B I. TECHNICAL FIELD

This invention relates to matter-wave interferometry involving neutral atoms and molecules. Its applications include, but are not limited to, uses as an accelerαmeter, a gyroscope, a gravimeter, a gravitational gradiα eter, an

11 instrument that can measure departures αf its αtn motion from an inertial, gravity free and/αr freely falling reference frame, a component or set of components for an inertial navigation and guidance system, an instrument that can remotely measure the distribution of mass within an

IB inaccessible volume, a seismograph, an instrument for determining the mass distribution of the earth itself, an instrument for locating underground natural resources such as petroleum, and an instrument for geodesy and gravity surveying that can be employed above, on, or belαui the

SI earth's sur ace.

The invention differs from previous art in that it employs quantum- mechanical interference of matter ωaves, i.e. de Brogue waves associated with particles with

SB παn-zerα mass. In particular, it involves the use αf matter waves associated uiith loω energy neutral atoms and/or molecules. As a result, it is dramatically more sensitive than interferometer arrangements that employ the classical-wave properties of light.

31

For simplicity, the words "atomic" and "atom" when used herein shall mean "atomic and/or molecular" and "atom and/or molecule", respectively, unless otherwise denoted. Such usage does not restrict the scope αf the invention.

3B The term "matter waves" refers herein to the quantum mechanical de Brogue waves associated with the propagation αf particles with non-zero mass.

I A. MEASUREMENT OF DEPARTURES FROM AN INERTIAL FRAME

Instruments which can sense departures of their own reference frame from an "inertial reference frame" are of important practical and commercial use, for example, in the area αf inertial navigation and guidance. Such departures B are limited by Chasle's and Euler's Fixed-Point Theorems αf classical mechanics to two basic kinds: rotations, and accelerations. The inertial effects of local accelerations Cvia Einstein's Equivalence Principle, which experimentally is known to hold to very high accuracy) are

II indistinguishable from those due to gravitational fields. The effects of simultaneous rotation and acceleration are interlinked via the Cαriαlis and centrifugal farces.

B. THE DISTINCTION BETWEEN CLASSICAL WAVES AND MATTER

IB WAVES

Two important but mutually distinct classes αf wave-like phenomena are classical waves and quantum-mechanical matter waves. Classical waves can always be described in terms αf mathematically "real" number

SI valued wave amplitude. An important class of classically describable waves are those associated with electromagnetic radiation Cincluding light). Such waves are described by Maxwell's equations. In a vacuum they propagate at the speed of light with equal group and phase velocities. Until

S6 the advent of quantum mechanics in the early twentieth century, all wave-like phenomena were thought to be of the classical variet .

Quantum-mechanical waves are fundamentally different 31 from classical waves. The term "matter waves" refers here to the quantum mechanical waves associated with the propagation αf particles with non-zero mass. Their wave amplitude can only be described mathematically in terms αf "complex" numbers. Their propagation is governed by the 36 Schrόdinger equation which inherently involves the use of Planck's constant and the square-root of -1. The formalism of quantum mechanics and the so-called wave-particle

I duality contained therein describes the motion of matter waves and of the associated particles. The de Brogue wavelength αf a particle is Planck's constant divided by its momentum. These waves propagate with unequal group and phase velocities, the group velocity being equal to that of

6 the associated particle, while the phase velocity exceeds that αf light. The propagation of particles with non-zero mass when wave-like interference phenomena are involved can only be described by the formalism of quantum mechanics.

II C. INTERFEROMETRY

Interferometers are devices in which waves are allowed to propagate along two or more essentially independent paths and then to superpose. At a ^' point of superposition the waves will add constructively or destructively 16 depending upon the relative phases αf these waves. A measurement of the total wave amplitudes or intensities at such points is then a measure of the relative phase difference between the paths.

SI Interferometers have been built for both classical and quantum-mechanical waves, although the discovery αf quantum-mechanical wave interference postdated that of classical wave interference by half a century. A quantum-mechanical description of the waves is essential in

SB a discussion αf sensing inertial frame departures by a matter-wave interferometer. The opposite is true for a description of optical interfero etric inertial sensors. The latter can be analyzed accurately in terms αf the propagation of classical electromagnetic waves.

31

II. BACKGROUND ART

A. PRIOR ART IN SENSING ROTATION, AND ACCELERATION PLUS

GRAVITY

36 Priαr art for sensing departures from an inertial frame falls into three basic categories — mechanical devices, interferometric devices, and quantum-mechanical

I devices .

1. MECHANICAL INERTIAL SENSORS

Rotation is commonly sensed by the use of gyroscopes, although many other devices Ce.g. the surface curvature of 6 a rotating liquid, and a Foucault pendulum) can also sense rotation. Acceleration is commonly sensed by measurement αf either the displacement αf a restrained mass or the force necessary to restore the displacement of a restrained mass. Masses with elastic restraints Csprings) and masses with

II gravitational restraints Cpendulums or pendulums coupled to gyroscopes) are commonly used. One limitation associated with the use of a pendulum is that it can be used to measure only two αf the three spatial components of gravity plus acceleration, so that the third component if needed)

16 must be measured via other means. Devices which measure the third component are commonly called "gravimeters" . Broxmeyer tlnert ial Navigat ion Systems, McGraw Hill, New York, 1361) discusses prior art that can sense departures from an inertial reference frame, and its application to

SI the practical problems of inertial navigation and guidance. Application αf such sensors to inertial navigation and guidance systems in a gimbal-free system C'strapdσwn mode"), and appropriate equations and mathematical techniques for analysis are further discussed in NATO AGARD

SB lecture series notes C#95, Strapdoxim. Inert ial Systems, AGARD-LS-35, ISBN 9S-B35-0214-0; and #133, Advances in Strapdown Inert ial Systems, AGARD-LS-133, ISBN

9S-835-0351-1).

31 Measurement of a gravitational gradient requires sensing the farce of gravity at two separated positions, and determining the difference between the two forces. The classic method and apparatus for doing so was invented by Baron von EέStvόs more than a century ago. His apparatus

36 Cnow called the Eϋtvϋs torsion balance) comprises two masses at the.ends of a beam that is suspended on a low torsion fiber. The difference between the gravitational

I forces acting on the two masses provides a torque that causes the beam to rotate. The Eotvόs torsion balance is currently a standard tool for gravity gradient measurements.

B S. OPTICAL INTERFEROMETRIC INERTIAL SENSORS

It has long been known since the pioneering work αf Sagnac, Michelsσn and others in the early part of the twentieth century Cbefαre the development αf quantum mechanics) that an optical interferometer, comprised αf an

II arrangement in which two beams of light that circuit an enclosed area in opposite directions, is sensitive to rotational motion αf the interferometer. This phenomenon is known as the Sagnac effect. A review αf the Sagnac effect for light has been given by Post CRevs. Mod. Phys. 39,

IB p475, 1967). Chow et al. CRevs. Mod. Phys. 57, p61, 19B5) discuss the current state αf the art for optical interferometers that can sense rotation.

3. QUANTUM-MECHANICAL INERTIAL SENSORS SI Various quantum-mechanical devices for sensing rotations are discussed by Ppmerantsev and Skrαtskii CSoviet Phys. Uspekhi 100, pl47, 1970). These do not, however, involve the use of matter-wave iπterferαmetry.

SB B. PRIOR ART IN QUANTUM - MECHANICAL MATTER - WAVE INTERFERQMETRY

Electron matter-wave interferometers have been built and have practical applications in electron microscopy. Simpson CRevs. Mod. Phys. 28, pSS ¹ ., 1956; Simpson Rev. Sci. 31 Instr. 25, pll05, 1954) and Gabαr CRevs. Mod. Phys. 28, pS60, 1956) discuss the theory and practice αf electron interferometers.

