIG. 26 provides a comparison among three beamformers 802, 804, and 806 intended to convert a 1 x N beam into an M x N beam at different angles. Beamformer 804 is formed from transparent sheets titled 45° relative to the input beam 814, resulting in downward transmitting output beam 822 that is angled 0° from a vertical or, more specifically, a downward-pointed ray. Beamformer 802 is formed from a stack of sheets titled more than 45° so that a horizontal input beam 812 resulting in an output beam titled 45° from a vertical. Beamformer 806 is formed from a stack of transparent sheets titled less than 45° so that a horizontal input beam 816 results in an output beam tilted -45° relative to a vertical

[199] Accounting for Sneii's law, the splitting plane angle can be adjusted to deflect the output beam at angles other than normal to the output surface. This is advantageous when an angled beam in a cell, such as for crossing beams to form an optical lattice or trap is required, but minimal external optics is still desired. In this manner the length of the beamformer must necessarily lengthen along one axis per axis of tilt to accommodate the projection of the tilted beam with respect to the plane of the beamformer. To achieve this lengthening the thickness of the beamformer must increase or the number of elements must increase.

[200] A vacuum system 900, shown in FIG. 27, includes a vacuum cell 902 on which beamformers 802, 804, and 806 are mounted to define an optical trap, which can be readily adapted to form a magnetooptical trap MOT, a lattice, or a molasses, as is apparent to those skilled in the art.

[201 ] As seen in the schematic side-elevational FIG. 28A, in which beamformer 804 is omitted for clarity, beamformers 802 and 806 are arranged end-to-end so that some of the light entering beamformer 802 is transmitted into beamformer 806. Light 822 and 826 output respectively from beamformers 802 and 806 is transmitted into cell 902 at a -45 angle with respect to a downward ray. This defines an intersection region 1000 which is diamond shaped from the perspective of FIG. 28A. More specifically, beams 822 and 826 are orthogonal to each other.

[202] As seen in the plan view of FIG. 28B, which omits beamformers 802 and 806 for clarity, beamformer 804 is mounted on vacuum cell 906 so that it converts input beam 814 straight into cell 906. Within the intersection region output beams 802 (FIG. 28A), 804 (FIG 28B), and 806 (FIG. 28A) are orthogonal to each other so as to define an optical trap, that can be used to define a magneto-optical trap (MOT), a lattice, or a molasses.

[203] FIGURES 27, 28A and 28B use the plus and minus 45° outputs of beamformers 802 and

806 for the purpose of creating a crossed optical trap within a chamber while minimally consuming volume outside of the chamber. This may be contrasted to the shorter and more efficient standard beamformer 804 that launches at 90°s from its surface straight into such a chamber. Also note the last prism on the first expander is polished at 90° degrees and the last reflector is not 100% allowing the leftover beam (roughly 50% for this example) to launch into the next -45° beamformer in sequence forming two crossing beams from a single beam in minimal volume.

[204] An optical system 1 100, shown in FIGS. 29A and 29B, has a beamformer with conventional iow-profi!e cylindrical optics and roof prisms. In optical system 1 100, a spherical lens element 1 102, a first cylindrical lens element 1 104, and a second cylindrical lens element 1 106 are mounted on a beamformer 1 108. As shown in FIG. 29A, lens elements 1 102, 1 104, and 1 104, reform an input beam 1 1 10 to match the input of a reflector 1 1 12; reflector 1 1 12 reflects the beam so that it is input to beamformer 1 108. Using a beamformer as a base or lens or other optical element is a space-efficient way of implementing an optical system.

[205] One method of pre-expansion that costs at most twice the volume of the beamformer involves using cylindrical and spherical or aspherical optics to expand the beam from a small circular or near circular cross section to a 1 x N dimension beam prior to launch into the larger beamformer which will yield an M x N beam via an array of M (1xN) beams. Any combination of spherical, cylindrical or other refractory or prism expansion optics may be used in this first round of expansion and may utilize the back plane of the beamformer as an optica! mount to fold the expander into a compact module.

[206] Modern deployable devices tend to operate using diode lasers. Whether these couple straight to a fiber or to the device, the output of both typically requires a conical volume of clear aperture for the beam to expand in free space or in glass, until it gets to the desired dimensions at which point a refractive optic is typically used to collimate the beam. After expansion any swept optical path not spent in the device further consumes volume in the device. Therefore beams requiring a cross sectional area of say an inch then consume at least a cubic inch per beam. This quickly consumes significant volumes rendering devices too impractical or bulky for personal-sized units, limiting deployability and robustness to shock and vibration.

[207] Beamsplitters disclosed herein can cut the consumed volume down typically by at least a factor of 4 and often by a factor of 10 or more. Some applications may call for beams that are symmetric or asymmetric (one axis longer than the other). As asymmetric is the more complex case it is discussed as the example. To achieve economical beam expansion(both volumetric and financial) with conventional reflective optics one may start by using 2-3 cubed beamsplitters of ratios such as 30:70, 50:50, and 100:0. Glued back to back, these beamsplitters consume a volume less than that required by cylindrical optics while suffering minimal wavefront aberration. Thus an array of three such cube splitters allows for a transformation of a 1x1 to a 1x3 unit beam area by effectively replicating the beam into three identical copies right next to each other.

[208] Gaussian beams are typically round in nature and therefore the fill factor of the resulting 1x3 beam may be undesirable. The poor fill factor can be mitigated in a few ways. First, one may over expand the incoming beam before it launches into the series of splitting cubes fully filling the clear aperture of the cubes and therefore the clear aperture (CA) of the resulting 1x3 beam. However uniformity may still be less than desirable due to the Gaussian nature of the beam.

[209] Second, a beam diffuser or engineered diffuser may be used at the input or output, though a smaller and therefore cheaper one is needed at the input. The tradeoff here is the diffuser often loses quite a bit of light, wavefront quality is lost, and the effective distance from the engineered diffuser to each of the segmented output beam parts may result in undesired and non-uniform beam cross talk, overlap, and quality.