Neutron matter-wave interferometers have been built

36 and are described by UJerner CPHysics Today 33, pS4. I960).

Werner et al . CPhys. Rev. Lett. 42, pll03, 1979) demonstrated the effect of the earth's rotation on the

quantum-mechanical phase of the neutron via the matter-wave equivalent of the Sagnac effect. Moreover, Colella et al. CPhys. Rev. Lett. 34, pl ^L -7S, 1975) demonstrated gravitationally induced quantum interference for neutron matter waves.

Here-to-fαrβ no one has offered a method for the application of the scientific principles thus demonstrated with neutrons for providing practical inertial sensing devices. Additionally, no one has provided here-to-fαre a method for distinguishing between the phase shift in a matter-wave interferometer due to rotation and that due to the combined effects of acceleration and gravity.

Altshuler and Frantz were issued United States Patent # 3.7B1.7S1 in 1973 for a "Matter Wave Interferometric Apparatus" . Their apparatus consisted αf a source of particles, a beam-splitter, a pair of beam reflectors, and a particle detector. In their invention, matter waves associated with particles emitted by the source propagate along spatially separated paths that enclose a finite area, in the process being redirected at the beam reflectors, to the particle detector. Alternative embodiments show the particle detector further broken down into a beam analyzer, followed by a detector. For the beam-splitter and analyzer, Altshuler and Frantz employed standing-wave laser transmission-gratings at Bragg's angle. For the beam-reflectors they used a single Bragg reflection into only one order at a crystal face or diffraction by standing-wave laser beams.

Expected uses for their invention included detection of rotation, acceleration and/or gravity. Ulheπ their interferometer is operated with charged rather than neutral particles, it Is also useful for the measurement of the magnetic flux threading the enclosed area.

Altshuler and Frantz also suggested deploying their

I invention in a spacecraft to detect the presence of another isolated abject in space, by sensing the gravitational attraction of the sensed object. Applicant nates that this made will not work since the spacecraft conveying their accelerometer/gravimeter will itself be attracted to the

6 gravitating isolated nearby abject, that is, it will free-fall toward the object and maintain itself in its own inertial reference frame. So doing, their accelerometer/gravimeter will sense no gravitational field.

II Despite the early date of Altshuler and Frantz's patent, impractical features of their invention have prevented its actual reduction to practice. Matter-wave interferometry using neutral atoms and molecules has yet to be demonstrated, nor has its sensitivity to rotation, and

IB acceleration plus gravity.

C. PRIOR ART IN THE USE OF GRATING INTERFEROMETERS AND THE DIFFRACTION OF MATTER WAVES

Wave-front division to produce a closed-circuit

SI interferometer has been accomplished by a number αf processes. A particularly useful means for doing so is to use diffraction. Diffraction by a single slit, however, allows a low throughput if large angle deflection is to be obtained. A high throughput is also desirable to allow a

56 reasonable signal level. A far more efficient means for such deflection that is familiar in physical optics is to use a diffraction grating. Since a diffraction grating presents a large frontal area tα the incident beam, its throughput is much higher than that of a single narrow slit

31 with the same deflection.

Weinberg et al. CJ. Sci. Instr. 36, pSS7, 1959) have described symmetric and asymmetric con igurations for a closed-circuit optical interferometer . Cthat demonstrates 36 interference of light) that uses, four diffraction gratings. In these cαπ iguratiαns the first grating causes the initial wave-front division, while the last causes the

B

- wave-front recαmb i nation and/or magnifies the fringe pattern. The middle two gratings Ccommαnly extensions of the same single grating) perform a path redirection so that the separated paths converge on the plane of the fourth grating. An important feature of these interferometer 6 geometry configurations noted by previous workers is their lack αf sensitivity to physical displacements of the gratings Ce.g. those due to vibrations).

Marton et al. CPhys. Rev. 90, p490, 1953; Rev. Sci.

11 Instr. 25, pl099, 1954) and Simpson (. ibid. ϊ used the asymmetric geometry αf Weinberg et al. and Bragg diffraction Cin transmission) by crystalline foils to produce a matter-wave interferometer for electrons. Bonse and Hart CAppl. Phys. Lett. 6, pl55, 1965) employed a

16 similar geometry and Bragg diffraction Cin transmission) by pure silicon crystals to produce a matter-wave interferometer for neutrons. The demonstrations by Colella et al. and Werner et al. cited above used the neutron interferometer of Bonse and Hart.

SI

Diffraction of the matter waves associated with neutral potassium atoms by a single slit has been demonstrated by Leavitt and Bills CA er. J. Phys. 37, p905, 1969) . Diffraction of the matter waves associated with

S6 neutral sodium atoms by near-resonant standing-wave laser light has been observed by Gould et al. CPhys. Rev. Lett. 56, pBS7, -19Θ6) . In their experiment, significant usable intensity is produced in eighth and higher order diffraction.

31

D. PRIOR ART IN SLOWING AND COOLING ATOMIC BEAMS

Two different methods to generate nearly mαnσ-energetic and, more importantly, slow atomic beams have recently been demonstrated. Schwartschild CPhysics

36 Today 3Θ, pl7, 1966) and Wineland and Itano CPhysics Today 40, p34, 19B7) discuss such techniques. Presumably, slow, cool molecular beams may be produced by similar means.

I Prodan et al. CPhys. Rev. Lett. 49, pll49, 19BS; see also Prodan et al. Phys. Rev. Lett. 54, p99S, 19B5; and Phillips and Metcalf Phys. Rev. Lett. 48, p596, 19BS) have described a technique to produce a temporally continuous beam. It involves the use of a tapered magnetic solenoid to

6 continuously Zee an shift the optical resonance wavelength αf the beam as it is slowed and coaled by a counter-propagating laser beam whose wavelength is near that optical resonance. Ertmer et al. CPhys. Rev. Lett. 54, p996, 19B5; see also Chu et al. Phys. Rev. Lett. 57, p314,

II 19B6) have described an alternative technique that produces a temporally pulsed beam. It uses a pulsed laser whose wavelength is swept Cchirped) during the pulse to maintain resonance as the atoms are being slowed and cooled.

16 The above techniques for slowing atomic beams also have the feature that they also cool the beam Cnarrow its velocity spread) without a severe reduction of its intensity Cflux per unit velocity interval). Mechanical velocity selectors Ce.g. those comprised of rapidly

51 rotating toothed disks or grooved wheels), although applicable here, have the undesirable feature that they severely diminish this intensity.

III. DISCLOSURE

S6

A. OBJECTS OF THE INVENTION

It is an object αf the invention tα provide practical matter-wave interferometers in a variety of con igurations that employ neutral atoms and/or molecules.

31

It is another object of the invention to provide practical matter-wave interferometers that employ neutral atoms and/or molecules, and that measure rotation rate.

36 It is another object of . the invention to provide practical matter-wave interferometers that employ neutral atoms and/or molecules, and that measure acceleration plus

gravity and/or acceleration plus gravity gradients.

It is another abject af the invention ta provide practical matter-wave interferometers that measure acceleration plus gravity and/or acceleration gradients, while simultaneously, independently measuring rotation rate.

It is yet another object of the invention to provide practical matter-wave interferometers that measure changes in their orientation, velocity and position.

It is yet another object αf the invention tα provide practical matter-wave interferometers that employ high-mass and/or low-velocity neutral atoms and/or molecules.