[210] Third, the collimated beam may be defocused or decollimated slightly to allow a slight expansion of the beam so that after the three segments exit they expand to overlap. This can yield nice wavefronts overall but interference between beams may be problematic. For magneto-optical traps (MOTs), this is usually less of an issue and may be corrected for with a very low magnitude diffuser or spatial scrambling optic. Indeed, for magneto optical trapping, a good wavefront is often not critical and minor scrambling can be beneficial to minimize optical coherent interference effects.

[21 1 ] Unfortunately a 1x3 cube beamsplitter array can be volumetrically inefficient, especially as an expansion telescope for expanding a small beam or fiber up to fill the clear aperture. However if we used an array of thinner beamsplitter plates at 45° (or other angles as desired, e.g., in a 3D MOT, where each successive splitter split an increasingly higher percentage of the beam) then a multi element splitter from say 5 to 50 layers could expand a n-by-n beam into an n-by-x*m beam where m=the number of layers of the beamformer stack. Alternatively the input beam may be elongated by turning a L-by-n beam into an L - by - x*m beam or turning a beam that is already expanded in one dimension into an output beam expanded by the same or a different factor in another dimension (typically but not necessarily an orthogonal dimension). Therefore a relatively thin stack of this beamformer optic can achieve the effective desired beam expansion or fill factor at a fraction of the total consumed volume and mass required by traditional refractive optics.

[212] There are scalable advantages to beamformer with stacked monolithic beamsplitters. For a high order beamformer, say with more than six elements, depending on the required intensity uniformity of the output beam, lower reflectivity layers may be "doubled up" in fabrication to save costs of making additional finely tuned reflective layers. For example in a 12 element array such as beamformer 604 (FIG. 24), elements 1 -2, 3-4, and 5-6 may be the same reflectivity. In this case, the ideal calls for reflectivities that yield P/N, where P=total power and N = number of layers where, for each segment m, the desired output power would be P/N. Then the desired reflectivity of each reflector m would be 1/(N-m+1 ). Therefore for a 12-element segment the reflectivities would be 0.0833 (1/12), 0.0909(1 /1 1 ), 0.1 (1/10), 0.1 1 1 (1/9), 0.125 (1/8), 0.143 (1/7), 0.167 (1/6), 0.2 (1/5), 0.25 (1/4), 0.33 (1 /3), 0.5 (1/2), 1 (1/1 ).

[213] However, to save cost, the ratios could be 0.83, 0.83, 0.1 , 0.1 , 0.125, 0.125, 0.167, 0.2, 0.25, 0.33, 0.5, and 1 . Alternatively the paired reflectivities may be an average of the two that were replaced. By doubling up the first six layers into three batches, the price at volume may drop by as much as 25% while only suffering an error in reflectivity of 1 1 % or less. Alternatively, the first six layers can have reflectivities of 0.087, 0.105, and 0.134 to bring deviation from ideal down to under 6%. Depending on the quality of the coating and the spec this may be within the range of the coating error.

[214] Another scalable advantage over cubed beamsplitters is using its initial apparent increased cost in fabrication into a strength. Splitter cubes are often 45°-45°-90° prisms that have to be polished to a precise specification and are then assembled by direct or adhesive bonding. Alignment of the triangles (triangular prisms) to make a cube is often critical and must be done individually. On the other hand, to make the stack, plates (sheets) are more easily made parallel by standard polishing practices, though more components are needed for a stack, each only requires two relatively simple polishing operations, and the coating operation likewise only deals with a single side coating whereas coatings of cubes often requires at least five faces (two of one triangular prism and three of another triangular prism) to be coated.

[215] In the initial assembly of the stack array each plate gets polished on both sides but coated on just one side. These sides may then be stacked sequentially and then the entire stack is tilted allowing the parts to slide in a shear-like fashion until a tilt angle of roughly half of the total turning angle is achieved, an angle dictated by Snells law for the output beam. They are then bonded at this angle making just about any angle beamsplitter from a 90° output to + or - 45° relatively easy to achieve. The top and bottom layers are then cut down to remove the points turning the stack into a rhomboid parallelogram. The parallelogram is then diced parallel to the top or bottom face to maintain the output reflected angle. The thickness of each slice is determined by the thickness of the slabs and the desired output angle in order to ensure 100% optimal fill factor for the given reflected angle.

[216] Given the nature of optical polarization off of reflective films it is ideal to select a linear polarization at which the stack is designed to operate. The linear input polarization then translates directly to an output linear polarization for all beams. If the polarization at the input rotates it may be impractical to maintain splitting ratios. However a thin polymer, crystal or other waveplate(s) may be mounted just after or adhered to the output surface of the beamformer adding a negligible additional volume to the device while enabling the desired target linear or circular polarization. Depending on the input polarization, and the collimated, focusing, or diffused nature of the input beam it may be desired to place a waveplate(s) at or on the input surface of the beamformer as well.

[217] Beamformers can be used as free space fiber coupled beam sources and may be mounted on tip-tilt stages to adjust pointing. Mounts may be typical ball spring mounts or low profile machined, electro-discharge machining (EDM), machined, micro electromechanical systems (MEMS), or 3D printed type flexures for minimal volumetric consumption of the mount and tight conformity to the beamformer. Materials may even include glass or silicon for thermal matching as well as traditional metals and polymers. Glass or ceramic flexures typically need to have careful surface finishes to reduce odds of fractures or failures during flexure, methods of adhesion may be clamping, gluing, eutects, tip, anodic or contact bonding.

[218] In cases where the materials of the beamformer are dielectric with minimal or no polymers, then integration of the beamformer into the vacuum cell or even as part of the vacuum cell walls, body, or window can further improve compactness and functionality of the system. In more advanced versions, one or more walls can be made out of a large area beamformer where light is coupled into the beamformer directly through the edge of the glass/former, or through a wedge prism on the surface just before the beamsplitter stack. Such surface beamformers can also be patterned gratings on the inner or outer surface of the glass with respect to the vacuum cavity; the patterns can be formed by photolithographic etching of the glass, or thermally "stamping" and removal of a sacrificial silicon grating negative. The grating or reflective layers may be written into the volume or bulk of the glass or holographic media through photorefractive effects, or ultrafast pulsed laser rastering or patterning in the bulk media.