It is a further object of the invention to provide practical matter-wave interferometers in which the deflection of the matter-wave paths is by diffraction by a slit αr slits in a solid material.

It is a further object of the invention to provide practical matter-wave interferometers in which the deflection of the matter-wave paths is by diffraction by slits in a solid material, arranged so that they farm a grating in one direction and a focusing grating in an orthogonal direction.

It is a further object αf the invention to provide practical matter-wave interferometers in which the deflection αf the matter-wave paths is by diffraction by apertures in a solid material, arranged so that they farm concentric, annular slits, including annuli that are circular or elliptical.

It is a further object of . the invention to provide practical matter-wave interferometers in which the deflection αf the matter-wave paths is by diffraction by

I apertures in a sheet of solid material, arranged so that propagation paths through an aperture of the sheet are an integral number of deBroglie wavelengths different from propagation paths through a different aperture.

6 It is a further object αf the invention to provide practical matter-wave interferometers that employ neutral atoms aπd/αr molecules in which the deflection αf the matter-wave paths is due to the electric-dipole-induced-image-electric-dipαle interaction

II between an atom and a conducting surface and/or the permanent-electric- dipole-image-dipole interaction between a polar molecule and a conducting surface.

It is a further object αf the invention to provide 16 practic a 1 matter-wave interferometers in which the deflection of the matter-wave paths is due to their interaction with an electromagnetic wave or waves.

It is a further object αf the invention to provide a SI practical matter-wave interferometer in which the deflection αf the paths αf the matter waves is due tα their interaction with an electromagnetic wave or waves, that is insensitive tα positional displacements of its components from each other, including displacements due to instrument SB vibration.

It is a further object αf the invention to provide a practical matter-wave interferometer in which the deflection αf the paths of the matter waves is due to their 31 interaction with an electromagnetic wave or waves, and that focuses the paths when a spread αf matter-wave beam energies is present.

It is another object of the invention to provide a

36 practical means for measuring the interference fringe pattern produced in a matter-wave interferometer by employing the interaction of a standing matter-wave fringe

IS

I pattern in the superposition region of an interferometer and a standing electromagnetic wave whose wavelength nearly matches that of the standing matter-wave fringe pattern, and by measuring the flux of radiations emitted by this interaction. 6

It is yet another object of the invention to provide practical matter-wave interferometers to measure both rotation, and acceleration plus gravity simultaneously and to distinguish between them, and that compensate for and

II approximately cancel the beam deflection due tα rotation and/or acceleration plus gravity through the application of external deflecting potentials and/or through mounting the interferometer system on gimbals.

16 It is yet another object of the invention to provide practical matter-wave interferometers tα measure both rotation, and acceleration plus gravity simultaneously and to distinguish between them, and that compensate far and approximately cancel the beam deflection due to rotation

SI and/or acceleration plus gravity through the application αf external deflecting potentials and/or through mounting the interferometer system on gimbals, wherein the applied potentials and/or gimbals are controlled by a feedback system that maintains null interferometer fringe shifts,

S6 and where! n the output signal is derived Cat least partially) from the error signal of this feedback system.

It is yet another object αf this invention to provide practical matter-wave interferometers for use as inertial

31 sensors, wherein interferometer geometry is measured and/or stabilized by the use αf X-ray interferometry along or near the matter-wave paths.

It is yet another object of this invention tα provide

36 a practical matter-wave interferometer far use as an inertial sensor, wherein the interferometer geometry is measured and/or stabilized by the use αf an optical

interferometer.

It is another object of this invention to provide an apparatus that can remotely measure the distribution of mass within an inaccessible volume, including portions of the earth itself.

It is yet a further object of this invention to provide an apparatus for locating underground natural resources such as petroleum and minerals, that can be employed above, on, or below the earth's surface.

Other objects, purposes and characteristic features will become clear in the following description of the invention.

B. SUMMARY OF THE INVENTION

The invention is a practical matter-wave interferometer or set of interferometers that provides a high sensitivity inertial sensor. It can assume a variety of con igurations, and employs the quantum-mechanical matter waves associated with the propagation of neutral atoms and/or molecules. As an inertial sensor, it can measure rotation rate, acceleration plus gravity, or both simultaneously and distinguishably. Correspondingly, the output signals from the interferometers can be used to determine position, velocity and orientation. In a particular class of configurations, it can measure gravitational gradients and/or rotation axis position and orientation. Furthermore, the use of the invention is not limited to the domain of an inertial sensor, but can sense other influences to the matter waves including a variety of electromagnetic interactions of atoms and molecules as well as many other fundamental physical interactions such as the newly sought composition-dependent fifth-force.

The matter-wave path geometry is configured so that the paths enclose a finite area and/or are displaced from

each other in position. The path positional displacement makes it sensitive to gravitation and acceleration, while the enclosure αf a finite area makes it also sensitive to rotation. The class of path configurations useful for measuring gravitational gradients are generalizations αf a basic figure-eight geometry. They consist αf two Car more) area enclosing loops Cand/αr pαsitionally displaced path-pair segments) sequentially cascaded with each such enclosure Cand/or displaced path-pair segment) displaced from the position αf the next, and with each such enclosure Cand/αr segment) circuited in the apposite sense Cclackwise or counter-clockwise) of the next.

The matter-wave path deflections necessary to achieve these geometries are produced by a variety of means. These include diffraction αf the matter waves by one or more slits in solid materials, deflection by the electric-dipole induced image electric-dipole interaction between an atom and a conducting surface, deflection by the permanent electric- dipole image-dipole interaction between a polar molecule and a conducting surface, deflection by the interaction between a propagating particle and electromagnetic fields and/or waves, by Bragg reflection from a crystal surface, and deflection by various other applied potentials.

The invention is configured in a variety of ways. A particular class of configurations renders it insensitive to positional displacements αf its components from each other, including displacements due to instrument vibration. Another class allows it to focus the paths when a spread of matter-wave beam energies is present, and/or tα select a narrow range of matter-wave beam energies.

An additional feature of some configurations of the invention is a method for determining the phase of a standing matter-wave interference fringe pattern produced in the interferometer superposition region. These

configurations employ the interaction of the standing matter-wave pattern with a grating Car with a standing electromagnetic wave that acts as a grating) whose spatial periodicity Cwavelength) is nearly matched with that αf the standing matter-wave fringe pattern, and then image and detect the resulting flux αf emitted interaction products.

Another feature of the invention is its ability to compensate for matter-wave path deflections that are due to inertial effects. It employs a variety of means. One method is to rotatiαπally mount each interferometer on gimbals. Another is to apply additional potentials that deflect, and/or retard, aπd/αr accelerate the matter-wave propagation. The applied potentials and/or gimbals can then be controlled by a feedback system that maintains null interferometer fringe shifts. The output signals for the system are then derived from the uncancelled phase shift and from the error signal of this feedback system.

Matter-wave path geometry is stabilized Cor otherwise compensated) within the invention by a variety of means.

One such means is the use of X-ray interferometry along or near the matter-wave paths. In such a case the X-ray wavelength approximately matches that of the matter wave.

Another means for geometry stabilization is to use optical wave interferometry. The sense and direction of changes in the interference pattern that are due to inertial effects are monitored by the insertion of additional matter-wave phase delays. These delays are produced by the application of additional potentials. Moreover, these additional phase delays can also be used as another monitor of matter-wave path geometry.