[219] Beamformers can be glass or other transparent material. Depending on wavelength, beamformers can be silicon for long infrared (IR) or other media transparent to the wavelength of interest. Beamsplitting layers can be surface coatings such as but not limited to IBS, EBS, CVD, or reflection properties may be achieved through refractive effects from rastered, imaged, doped, or optically patterned/interfered gratings, planar refractive indices, gradient indices, or nano-structured surfaces or layers to define reflection or splitting layers. Topographical or bulk meta-materials may likewise be used to define layers or coatings.

[220] Beamformers may be individual beam to line generators, line to large area beam generators, or even beam to large area beam generators by mounting a b2l and I2A generator in sequence and even glued with the output of one matched to the input of the second with or without a waveplate or diffusive element sandwiched between.

[221 ] Beamformer I2A generators can first have a cylindrical telescope or refractive line generator as the pre expansion optic. Such a telescope can be mounted in line or even folded with turning mirrors and mounted to the top surface of the I2A generator effectively doubling its "thickness" but keeping the form factor smaller than conventional free space optic approaches.

[222] Output faces of beamformers may be anti-reflection (AR) coated, but, if the surfaces are to be in close proximity to waveplates or the window of an optical cell, then an index matching fluid or glue may be used to simply optically couple the parts by direct contact. An adhesive like Norland UV cured optical glues work well for this, effectively negating the need for AR coatings on intermediate optics that will be part of a sandwich or stack. Therefore only the input optical surface to the assembly, such as the waveplate or diffuser, and the output surface, such as the inside of the cold atom cell, need consider being AR coated.

[223] Where assemblies and orientations are to be permanent an adhesive may be used, where some adjustability such as waveplate rotation may be required, an index matching fluid may be used; the part can be affixed with an engineered accommodating gap to allow for rotation while minimizing fluid dryout. It would however be preferable that all waveplates be pre aligned and affixed before component installation. The backside of the beamformer opposite the output beam, or on the unused edge of the beamformer may also be used as an optical bench to which pre-expansion fibers, cylindrical or other optics are adhered minimizing the assembly and defining a second optical plane parallel to the beam expander.

[224] The multi-stack beamformer can be replaced with a volume holographic diffraction/reflective element to achieve the same effect with thinner materials, and more engineered expansion properties. One holographic element may expand the entire beam sequentially or at the same time. Two elements may be stacked coupling into each other at one end and laminated together for optimal coupling to take light straight from an uncollimated fiber. A combination of holographic beamforming and waveguiding may be used to take the output of a fiber and convert it to the desired beam profile. Any combination of the above may be combined for maximum efficiency or effectiveness in form and function.

[225] Through heating of engineered reflection layers, a beamformer can be tuned for the wavelength or wavelengths of interest or to tune polarization or behavior of different polarizations of the same beam. Conductive and insulative layers such as ITO and Si02 Ta05 can capacitively modulate performance by applying a potential across individual layers with small patterned traces on the backside, or applying a potential across the entire stack. Piezoelectric coatings or substrates with careful alignment of crystalline axis to linear polarization of the beam can likewise allow selective modulation.

[226] Multi-wavelength beamformers can involve engineering the same desired S or P polarization at the desired same reflectivities for multiple beams. This engineering can be done using metal coatings of very small thicknesses in the single to tens of nanometer regime, or with dielectrics tuned for angled reflectivity of each wavelength at the desired linear polarization. Advantageously, the stacked structure helps hold and protect fragile thick dielectric coatings by sandwiching them between adjacent substrates.

[227] As with most optical components, the beamformer may be used as a beam sampler to take a low profile sampling of the beam. The sampled beam can then be magnified to the limit of constructive and destructive interference; alternatively a scrambler can be used to extend this limit. The sampler can take a weak sampling of a beam but get a magnified readout of the sample by virtue of an aligned array of beamsplitters. In this case, the beamsplitters can have the same beamsplitting ratio, that ratio being weak to minimally perturb the through beam.

[228] One can image through the beamformer. While the image will have slices of ever increasing attenuation taken from the transmitted image, it does allow for limited viewing and tuning of MOTs or other phenomena within the cell that may otherwise be completely covered by the input optics. Indeed, especially for wavelengths farther off from the designed wavelength of the sampler, it may be more reasonable to image through it to obtain useful information from the cell. Again carefully engineered layers can permit transmission with minimal perturbation of one wavelength far removed from the for purpose beam expansion wavelength.

[229] The beamformer can be used in a nested cell. The nested cell consists of an outer vacuum chamber with an inner vacuum chamber suspended within the outer chamber, the inner vacuum chamber having a means of heating, a means of alkali atom injection, a hole between the inner and outer vacuum chamber to allow atoms to flow and it may or may not have an active pump in conjunction with one or more passive pumps. The inner chamber has multiple mirrors or reflective surfaces that are used to bounce at least one laser beam multiple times to establish an optical trap possibly with dual counter spin helicities.

[230] A cold atom source cell can be suspended within a second larger outer vacuum chamber. The mechanisms of suspension may include Kapton film, thin silicon, thin glass, or other means of rigid materials or materials under tension to precisely define and hold the position of the inner cell with respect to the outer cell. The mechanisms of suspension are designed for minimal thermal conduction between the inner and outer cell to thermally isolate the inner cell by floating it in vacuum allowing for any heat imparted to the inner cell to be maintained as efficiently as possible. The suspension mechanisms may further be made of an electrically conductive material to provide an electrical path to electrically heat the inner cell, or they may have electrically conductive materials laminated, plated, or otherwise adhered to them for this purpose. The suspension structures can be anodically bonded, TLP bonded, or bonded by other high temperature robust methods of affixing or by virtue of mechanical clamping and tensioning be fixed.