When interferometers whose slits have a rectangular geometry are used with each one producing only one result and propagating atoms with a single mass and energy, then six interferometers are needed to measure simultaneously the three components of the rotation vector plus the three

ID

components of the acceleration plus gravity vector. If more than one mass and/or energy is propagated through each interferometer, then the number of interferometers needed tα accomplish the same task can be reduced tα three, since each interferometer can produce two results. Moreover, axi-symmetric configurations for the invention may be used tα reduce the required number even further, since an interferometer in such a configuration can provide again twice as many simultaneous results for measurements related to two simultaneous orthogonal axes. An important class of applications for gravity gradiometers requires απly one interferometer in an axi-symmetric configuration.

Focusing αf the atomic beams and matter-wave propagation paths is another important feature of the invention. The geometries αf many of the configurations of the invention allow focusing a spread of beam energies. In addition, various geometries for the invention allow additional geometrical focusing through the use αf principles well known in the field of physical optics, herein ad a pted to the new and unfamiliar area αf neutral-atαm propagation.

The invention has applications in any area traditionally used for inertial and gravity sensors, such as navigation, geodesy, etc. In addition its unique features involving quantum-mechanical matter-wave interference permit additional applications such as measuring an electric current. Another important class of applications is further created via the extreme sensitivity of the invention as an inertial and gravity sensor to areas where existing sensors lack sufficient sensitivity tα be useful. One of these areas is the application to mass tomography, wherein the mass distribution αf an inaccessible volume is measured. Industrial inspection, and petroleum exploration are then facilitated by use of the invention.

IY. BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a diagram of a simple interferometer for neutral atom and/or molecule matter waves.

Figure 5 shows three interferometer orientations that may be employed in a system of six interferometers that simultaneously sense rotation and acceleration plus gravity.

Figure 3 is a diagram of a simple interferometer for neutral atom and/or molecule matter waves in which the deflection of the matter-wave paths is enhanced by interactions between a propagating particle and its electromagnetic image inside a central conducting barrier.

Figure 4a is a diagram of a simple laterally asymmetric longitudinally symmetric grating interferometer for neutral atom matter waves.

Figure 4b is a diagram of a simple laterally and longitudinally symmetric grating interferometer for neutral atom matter waves.

Figure 4c is a diagram of a simple laterally and longitudina 1 ly asymmetric grating interferometer for neutral atom matter waves.

Figure 4d is a diagram of a simple laterally symmetric but longitudinally asymmetric grating interferometer for neutral atom matter waves.

Figure 4e is a diagram of a simple figure-eight path laterally asymmetric grating interferometer far neutral atom matter waves, useful for sensing gravitational gradients.

Figure 4f is a diagram of a simple figure-eight path

IB

I laterally symmetric grating interferometer for neutral atom matter waves, useful for sensing gravitational gradients.

Figure 5 shαws a two-slit interferometer for neutral atαm aπd/αr molecule matter-waves with the inclusion of a 6 differential phase shifter in the lower path and a fringe mask in front of the detector screen.

Figures 6a and 6b are plan and side views of an embodiment of the invention that uses the pulsed atomic

II beam slowing technique, path deflection by diffraction by slits in a solid material, and X-ray geometry stabilization. This set of components resides inside the coil set shown in Figures 9a and 9b.

16 Figure 7a is the plan view of an embodiment of the invention that uses the continuous atomic beam slowing technique, path deflection by diffraction by electromagnetic standing waves, and geometry stabilization by an X-ray interferometer system. Most of its components

51 reside inside a modification αf the coil set shown in Figures 9a and 9b.

Figure 7b is a perspective view of the differential phase shifter used in Figure 7a. Electric current flows in S6 and out of the conducting ribbons through the cylindrical wires connected tα their ends.

Figure Ba is a plan view of an embodiment of the invention that uses the continuous atomic beam slowing

31 technique, path deflection by Bragg reflection an crystal faces. Its geometry is stabilized by X-ray interferometry Ccomponents not shown) in a manner similar to that of the embodiment αf Figures 7a and b. Most αf its components reside inside the coil set shown in the diagram of Figure

36 10.

Figure Bb is a plan view of an alternative path and

I crystal configuration tα that αf Figure Ba. It is used for measuring gravitational gradients. Most of its components reside inside the coil set shown in the diagram αf Figure 10.

6 Figures 9a and 9b show magnetic field coil sets used with the embodiments of Figures 6a, 6b and 7a. The windings shown in Figure 9b may be placed either inside or outside αf the longitudinal current carrying bars 131 - 145 shown in Figure 9a. When these coils are used with the embodiment

II of Figure 7a, the windings of the solenoid coil are displaced slightly to allow passage of the atomic and laser beams between them.

Figure 10 shαws an alternative magnetic field coil set 16 that is used with the embodiments of the diagrams of Figures Ba, and Bb. Tα improve clarity, solenoid 150 is not shown.

Figure 11a shows a combined collimator and grating

51 that may be used tα combine gratings 16, SO, Gl and GB with their associated collimating slits onto a common plane in embodiments that utilize the geometries of Figures 4a through 4f. Its use reduces the number of sheets containing slits, through which the matter waves must pass. In the

56 embodiment of Figures 6a,b it may be used in place of slit 11 and additionally inserted immediately ahead of hot wires 21 to provide a fringe mask, thereby allowing that embodiment to utilize geometries similar to those of Figures 4a-d.

31

Figure lib shows a combined collimator and grating that may be used to combine gratings IB, G5, G3, G4, and G5 with their associated collimating slits onto a common plane in embodiments that utilize the geometries αf Figures 4a

36 through 4f. Its use reduces tha number of sheets containing slits, through which the matter waves must pass. In the embodiment of Figures 6a,b it may be used in place of slits

50

17 and 19, thereby allowing that embodiment to utilize geometries similar to those αf Figures 4a-d.

Figure lie shαws an alternative slit arrangement to that αf Figure lib that utilizes Fresnel optics to achieve focusing in a direction parallel tα the slit long direction.

Figure lid shαws an axi-symmetric slit configuration for an axi-symmetric interferometer that can be used in place αf the configuration αf Figure 11a.

Figure lie shαws one quadrant of an axi-symmetric slit configuration that can be used in an axi-symmetric interferometer in place αf the configurations of Figures lib and lie. The full slit configuration has slits that approximate circular rings, broken by radial structural features.

Figure llf shαws an axi-symmetric slit configuration utilizing Fresnel optics that can be used to generate a parallel input atomic beam for an interferometer. This configuration includes a gradation αf the slit widths and spacings.

Figure llg shows a coaxial elliptical slit configuration utilizing Fresnel optics that can be used to generate a parallel input atomic beam for an interferometer. This configuration also includes a gradation αf the slit widths and spacings.

Figure 15a shows an embodiment αf the invention that is suitable for use in petroleum exploration when lowered into a bore hole. It consists of two orthogonally oriented, gradiometer-cαnfigured interferometers, whose axes are each parallel to the axis of the bore hole.

Figure 12b shows an alternative embodiment to that of

I Figure lδa, consisting of a single gradiometer-cαnfigured interferometer. It utilizes the axi-symmetric gratings of Figures lid and lie.

Configurations involving interchange aπd/αr B substitution of components from those indicated in these Figures provide additional preferred embodiments.

V. BEST MODES FOR CARRYING OUT THE INVENTION

II A. PRINCIPLES OF OPERATION OF THE INVENTION.

1. A SIMPLE MATTER-WAVE INTERFEROMETER ARRANGEMENT.

A simple interferometer arrangement for neutral atom matter-waves is depicted in Figure 1. Cits geometry is

16 similar to that of the classic Young's double slit experiment for light.) Atoms of mass m are emitted by source Ξ, and are collimated by narrow slit SO. Source 5 may be, for example, a simple oven. From slit SO, the matter waves associated with the atoms propagate via two

51 simultaneous paths PI and Pδ through narrow slits SI and SS where they diffract and/or are deflected by various applied potentials, and thence to a detection screen 4, where the wave paths superpose after having thus enclosed a finite area A. The flux αf atoms impinging on the screen 4 is then

56 detected at various locations on the screen in such a way that the interference fringe pattern thus formed via the different lengths along the two paths is measured. The fringe shift caused by any path phase differences is measured by an array of detectors comprising screen 4 that

31 measure the image of the interference fringe pattern.

5. MEASURING ROTATIONS.

First assume that the above arrangement is rotating about an axis perpendicular to the plane formed by the two

36 paths and located at the center, αf the enclosed area. A different choice for the rotation axis will introduce centrifugal accelerations not equal for both paths. That

S3

case will be discussed in a subsequent Section.) If one views the atoms as propagating in an inertial reference frame, then the apparatus is rotating relative to this reference frame. If the rotation is in a clockwise sense, then the distance along the upper path to the detectors will be lengthened relative to that along the lower path, since the slits and detectors will move during the propagation from the source SO to the detectors. Thus, the detectors will sense a phase shift due to the rotation of the apparatus.

Tα calculate this phase shift, one must employ quantum mechanics and consider the matter waves as propagating in a rotating reference frame and include the effects of Carious and centrifugal potentials acting upon them during their propagation. The calculation is simplified by use of the WKB approximation.

If p is a unit vector perpendicular to the plane αf the paths, A is their enclosed area, ft Cradiaπs) is the phase shift between the two paths due tα rotation, then the component of the rotation rate vector, Ω, Cradians per second) in the direction p is given by

ft h Ω . p - , CD

4 π m A

where h is Planck's constant. The sensitivity of the interferometer to rotation can be increased by allowing multiple circuits about the enclosed area, by increasing the enclosed area, or by increasing m, the mass αf the propagating particles.

This simple interferometer can thus measure rotation rates about an axis perpendicular to its plane. An instrument composed of three interferometers, each sensing a different component of Ω can thus be employed to measure all three components of the rotation rate vector, Ω, of the

I instrument as a function of time. Integrating Ω with respect to time Caccounting far the lack of commutativity of successive rotations), one can then obtain the time-dependent orientation αf the interferometer.

6 An analogous arrangement in which the propagating waves are light is far less sensitive to rotation than is the one described above using matter waves. Inverting Eq.Cl) for matter waves, the phase shift in terms αf the rotation rate and area are given by

4 rr m A CΩ • p)

II /?Cm>0) - ,

whereas the analogous relation for the interferometer using light Cor other electromagnetic radiation) is

4 n A CΩ • p) /SClight) - — λ c

16 where λ is the wavelength of the light and c is the speed of light. Far the same areas, the ratio αf the sensitivities is then mλc/h. For example, taking m equal to the mass of a Hg 202 atom and λ equal to 63SB A f, i.e. the wavelength of a helium-neon laser, the ratio of the

SI sensitivities is then roughly 10 ¹¹ . Even though it is straightforward tα allow the light tα traverse many circuits αf the enclosed area, thereby increasing the area of an optical interferometer tα many times that achievable with a matter-wave interferometer, this ratio is so large

56 that it is exceedingly difficult for an optical interferometer to approach that of a matter-wave interferometer tα rotation.

3. MEASURING ACCELERATIONS. 31 Next, assume that the whole arrangement is accelerating and/αr under the influence of gravity. If one considers the interferometer to be in an acceleration free

54

reference frame with an equivalent pure gravitational field acting upon it, then the atoms propagating in it will sense the effective gravitational potential. Since the paths are displaced from each other in this potential, atoms propagating through slit SI will sample a different gravitational potential from those through slit SS. As a result, each path will experience a different phase shift.

The net phase shift between the two paths may be calculated by employing quantum mechanics and using the appropriate gravitational potential along the paths. The use of the WKB approximation again simplifies the calculation. So doing, one finds the component of the acceleration plus gravity vector, a+g, in the direction d in terms of the resulting phase shift, , to be given by

TT m L y

where d is a unit vector in the plane of the paths, perpendicular to the line between the source and detector, L is the path length from source to slit and from slit to detector, y is one half the spacing between the slits, and E is the particles' kinetic energy. CFαr simplicity, all four diagonal path lengths have been taken to be equal.) Thus the interferometer will sense a phase shift due to the net real acceleration of the apparatus plus the equivalent acceleration due tα gravity. If the interferometer is neither rotating nor in a gravitational field Car in a known gravitational field whose influence can be subtracted), then the first integral with respect to time αf Eq.CS) yields the interferometer's velocity component in the direction d, while the second integral yields the position component in that direction.

An analogous configuration ^" . n which the propagating waves are light is far less sensitive tα acceleration plus

gravity than is the one described above using matter waves. Inverting Eq.CS) for matter waves, the phase shift in terms αf the rotation rate and area are given by

i. s π m L y Ca + g) o»Cm>0)

E

" / B whereas the analogous relation for an interferometer using light is

4 n L y |Ca + g) • d| αClight) - λ c ²

where λ is the wavelength of the light and c is the speed of light. For the same areas, the ratio of the sensitivities is then h v

where v is the velocity of the atoms. If one takes m equal to the mass of a Na atom, v equal to 50 m/sec Ccomparable to that produced easily with sodium atoms in laser coaling and slowing experiments), and λ equal to the wavelength of a He-Ne laser, the ratio of the sensitivities is then roughly 1.4 • 10 . Even though it is straightforward to allow the light paths, once separated, tα fold back and forth many times, the sensitivity ratio is so large that it is exceedingly difficult for an optical interferometer to ap p roach that of a matter-wave interferometer to acceleration plus gravity.

4. SIMULTANEOUSLY MEASURING ROTATION AND ACCELERATION PLUS GRAVITY When rotation and acceleration plus gravity are present simultaneously, then the interferometer arrangements described above will give phase shifts that are due tα bath causes. Far an '--arbitrary rotation axis, there will be a phase shift contribution from the

centrifugal force proportional to £ when the center of rotation is not at the center αf the enclosed area. CThis contribution was temporarily neglected in the discussion of rotation above.) If the center αf rotation is remote from the interferometer, the centrifugal force may be approximated as a simple linear acceleration. If not, then additional phase shift terms of second order Cand perhaps higher order terms due tα other effects) will contribute tα the net phase shift and the analysis becomes more complicated Cbut still quite tractable) .

The higher order phase shift contributions will involve products of the effective acceleration and rotation rate, each "taken to various powers. Only the first order analysis will be described here, but this simplification to the description αf the invention does not indicate a limit tα the capabilities αf the invention.

Consider an apparatus composed of six interferometers, labeled, 1-6, and denote the associated p and d vectors, masses, areas, dimensions and energies by corresponding indices. Interferometers 1-6 employ particles with masses m -in and energies E-E _^ respectively, but with either m different from m or E different from E . Similar restrictions shall also apply to 2 and E2„ relative to rnS and E . and to πi and E _β relative to in and E _^ . respectively. Next, let e , e and e represent three unit vectors specifying the coordinate system in the apparatus reference frame. Further, configure the interferometers 1-3 so that one αf each of the three d vectors is along each of these axes, and one of each of the p vectors is also along each αf these axes. Also configure interferometers 4-6 in a similar fashion. For example, let us take p -p -d -d -e , p 2-p5-d1-d4-βy,' pβ-pl-d2-d5-•z,' as is shown in Fig-ure 5.