[231 ] Suspension members may be a bonded Kapton or polyimide film for HV applications which is advantageous to the ability to sandwich copper or metal traces in the polyimide film as a flex circuit as well as a suspension member. On the other hand, it can be useful to suspend the inner cell using thin glass structures bonded to the inner chamber and to a recessed and surface polished level of the outer chamber. This method allows for more rigid mounting that is CTE (coefficient of thermal expansion) matched, but risks fracture from differential heating due to compression as the inner cell heats with respect to the outer cell, or worse, fracture when the outer cell expands more than the inner cell.

[232] n-plane expansion channels can be machined and etched to allow for uniform expansion without fracture, though the final etching smooths the surfaces. Methods of achieving this polish may be an isotropic polish, an HF vapour anneal, a polishing slurry jet, or heating to slumping temperatures to allow softening and minor reflow of the edges. The suspension structure can instead be thin silicon with the same caveats as glass, though etching processes for patterned silicon is more easily controlled.

[233] Suspension members may also be formed by etching. A single silicon wafer may be used within which all of the necessary etching and processing is done to form the reflectors and other structures. As one of the final fabrication steps of the silicon wafer, a nitride that was patterned at some point in the process in a select region of the suspension members is flip-side machined and then etched to the nitride which acts as an etch stop. A patterned copper trace on either side of the nitride may be used to make it a bit more robust and provide the electrical path to the suspended cell, while the cell itself is essentially fabricated from a single piece of silicon. However, to achieve this, it can be advantageous to perform an initial machine operation to countersink one side, polish, and then nitride the entire wafer before proceeding to fabricate the remainder of the structures. This allows for a suspended structure which has an optical window independent of the outer optical window. Note, regardless it is likely necessary to pattern an AR coating on all optical windows to minimize parallel surface etalon effects and reflection losses on launch into the cell.

[234] Suspension structures may be used to actuate position such as fine tuning pointing or translation of the atom beam. Such techniques would suggest an H-bridge type electrical circuit in which four to eight or even more independent suspension arms or filaments would have selectable electrically resistive, or optically selectable, traces, one per arm. All or some subset would converge on the inner cell making a network of selectable circuits through these suspension arms. Selecting which arms to run divert current through would lead to their expansion which could be used to tip, tilt, rotate, and translate the inner cell. In most cases this is redundant to adjustments that could be made with magnetic and optical alignments.

[235] Alternatively, given thin walls of the inner cell, such traces over the inner cell with more structured subcomponent reflectors can be used to tune the field, but with much more complex results optically. The ability to point the atomic beam by this method would primarily be useful for very low atom fluxes where a relative handful of cooled atoms leave the inner cell. Such low fluxes may be due to ultra-small diameter and long apertures linking the inner cell to the outer, or due to low temperatures and pressures for very sensitive experiments. The inner cell consists of a partially or fully hollow structure within which optical reflectors are fashioned onto the inner surfaces or out of the inner surfaces. The optical reflectors are sufficiently reflective through plating, coating, or other means to effectively and, to a high degree of efficiency, reflect an optical beam multiple times with sufficiently low loses to allow for multiple reflections to effectively fill most of the inner cavity.

[236] The inner cell further has a means of alkali metal injection such as a region machined into the bulk of the mirror substrate without interfering with the optical trap. An alkali source is installed and sealed or affixed in place such that, when heated, alkali vapours are directly injected into the suspended cell. Alternatively, an alkali injector module can be fabricated independently and later installed or affixed to the inner hollow reflector structure with a conductance channel connecting the inner cell to the injector module.

[237] The inner cell can have resistive heater elements attached to its outer surface or integrated into its structure. The resistive heater elements allow for resistive heating of the inner cell to maintain an elevated temperature, whereby the alkali pressure of the inner cell is maintained thermally.

[238] The inner cell has a dielectric or structural coating, e.g., heat absorbers or black silicon. The coating allows for optical absorption of photon energy to heat the inner cell by absorbing radiation directly intended for this purpose. Alternatively, the coating can absorb the trapping laser at the end of the chamber after it has bounced multiple times through but before it retro reflects and scatters in a manner counterproductive to the cooling of the alkali atoms. These absorptive features may also line the seams of the chamber to reduce scatter from misalignment of the laser into the chamber, and to likewise more uniformly distribute optical absorbed power.

[239] The inner cell has micro grooves or channels that are sealed off after being vacated and partially filled with a working fluid to affect a heat-pipe structure to more uniformly distribute heat along the suspended cell to maintain a more uniform temperature given that the means of heating and suspension might otherwise lead to undesirable temperature gradients.

[240] The inner cell has reflective and absorptive regions such as polished and black silicon or black glass regions, not a part of the intended optical path, to balance emissivity of the chamber to further balance or adjust the temperature gradient of the cell.

[241 ] The multiple reflections within the inner cell can be from a single beam split by multiple reflectors. The beam can be bounced in multiple right angles to affect a multi-axis optical trap with a high volumetric fill factor of the inner hollow volume. The beam can efficiently and effectively cool atoms from a thermal kinetic gas state to an optical and/or magneto-optical trapped state along at least two effective axes of cooling. This cooling can establish a column or linear periodic series of cooled atoms. The cooled atoms align to an aperture for at least one end of the cell from which the atoms are allowed or encouraged to escape at a higher rate than would the thermal uncooled atoms in the same volume. Embodiments may be of a triangular pyramid, a square base pyramid, a roof prism, or some mix of the three.