Obviously, there is more than one way to do this, and any choice will suffice. Other configurations are also possible with the unit vectors β , β and β not orthogonal, as long

I as they not all lie in the same plane. Then, the phase shifts γ through γ for the six interferometers will be given by r _± " C _± Ω _χ + D _± Ca+g) _y + QCΩ, Ca+ ^.m^ E ₄ _ + S^E^m^ ,

^ ₂ " ^C ₂ ^Ω _y ^{+ D} ₂ ^Ca+9:) - ^{+ Q} CO.C» ⁺ fl5 _a ,m _β> E ₂ 3 ⁺ S ₂ CE ₂ ,m ₂ ⁾ , -

6 γ ₃ - C ₉ Ω _β + a+g) _χ ⁺ OCΩ, Ca+g) _χl m _g , E^ + S ₉ CE ₃ ,m _a ) , C3)

^r * " ^C Λ ^{+ D} _ _t ^Ca+ 9 ³ _y ⁺ OCΩ, Ca ⁺ g ⁾ _y ,m _-t ,E + S^CE^rn^ ⁾

r _s ' C _s O _y + D _β Ca+g) _ι + OCΩ, Ca+g) _ι ,m _s ,E _s D + S _β CE _s ,m _s ⁾ ,

^ - ^C A ^{+ D} _« - ^c » ⁺ «> _« ⁺ OCΩ,Ca ₊ g ⁾ _χ ,m _<J ,E _<$ D + S^ E^ ^ , where Ω Ω , and Ω are the x,y and z components of the

II rotation rate Cangular velocity) vector Ω and Ca+g) ,

Ca+g ⁾ and Ca+g) are the x,y and z components of the acceleration plus gravity vector Ca+g). The coefficients C. and D. are given by

¹ 4 π m. A.

16 C _. __-—-- ,' and

The function OCΩ, Ca+g) ,m _k ,E _k /) represents the small higher order terms, while the functions S.CE.,m.) represent the 51 inserted phase delay. The contribution to this function due to centrifugal forces is given by the line integral around the full two-path circuit

1. s ^m k r ^* 2

OCΩ. , ,'Ek, )-•ntri..f,. - /—= . φT CΩ x r ^• ea) ds

where β is a unit vector ^h paral?lel tα the path at a point 56 along the path, r is the vector, from the center of rotation tα that point, and ds is the differential of path length.

SB

The set of equations C3) can be solved simultaneously to yield the rotation rate vector Ω and the net acceleration plus gravity vector Ca+g) in terms of the six measured phase shifts Y _L through γ©. In applications requiring high accuracy, the centrifugal force and other high order terms may be included. To do so, the radius vector r can be determined iteratively by integrating these equations to determine the position αf the center αf rotation and correcting for the contribution by these terms. An alternative procedure for finding r is tα augment the i n te r ferometer set with matter-wave gradiαmeters Cdescribed below) tα measure r directly. Thus, an interferometer set is capable of independently measuring rotation and acceleration plus gravity simultaneously.

5. LIMITING ATOMIC BEAM-SAG

The above phase-shift calculations have neglected transverse displacements of the paths due tα the effects of rotation and acceleration plus gravity, and have assumed these tα be straight-line trajectories. In the presence of rotational and gravitational Cor the equivalent due tα acceleration) forces an a propagating atomic beam, the beam will be deflected from a straight trajectory to a curved one. Thus, when the particles are freely propagating in vacuum, the paths will be the trajectories of classical particles propagating under the same potentials. Such trajectories will not be straight, but instead curved by these potentials. They will approximate parabolic arcs. The curvature will increase with increasing rotation rate and acceleration plus gravity. At even moderate values αf these, the curvature may be so large as to prevent the beam from ever reaching the detectors. As a result, it is important that this curvature be removed far the construction of any inertial sensor system that is to achieve even a modest dynamic range.

Additional potentials can be applied along the particle trajectories to remove most or all of this

curvature. That is, in order to maintain straight beam trajectories, it is necessary tα apply an external compensating force tα the atoms that cancels the deflecting force. Said deflecting force must compensate both the effects of rotation and αf gravity plus acceleration. The force due to gravity plus acceleration can be compensated by applying a potential gradient in the direction of the net force due to gravity plus acceleration. The farces due ta rotation can be compensated through the use of a gimbal system that maintains a fixed orientation for the interferometer system. They may alsα be compensated through the use αf a velocity dependent force when a variety of atomic momenta are present in the interferometer system. When all atomic momenta present in the system are nearly the same, approximate compensation may be achieved by the application of a force perpendicular to the momenta. In terms αf a quantum-mechanical description of the motion αf the atoms, application of such a force translates into an externally applied potential gradient. For long, thin diamond shaped interferometer path geometries and negligible spread in beam momenta, a potential that increases linearly about a direction perpendicular to the interferometer axis will straighten the trajectories.

A potential gradient that will satisfy the above requirements is available for a limited range of conditions. It consists of a magnetic field with a gradient αf its component that is parallel to the atoms' magnetic moments. Such a field compensates for sag over a narrow range of velocities and for one mass at a time when beam sag due to both rotation and acceleration must both be removed. However, it limits beam sag for a wide range of beam velocities when only the beam sag due to acceleration plus gravity must be compensated. When no rotation is present Ce. g. when the system is mounted on gimbals), such a potential gradient only compensates for sag due to acceleration plus gravity for one mass value at a time, since the magnetic deflection force is independent of a

particle's mass, while its force due to acceleration plus gravity is proportional to its mass.

The applied potential will produce additional phase shifts in the interferometer. However, if the inertial potent i al s are canceled by the externally applied potential, then so will be the phase shifts that are due to them. Thus, an externally applied field that removes the path curvature, alsα produces no net phase shift in the interferometer.

A feedback system that applies a potential that maintains straight trajectories will then apply a potential that keeps the phase shift αf the interferometer null. Correspondingly, the magnitude αf the applied potential necessary to keep the phase shift of the interferometer null is a direct measure of the combination of rotation and acceleration plus gravity that the system seeks to measure. That is, the error signal in such a feedback system provides a direct output signal αf the interferometer.

For systems using polar molecules, electric field gradients will accomplish the same end. Examples of magnetic field geometries with the necessary gradients are given along with the preferred embodiments of the invention. It is recognized, however, that other geometries and potentials exist which will accomplish the same end, and that the scape of the patent is not limited to the examples αf geometries and potentials presented below.

6. DIFFRACTION BY REFLECTION FROM CRYSTAL SURFACES

Classic experiments by Davidson and Germer, by Esterman, Frisch and Stern, and others have demonstrated that electrons, atoms, neutrons, etc. show diffraction phenomena in reflection by the surface of a crystal. This effect is known as Bragg reflection. Applicant has devised closed-circuit interferometer geometries that employ Bragg reflection of neutral atoms from crystal faces, which has

I never been done, here-to-fare. Examples αf geometries that are sensitive to inertial effects are presented below. It is recognized, however, that other geometries exist which will accomplish the same end, and that the scope of the patent is not limited to the examples of geometry presented

6 below.

While the above classic experiments generally employed naturally grown cleaved crystals such as LiF Cor other chemical salts), applicant proposes a preferred use of

II artificially grown large crystals such as those grown from purified silicon.

A noteworthy distinction between applicant's invention and that by Altshuler and Frantz is that applicant's

16 crystal face beam reflectors also function simultaneously as beam-splitters by employing simultaneous diffraction into more than one distinct order. The mode of operation αf the crystal faces employed by Altshuler and Frantz exhibited only diffractive reflection at a single angle,

51 and thus is ineffectual as a beam splitter.

7. DEFLECTION BY IMAGE FORCES

Figure 3 is a diagram of an interferometer, similar to that of Figure 1, in which the thin sheet between slits SI

S6 and SS is replaced by a suitably shaped Cfαr example cylindrical) conducting barrier B. The electric-dipole-induced- electric-dipole force between a passing atom and its electrical image farmed inside the barrier will produce a deflecting force that will direct

31 the ato ms o nto paths that converge in the beam recombination region. The existence of such forces Cakin to van der Waal's forces) has been demonstrated by Raskin and Kusch CPhys. Rev. 179, p71S, 19B9) . As a result, a wider spacing between slits SI and SS can be employed than that

36 which can be used when the deflection of the atomic-beam paths at slits 51 and 55 is by diffraction alone. A wider spacing, in turn, translates into greater enclosed area and

- greater path displacement, and hence into higher sensitivity.

It is evident that deflections of polar molecules Ci.e. those with permanent electric dipαle moments) will be

6 obtained alsα w hen such are in the proximity of a conducting surface. In this case the interaction is between the permanent electric dipole moment of the molecule and its image inside the surface. The configuration for the usage of this interaction to obtain large beam deflections

11 when polar molecules are the propagating species is similar tα that αf the dipαle-induced-dipole interaction discussed above.

B. DIFFRACTION BY ELECTROMAGNETIC GRATINGS

IB A diffraction grating for neutral atoms Cand molecules) can be formed from a standing wave electromagnetic beam Csuch as that produced in the cavity αf a laser) that is nearly resonant with an atomic transition of the atomic species. Such an electromagnetic

51 beam passing transversely through the atomic beam will interact with the atoms more strongly at its field maxima than at its minima. The interaction will scatter atoms Cor otherwise shift their quantum-mechanical phases) on a spatially periodic basis along the path of the

SB electromagnetic beam. As a result, the electromagnetic beam will act as a diffraction grating. A suitable shape for the electromagnetic beam is that αf a ribbon.

If the incident beam of atoms impinges diagonally on 31 the standing- wave electromagnetic beam, then the frequency αf a traveling-wave decomposition of the standing wave will be Dαppler shifted commensurate with the velocity component of the atoms along the traveling wave. Different angles of incidence of the electromagnetic beam with the atomic beam 36 will produce different Doppler shifts.

In cases where the Dαppler shift is large relative to

I the resonance width, then for only a narrow range of such angles will the atomic transition's absorption spectral width overlap that of the electromagnetic wave's spectral width. Thus, atoms in only a narrow range of incidence angles will interact with the laser beam, i.e. those far

6 which the natural atomic resonance overlaps the laser frequency. Two such resonances will occur symmetrically located at equal angles either side αf a perpendicular to the standing electromagnetic wave. The angles for such a resonance will depend upon the beam's velocity. If atomic

II beam cαllimatiσn limits the incidence angles, then the grating will act as a velocity selector alsα. If two standing wave electromagnetic beams are simultaneously superposed at a small angle with respect to each other, then resonances through the same atomic beam collimator

16 will occur at two different velocity groups. The two velocity groups propagating along the same path can be used by the interferometer cell to distinguish rotation from acceleration plus gravit .

SI In cases in which the natural resonance width is comparable to αr less than the Dαppler shift due to the atomic beam velocity, Doppler velocity selection will not occur. Nonetheless, velocity selection by the natural action of a grating will still occur. In such cases the

56 transmitted velocity spread of the gratings can be limited by suitably placed slits.

A standing-wave electromagnetic beam can be produced by reflecting a laser beam back upon itself by a mirror.

31 Another means for producing such a beam is provided by the standing-wave naturally produced inside the resonant cavity of a laser.

9. CLOSED-CIRCUIT MATTER-WAVE INTERFEROMETERS USING 36 GRATINGS

Applicant has shown that it is perfectly consistent with generally accepted principles of modern physics tα

construct a closed-circuit matter-wave interferometer that uses diffraction gratings, although such has never been done here-tα-fore. Either gratings comprised αf a series αf slits in a solid material αr near resonant electromagnetic standing-waves will form a suitable grating for neutral atom matter waves. CThe two slit case depicted in Figure 1 is the simplest example αf a multi-slit solid material grating) . The gratings may be used in a neutral atom matter-wave interferometer for wave- front division, redirection and recombination. Gratings with a narrow spatial periodicity facilitate the deflection αf atomic matter waves tα large angles. Such gratings will achieve even larger deflections by working in a high diffraction order. Large deflections, in turn provide high sensitivity when the interferometer is employed as an inertial sensor.

Geometries, analogous to those by Weinberg et al. , are suitable for such an interferometer. Applicant has devised generalizations of their geometries that alsα are employed. Both symmetric and asymmetric geometries, and even figure-eight geometries Cfαr use as a gradiometer), are used. The diffraction gratings in a neutral-atom closed circuit interferometer are configured to accept simultaneously either various integral multiples of velocity Caπd/or wavelength) in different diffraction orders along the same paths, αr to accept different velocities in the same or different orders along different paths, depending on the symmetry properties chosen for the path geometry.

Weinberg et al. discussed both laterally symmetric and asymmetric, but only longitudinally symmetric geometries. However, virtually all subsequent applications of their work by others involved the use αf laterally asymmetric, longitudinally symmetric geometries. In particular, all closed circui t matter wave interferometers that use diffraction for path deflection built here-to-fαre, including the electron interferometer αf Marton et al. and

I the neutron interferometer αf Bonse and Hart, employ a laterally asymmetric, longitudinally symmetric geometry. Moreover, both αf these applications of Weinberg et al.'s geometry use zerα'th and first order diffraction on the first and last gratings and first order diffraction on the

6 middle gratings Cas did Weinberg et al.) . The limitation to zerα'th and first diffraction orders in prior matter-wave interferometer is due to the fact that such interferometers for electrons and neutrons use Bragg diffraction. In the present case, the above limitation on diffraction orders

II does not apply since planar Ctwo dimensional) gratings are used instead.

Suitable matter-wave path and grating configurations for a neutral atom matter-wave interferometer are shown in

16 Figures 4a - 4f. In these Figures the gratings are comprised either αf slits in a solid material, or of standing electromagnetic waves. Matter waves are emitted by source 5, collimated by slits 10 and detected by detector 6. Additional baffles 15 select grating diffraction orders.

SI In Figures 4a - 4d, the first grating is 16, the last is SO, while the middle two Cshown here as extensions of the same grating, but not necessarily restricted to be so) is IB.

56 Figure 4a is a diagram αf a simple laterally asymmetric, longitudinally symmetric grating interferometer for neutral atom matter waves. When the diffraction at the first grating 16 and last grating 50 is in zero'th and first order for the two paths, and is first order at the

31 middle gratings IS, then the geometry is the same as that employed by Weinberg et al. , by Martαn et al. and by Bonse and Hart. Especially useful cases for large enclosed area neutral atom matter-wave interferometers, however, occur for diffraction at the first grating 16 and last grating 50

36 in zero'th and a high order n for the two paths, and in order n at the middle gratings IB.

Figure 4b is a diagram of a simple laterally and longitudinally symmetric grating interferometer for neutral atom matter waves. When the diffraction order at the first grating 16 and last grating SO is plus or minus one, while it is two at the intermediate gratings IB, then we have the laterally and longitudinally symmetric case discussed by Weinberg et al. Especially useful cases for large enclosed area neutral atom matter-wave interferometers occur for diffraction at the first grating 16 and last grating SO in high order ±n, and in order Sn at the intermediate gratings IB.