[242] In another embodiment, a single expanded beam hits a diffractive element that splits the beam into multiple beams of proper dimension and direction with reflector angles adjusted to launch the beams properly into the hollow reflector cavity. In another embodiment, the single beam follows a complex path covering the entire inner volume of the trap before retro-reflecting back along its path to complete the optical trap. The single expanded beam can then be launched into a hollow chamber including a roof prism set of 90° reflectors, a series of 45° or 90° reflectors. Alternatively, the beam can be launched into a grating with an axis of symmetry along the length of the high pressure HV hollow cavity chamber with the axis exiting an aperture in the chamber to connect it to the outer HV, UHV, or XHV vacuum chamber. In the case of the grating reflector, the grating can be a single homogenous grating. The grating can have a stated axis of symmetry that efficiently splits the power between the +1 and -1 order at a specific angle for the target optical trap wavelength. This creates a long pair of beams crossing some distance above the centre axis of the grating, establishing a 3-beam trap with the single incident vertical beam and the two angled diffracted beams.

[243] In a variation, the side walls and window opposite the plane grating are polished optically and reflective for the side walls, e.g., using a high reflector coating or metallization. The top window, through which the incident beam transmitted, can be coated on the outside with a high transmission coating at normal incidence. Alternatively, the target launch incidence can be at angles matching the grating's +/-1 diffracted orders the dielectric coating to provide maximum reflectivity. This configuration creates an optical recycling of the diffracted light; the diffracted order can be adjusted to properly beam balance.

[244] Alternatively, the side walls may be coated with a high absorption material such as a gradient index black silicon or black glass structural coating to minimize stray light beyond the first diffraction event minimizing any scattered light in this inner or to the outer chamber. Further the aperture leading to the outer chamber and the outer chamber walls themselves may be coated with a similar high absorption material to reduce light scatter, and reduce power needed to maintain the elevated temperature of the inner cell.

[245] Alternatively, the side walls may be optically polished to maximize reflectivity. The windows to the inner and outer cell have a high quality AR coating over a broad angle range; this maximizes light transmission back out of the cell rather than risk scattered light bouncing around in an uncontrolled manner for experiments that would rather dump the optical power outside of the cell. AR coatings can be tailored to normal incidence and the most probably diffracted angle of incidence to maximize efficiency of photon removal and scatter minimization. In another embodiment, a combination of high reflectors, high absorption surfaces, and high transmission windowed regions are selectively fabricated to tailor the above effects.

[246] Assembly of the inner hollow chamber can be achieved via anodic bonding of glass, crystalline, or ceramic materials with intermediate bonding transition layers or even with direct contact bonding between similar materials. It can further be achieved by TLP, or diffusion bonding of similar materials as well as metals and materials not traditionally bondable by such means. Or it can be assembled further by direct contact bonding of similar materials or even dissimilar materials with sufficient compliance designed into the structures to allow for minimal stress induced structural failures or delaminating during heating. This compliance can be achieved by integrating thin strain-relieving bellow or flexure like structures especially through polishing and etching of same said structures post machining or as the sole fabrication step for the sub-components.

[247] Forming of the mirror components may be achieved by machining into a GCC (Glass, Crystal, Ceramic) or even metal material, such as with silicon, via a grinding abrasive machining process to remove the bulk of the material at the desired angle or structure. The surface can then be refined to an optical reflector by machine polishing with finer grits, slurries, with rotating grinding bits or by vibratory, orbiting, or ultrasonically actuated bits that polish individual planes or are structured as a negative of the form to polish the complimentary shape. Such polishing components may be fabricated, at least in part, as flexure-based resonant or quasi-resonant structures to convert actuation along a single axis to a multi axis motion to enable more uniform polishing to achieve superior planarization at complex concave or other difficult geometries. [248] Tooling for the flexure- based tool may be fabricated via etching processes, electro- discharge machining processes, or 3D additive printing processes with appropriate materials which may include but are not limited to metals, glasses, and ceramics, and polymers or composites and assemblies thereof. Polishing may be improved using conventional or modifications of a chemical-mechanical polish slurry for substrates such as silicon. Such silicon substrates may be desirable to enable assembly and bondability to other GCC materials such as Pyrex or aluminosilicates.

[249] Alternatively pre-assembled cuvettes or rectangular cells can be used and coated by the above processes on the inside for reflection. The cell uses mounting components, end caps with one hole and a hole machined to allow launching in the side into the cell.

[250] Assembly of cavities can be achieved by single side etching/machining and polishing in silicon. This can be followed by reflective plating/coating. The two halves or multiple subcomponents are flipped into symmetric contact. Bonding can include contact bonding for straight silicon to silicon for complementary or conforming polished surfaces. Anodic bonding may be used with intermediate Pyrex thin layers, which may also be part of the suspension structure. TLP, diffusion bonding, or thermal compression bonding may be used as part of the polyimide or similar suspension attachment procedure to close the two halves at the same time. Parts can also be "wire tied" together with materials such as nichrome, tantalum or other pure malleable wires. Suspension members may also consist of such wires.

[251 ] Melt bonding or slump bonding or frit bonding can be achieved with thin intermediate layers that melt at low temperatures (defined as temperatures below which already attached components and plating materials will not fail or degrade appreciably, typically under 570°C). Flip assembly may be achieved in a large array of components from a wafer and then singulated by dicing, cleaving, or other common singulation techniques of components from silicon wafers.

[252] Forming of the grating components can be achieved by standard etching or stamping techniques. It is generally advantageous to etch in silicon for the established MEMS processing and material compatibility for subsequent assembly. Coatings of the grating can be advisable to improve diffraction efficiency. Multi step etching and masking processes can be used to make blazed, stepped, or angled structures to improve diffraction efficiency along preferred orders such as just the +1 or both the +/-1 order. Coatings may consist of dielectric HR coatings or metal coatings via thermal evaporation, sputtering, electroplating, or combinations thereof. Gratings formed in such ways have the advantage of being UHV compatible and can therefore be placed in the inner chamber to maximize optical efficiency and path length maximizing trap volume. Further, getter materials can be plated to the grating or near the region of the grating to absorb undesirable gasses as close to the MOT as possible for situations where pressure near the optical elements is critical for MOT behavior where background pressure is critical. [253] Additionally, using selectively grown and etched oxides or metals such as by line of site deposition on blazed structures or angling the deposition to mask certain faces of a grating etched structure, a passivation or activation layer may be deposited or etched from select faces to enable high reflective or high absorption coatings on select faces. For instance, a sacrificial metal or oxide mask can be used to protect certain faces of subsequent respective oxide or metal coatings after which an etch or removal process targeting the first layer is used to remove the coating from the undesired face. By this method, for example, raised sections and select side walls may be highly reflective while others are native or highly absorptive. Material deposited can also be used to tailor polarization effects.

[254] Glass reforming via reflow of Pyrex or similar (for silicon substrates) at melting temperatures may be used to form more integrated windows or compound substrates prior to final polishing of substrates. Silicon structures may be machined by the methods mentioned above before cleaning and melting glass over or through the machined or etched channels, holes, or structures, then further machining or polishing can be used to create the appropriate integrated structure such as a low profile integrated window in silicon where the profile of a window bonded the outside of the silicon structure would consume limited or unnecessary volume inside the vacuum chamber. Such integrated windows further benefit from minimal mass and will therefore be more uniform in temperature Likewise reflow about silicon structures can be used to create electrically or, to a lesser extent thermally, isolated structural mounting points or feedthroughs. The silicon of the feedthrough through a silicon hole with a glass insulator may be of two different doped silicon substrates such that the larger bulk substrate is more resistive, while the feedthrough structure is more highly doped to be conductive. The advantage of such a feedthrough is low CTE mismatch and minimal profile, volume, and thermal mass.

[255] Reflowing glass can also be used over a pre-polished and even an AR coated or other dielectrically coated or structured surface such as a grating. The silicon negative is then etched away via a hydroxide or other silicon etchant that minimally attacks the glass structure or even the coated structure to allow for an effective negative molding of a structure, even a hollow channel, with optically polished surfaces or grating etched surfaces, both of which are easier on a convex part such as a rectangular silicon plug, than they are on the inside of any convex feature. By this method gratings that were only achievable in silicon may be HR coated, or AR coated as appropriate for the glass, and then the structure and possibly the coating may be transferred to a convex or enclosed structure of glass.

[256] Further coating of the glass or silicon structural inner dimension/diameter can be achieved via chemical vapour deposition to achieve anti-reflection or high reflector coatings with dielectrics. Alternatively a wire filament drawn through the hollow cavity may be used to plate via- line-of-sight thermal evaporation, the inside of the structure. Further electroplating with a single or multiple plating and etching cycles can be used to deposit metal coatings. Multiple coatings and partial to near complete etching can be used for concave glass or silicon structures to uniformly plate the surfaces with optical or near optical finishes where each etch cycle conditions the surface to enable superior successive plating attempts, or by leaving behind seed atoms for successive plating's. Combinations of these methods can be used to put down seed layers such as by melt and etch transfer of coated surfaces of easily evaporated metals or noble metals, followed by electroplating of the inner glass walls. For transfer of metals surfaced parts through the glass reflow process, one can use pressurized forming noble gas, or even vacuum environments, depending on the composition of the metal and glass.

[257] Magnetic fields can be established: by at least one pair of coils with subsequent pairs along orthogonal axis; with sets of permanent magnets likewise in multiples of two sets to establish similar optical axis; or by single complex shaped and polled magnets which allow for magnetic nulls to be established at distances no greater than the effective diameter of the magnet. The null may be established along an axis of symmetry such as that from a ring magnet polled axially which exhibits a null along the axis some distance from the centre of mass at a distance less than the diameter of the magnet.

[258] This magnetic null may be adjusted by complex topographical structuring of the magnetic surface and subsequent complex polling either symmetrically or periodically with homogenous or inhomogeneous field strengths for each polled section to more precisely tailor the magnetic field gradient about the null. Sets of magnets on a single side of the MOT may establish the null by say using a ring magnet or a set of magnets to approximate a ring establishing the null, while a second magnet or set of magnets installed along the axis of the first set with a slight offset from the centre of mass of the first set are used to shim or fine tune the centre position or magnetic gradient from the null.

[259] Coils can be mounted externally to the vacuum chamber. Alternatively, the coils may be integrated into the substrates defining vacuum walls of the vacuum chamber through MEMS like etching and deposition processes or via etching and plating processes such as electroplating on patterned surfaces or within etched, machined or grown channels. Successive sections of coils may be connected via flip-chip or bonded stacking methods or by direct contact during assembly of stacks. Conduction paths for coils or other traces can be established via patterned doping or ion treatments and or etching or altering the surface of substrate materials such as silicon or glass or via high voltage ion metal, salt, or doping or thermal diffusion based ion migration and alignment techniques.

[260] The atom injector module can be a tube, a bonded tube structure, or a stacked bonded glass-silicon or other type of structure. An alkali source and possibly a getter or other pressure affecting material can be installed within the injector module. The alkali source may be a salt, pill or other material, composite, alloy, or loaded substrate that, when heated, stimulated, or excited with thermal, photonic, or electrical energy, produces a plurality of alkali atoms in vapour form. The atom injector having at least one optical window which may or may not be a membrane material such as silicon nitride, silicon, Pyrex, Kapton, graphene, graphite, or other sufficiently vacuum tight material sealed over a channel or chamber connecting to the alkali source.

[261 ] The atom injector can then be fabricated before final assembly of the vacuum system by forming, machining, and then installing into a glass, silicon, metal, ceramic, or other structure, or composite structure, the alkali source material. Then the module can be vacated. Then the module can be sealed with the membrane material or another seal independent of the membrane material.

[262] This module can then be singulated from a larger array, cut from a larger bulk substrate or otherwise extracted and handled in atmosphere without contaminating the inner vacated chamber or channels. The module can then be stored and at a later date installed, or bonded to the inner hollow chamber before pulling vacuum on and sealing the outer chamber. Before or after the final seal, but after pulling vacuum on the outer chamber, the alkali source module may then be connected to the inner chamber by compromising, or adjusting the permeation properties of the membrane seal between the alkali module and the inner chamber it is installed to. Passive getter materials can be located within or on the surface of the atom injector module to absorb undesired gasses or by-products of the production of the alkali atom vapour to minimize contamination of the vacuum chamber.