Figure 4c is a diagram αf a simple laterally and longitudinally asymmetric grating interferometer for neutral atom matter waves. Figure 4d is a diagram of a simple laterally symmetric but longitudinally asymmetric grating interferometer for neutral atom matter waves.

Figure 4e is a diagram of a simple figure-eight path laterally asymmetric grating interferometer for neutral atom matter waves. Figure 4f is a diagram αf a simple figure-eight path laterally symmetric grating interferometer for neutral atom matter waves. The configurations in Figures 4e and 4f are useful for sensing gravitational gradients.

The chromatic Cwavelength dependent) properties of a neutral-atom matter-wave interferometer formed from a sequence of gratings are quite remarkable. Laterally symmetric cases provide a natural focusing mechanism far the paths onto the superposition region that is independent of the wavelength. Focusing is useful tα provide a high throughput flux when the input atomic beam contains a wide spread of wavelengths. Laterally asymmetric cases provide a dispersive mechanism that facilitates selection αf a narrow band of wavelengths from among those in the input beam.

The geometries depicted in Figures 4a through 4f can

I be simplified and improved by reducing the number of solid sheets with slits Cbaffles) through which matter waves must propagate. For example, in Figure 4b the beam after exiting oven 5 and the collimating slit in the left sheet of collimator 10, must then pass through slits in six more

B sheets before it reaches detector 6, notably the right sheet of collimator 10, grating sheet IB, the left sheet αf collimator 15, grating sheet IS, grating sheet 50, and the right sheet of collimator IS. The effect of a collimating sheet with slits adjacent to each grating is to limit the

II effective illumination and/or number of effective slits in the associated adjacent grating. The same end can be accomplished, however, simply by combining the grating and associated collimator sheets onto a single planar sheet.

IB The slit arrangements αf Figures 11a,b provide examples of adjacent sheets thus combined. For example, in Figure 4b the right sheet αf collimator 10 can be combined with the sheet αf grating 16 to form a sheet with the configuration of Figure 11a, the left sheet of collimator

51 15 can be combined with the sheet of grating IB to form a sheet with the configuration of Figure lib, and the sheet αf grating SO can be combined with the right sheet of collimator 15 to again form a sheet with the con iguration of Figure 11a. So doing, the six aforementioned sheets have

Ξ6 been reduced to three. Similar combinations Cand/or replacements) can be applied to the other con igurations αf Figures 4a-4f.

Another improvement to the geometries of Figures 4a - 31 4f is to provide focusing in a direction parallel to the slits' long direction by applying mathematical principles for wave propagation discovered by Fresnel and frequently applied in the field of physical optics for light and other forms αf electromagnetic radiation. Here, applicant applies 36 this mathematics to the unfamiliar area αf optics for neutral atom propagation through slits in solid sheets. An example of a slit configuration expected to provide

focusing is given in Figure lie.

The aperture configuration of Figure lie is a modification of that of Figure lib, wherein the slit group 570, present in both Figures lib and lie, has been replicated end-to-end and displaced upward, with the slit length for each additional group decreased in length from that of an interior group. This replication then forms the three slit groups S7S, S73, and 574. A similar downward replication farms a similar set αf groups S79. Likewise replications αf slit group 571 form the multiplicity of slit groups 57B.

The displacements and slit lengths associated with these replications is such that the propagation path length from a point on the preceding grating through a given slit to a point an the subsequent grating is lengthened by an integral number of deBroglie wavelengths over a path between the same two points threading an adjacent slit or slit group. With this configuration, paths from outside groups αr outside slits combine in-phase with other paths. In-phase path recombination provides a focusing mechanism tα provide enhanced throughput. Although exactly this process occurs in diffraction of matter waves by a grating, the graded spacing allows adjustment for the finite geometry of the interferometer Cexactly even spacing will apply for an infinitely long device) .

Both the focusing improvement and the above sheet number reduction improvement can be accomplished simultaneously using the slit con igurations of Figures 11a and lie in a modification to the geometry of Figure 4b. This modification is then similar to that described above for reducing the number of baffling sheets using Figures 11a,b. As above, the right sheet of collimator 10 is combined with the sheet αf grating 16 to form the slit configuration 569 of Figure 11a, and the sheet of grating 50 is combined with the right sheet of collimator 15 also

tα form the configuration of Figure 11a. Now, instead of using the slit configuration of Figure 4b for the middle pair αf gratings, the left sheet of collimator 15 and the sheet of grating 18 are replaced by the single sheet slit configuration of Figure lie. The result is increased particle throughput.

A further improvement to the rectangular slit configurations αf Figures 11a,b allows combining two orthogonally oriented interferometers with parallel axes into a single inter erometer. The slit con igurations of Figures lld.e consist αf concentric annular slits cut through a sheet of solid material. The annular slits 580 of Figure lid are approximately evenly spaced from the outer most ring tα the center. In Figure lie, the annular slits 585 are approximately evenly spaced but do not extend to the center. Instead, the central portion 583 is solid. Radial arms 5B1 in both Figures lid and lie provide structure to support inner solid rings. Alternatively, structure not in the plane of the sheet can provide support for these inner portions αf the gratings.

An axi-symmetric interferometer is created using the slit configurations of Figures 11a and 11c by a modification to the geometry of Figure 4b. This modification is again similar to that described above for reducing the number of baffling sheets. The right sheet of collimator 10 is combined with the sheet of grating 16 and replaced by the single sheet slit configuration of Figure lid. The sheet αf grating SO is combined with the right sheet of collimator IS also to form the configuration of Figure lid. For the middle pair αf gratings, the left sheet of collimator 15 and the sheet of grating 18 are replaced by the single sheet slit configuration of Figure lie. It will be seen that with such replacements, any plane containing the axis of such an axi-symmetric interferometer reproduces the two-dimensional slit arrangement geometry of Figures 4b. That is, the two-dimensional geometry

intercepted by this plane still consists of a single set of slits at the first and third sheets and two widely spaced groups αf slits at the middle sheet.

An advantage of the axi-symmetric interferometer geometry thus created is that inertial effects can displace its fringe pattern at the final grating Caπd/αr detector) in both a vertical direction Cas in the plane of the drawing of Figure 4b) as well as in a direction perpendicular to the plane αf the drawing. Similar grating geometry replacements may be applied to the con igurations αf Figures 4d and 4f. Figure lδb shows utilization αf the geometry αf Figure 4f with such replacements.

Applicant's calculations Cusing Fresnel's mathematics) for this axi-symmetric and combined sheet modification to the interferometer of Figure 4b yield the fallowing results. The calculation employs neutral potassium atoms at a velocity 10 meters per second and the spacing between successive grating sheets is R - 1 meter. The deBroglie wavelength of the atoms is about λ s_ 10 Angstroms. The number R F Cthe first Fresnel zone radius for matter waves) is defined equal tα the square root αf the product αf the atomic deBroglie wavelength, λ, and the longitudinal spacing between the first two grating planes R. Far the above parameters we have __ 35 microns.

The first grating has the configuration of Figure lid. A favorable outer radius for it is slightly less than R . This grating may have any number αf circular slits Cincluding only one) with the central point either open αr closed. In the present example all slits have the same spacing R Cperiodicity) and thickness, although in other embodiments it may be favorable to vary the thickness from one slit to the next. The first grating turns an incoming parallel matter-wave beam into a