[263] The membrane can be a selectively permeable membrane comprising graphene, graphite, a piezo based material, an intercalable material or similar to allow for thermal or electrical actuation of the permeability of the membrane. The membrane can include a thin film over the membrane which can be impermeable graphene until it is intentionally compromised, or a crystalline material which may be heated or stressed to introduce micro fractures through which controlled heating or electrostatics may control the permeation rate through a mostly intact membrane.

[264] The structure of the alkali module can be a tube with a membrane on one end or installed over a sidewall polished down to breach the circumference at one point, or wrapped with a membrane to seal the breach at least temporarily. The structure may alternatively be a stack of a GCC (glass ceramic crystalline) material such that individual layers are machined with certain features then aligned and assembled to adjacent layers to form a cavity with a rectangular cross section in at least one axis. One of the layers can be the entire membrane or comprised partially of the membrane as formed by selective and careful etching, polishing or other methods of material removal. The membrane can be grown or laid over a small hole or grid like scaffold with materials such as silicon, oxides or nitrides of the scaffold grid, or graphene or other atomically perfect planar materials similar to graphene.

[265] Vacuum quality of the cell may become compromised over time due to permeation of noble gasses through the glass as noble gasses cannot be removed with passive getters. A low permeation or zero permeation barrier on the surface of the glass, such as a layer of atomically perfect graphene, can be used to mitigate the permeation. The glass can consist of an aluminosilicate CTE matched to silicon such as several modern display glasses with a CTE around 3x10 ^"6 m/m. Such glasses can lower the permeation rate several orders of magnitude.

[266] Another technique can be a barrier vacuum between the cell and another cell; within the outer cell, only a roughing vacuum is necessary. This can be achieved by establishing a second outer chamber to the first outer chamber that uses the same silicon backbone but has at least one countersunk and polished perimeter plane. Such stacked windows, separated by at least a few hundred microns to account for vacuum pressure bowing to prevent touching, can leverage AR coatings to minimize etalon effect and losses just launching light into the cell. Alternatively the cell and external mount and optics can be encased in an outer vacuum chamber with a rough vacuum pulled to the same effect and with a lot less complexity on the inner cell, though it would increase the volume more than adding another layer to the cell itself would.

[267] Vacuum quality can be improved by installing a miniature ion pump into the cell and firing it periodically. Such a pump can be completely devoid of any magnetic material and only periodically, depending on the diffusion rate of the cell, have the magnets temporarily installed for a short vacuum maintenance cycle. During this cycle, any getter material may be heated to degas the surface into the ion pump and diffusion captured gasses that are mobile more into the bulk to refresh the getter material. Such a pump involves only a minimal addition in volume by utilizing only titanium and silicon. Alternatively, the pump can be made entirely of glass and silicon such that the silicon wall itself acts as the anode, while a second electrically isolated wall acts as the cathode in either a symmetric or split style pump.

[268] FIG. 30 is a flow chart of a process for making a MOT cell. FIG. 31 is an image of an MOT cell. The laser beam window size may vary up to 100% of top surface.

[269] A process for fabricating a MOT cell can begin with machining of 45° grooves on the face of at least one rectangular piece of silicon. Further processing of the machined surfaces makes them flat enough for optical mirrors. The methods for etching the surfaces include anisotropic etches (an example of which is shown on the right of FIG. 31) and isotropic etches. After the 45° grooves have been smoothed to optical quality, a layer of metal, or other reflective coating will be deposited. The metal has good reflectivity at the laser cooling wavelength (e.g., 780 nm for rubidium, 852nm for caesium). The metal does not oxidize rapidly in air, either by its nature or because of a passivation coating, so that the parts can be handled easily. Gold is not a good candidate, as gold forms intermetallics with alkali metal species.

[270] The rubidium capsules are small vacuum cells fabricated from glass and silicon. See FIGS. 32 and 33. They contain an alkali metal source and non-evaporable getter. Conductance channels are created by machining the bulk silicon. The top side (top picture on the previous slide) is sealed via anodic bonding of a glass cover plate. [271 ] On the back side of the capsule, the output channel is sealed with a membrane (e.g. silicon nitride or silicon oxide). The capsule is bonded to a vacuum system. A high-power laser then ablates the membrane, opening up the capsule to the vacuum system. Note that the capsule is sealed under vacuum, so that atmospheric gases are not introduced into the vacuum system when the membrane is ablated. In addition to alkali metals, the capsules can be filled with other metallic/atomic/molecular sources. The capsules can be used for any vacuum system requiring a source of atoms/molecules, not just the atomic clock considered herein. FIG. 31 presents an alternate dispenser with long frustrated vapour path for vapour control.

[272] FIG. 34 shows an entire laser path for an entire integrated system. A beamformer may replace the cylindrical and spherical optics. FIG. 35 is a cutaway of the suspended cell enclosure. FIG. 36 is a suspended cell showing suspension members with electrical heating elements. As shown, the cell implements a double V MOT; in an alternative suspended cell, a single-V MOT is implemented. FIG. 37 is a side cross-sectional view of a suspended hollow cell showing geometry of an interior etched and polished chamber. In an alternative embodiment, a V-MOT is implemented.

[273] The present invention provides a beamformer with stacked monolithic beamsplitters. Herein, "beamsplitter" encompasses devices that split an incoming beam of visible and/or invisible light, e.g., infrared, ultra-violet, into spatially distinct output beams. The beamsplitters herein include transparent bulk elements and partially and completely reflective coatings. Such a device with a completely reflective coating is considered a beamsplitter "in the limit", even though it does not actually split a beam.

[274] Herein, a "beamformer" encompasses a device for forming or reforming a beam of light. More specifically, a device for generating a beam of light having a first cross section from a beam of light having a second cross section that is not congruent with the first cross section.

[275] A beamsplitter encompasses "monolithic" if the bulk of the beamsplitter is a single piece of material, and not an assembly of smaller macro-scale pieces. The fact that a beamsplitter includes reflective coatings and, in some cases, anti-reflective coatings, does not render the beamsplitter non-monolithic. However, cube beamsplitters that result from assembling triangular prisms are not monolithic.

[276] Herein, a "stack" encompasses a linear array of elements (e.g., beamsplitters) in which the elements are in contact with each other. Herein, sheets of transparent material bonded together are "stacks" of sheets. Herein, an "array" is an ordered arrangement.

[277] The beamformers carved from the stacks of sheets may be considered to be stacks of prisms. Typically, such a beamformer has an input or front prism that is a triangular or trapezoidal prism, while the remaining prisms can be rhomboid. A rhomboid prism encompasses a parallelepiped having four rectangular faces and parallel faces in the shape of rhombuses. A trapezoidal prism encompasses a parallel pair of faces in the form of nonrectangular trapezoids, and a parallel pair of rectangular faces of different lengths separated by a non-parallel pair of rectangular faces. A triangular prism encompasses a parallel pair of triangular faces separated by a trio of rectangular faces.

[278] Herein, a "prism" encompasses an object that is transparent to light of at least one frequency, the object having rectangular faces connecting parallel congruent polygonal faces. The parallel congruent faces may be, for example, triangular, rectangular, trapezoidal, or rhombic. Herein, "rectangular" encompasses quadrilaterals with two sets of parallel sides, with each side forming right angles with two other sides; herein, squares may be considered to be rectangles in which all sides of equal length. Herein, "trapezoidal" encompasses quadrilaterals with parallel sides of unequal length and excludes rectangles. Herein, "rhombic" encompasses quadrilaterals with two sets of parallel sides in which each side forms an oblique (non-right) angle with each of two adjacent sides.

[279] Herein, "monolithic" encompasses made from a single piece as opposed to being assembled from separate pieces. A cube beamsplitter is not monolithic because it is formed by bonding two triangular prisms together.

[280] Herein, "oblique" encompasses a relationship between two lines or planes that are not parallel and are not orthogonal, but that meet or otherwise intersect. Herein, a face of a polyhedron may be considered to be oblique if it does not form a right angle with any face adjacent to it. A face of a prism may be considered to be non-oblique if it forms a right angle with at least one other face of the prism. For example, in the illustrated embodiments, the front (input) and rear (reflective) faces of a rhomboid-prism beamsplitter may be considered to be oblique with respect to the other four faces; adjacent pairs of the other four faces may be considered to be orthogonal (forming right angles) with respect to each other. In the case of the illustrated triangular-prism beamsplitters, the rear face may be considered to be oblique with respect to the front (input) face and the output face, while the input face and the output face may be considered to be orthogonal to each other. In the cases of the illustrated trapezoidal prism, the rear face may be considered to be oblique with respect to all other faces, whereas adjacent ones of the other faces may be considered to be orthogonal to each other.

[281 ] Herein, "adjacent" may be used, as appropriate, to describe objects that are in contact with each other or are in an array and are closer to each other than are any two non-adjacent objects in the array. Herein, an "anti-reflection coating", aka, "antireflective coating" or "AR coating", may refer (as appropriate) to a type of optical coating applied to optical elements to reduce reflection, typically, so as to enhance transmission into or out of the optical element. The reflective coatings on the illustrated embodiments may have different reflectivities in two senses: 1 ) they are not all the same; and, more strictly, 2) no two are the same. In some embodiments, only the first sense may be applicable, as appropriate. [282] A beamformer disclosed herein in any embodiment, for forming a beam of light, may comprise a stack of prisms, each of the prisms being monolithic and having orthogonal faces and at least one oblique face oblique to the orthogonal faces, each prism being adjacent to at least one other prism in the stack; and reflective layers, each reflective layer being disposed between oblique faces of adjacent prisms, each pair of adjacent prisms having a respective reflective layer disposed therebetween, the reflective layers having different reflectivities. At least one of the prisms may be a rhomboid prism and at least one of the prisms may be a triangular or trapezoidal prism. The prisms may include plural rhomboid prisms and at least one of the prisms is a triangular or trapezoidal prism. Each prism may have a non-oblique face with an anti-reflection coating thereon. Each prism may have a non-oblique face without an anti- reflection coating thereon.

[283] A process for forming a beamformer, disclosed herein in any embodiment, may comprise forming a stack of transparent sheets having reflective coatings, each transparent sheet being bonded to at least one other transparent sheet, the reflective coatings having different reflectivities; and carving the stack to define an array of prisms, each prism having been carved from a respective one of the transparent sheets, each of the prisms being monolithic and having at least one oblique face, each prism being bonded to at least one other prism in the array. The carving may include polishing to form flat faces of the prisms. The carving may also involve dicing the stack prior to the polishing to form plural stacklets, the polishing converting the stacklets to prisms. Preferably, at least one of the prisms is a rhomboid prism and at least one of the prisms is a triangular or trapezoidal prism. The prisms may include plural rhomboid prisms and at least one of the prisms may be a triangular or trapezoidal prism. The process may further comprise applying anti-reflection coatings to at least one non-oblique face of each of the prisms. The process may further comprise applying anti-reflection coatings to exactly one face of each of the prisms.

[284] Although a few preferred embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes and modifications might be made without departing from the scope of the invention, as defined in the appended claims.

[285] Attention is directed to all papers and documents which are filed concurrently with or previous to this specification in connection with this application and which are open to public inspection with this specification, and the contents of all such papers and documents are incorporated herein by reference. All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and/or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features and/or steps are mutually exclusive. Each feature disclosed in this specification (including any accompanying claims, abstract and drawings) may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise. Thus, unless expressly stated otherwise, each feature disclosed is one example only of a generic series of equivalent or similar features. The invention is not restricted to the details of the foregoing embodiment(s). The invention extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed.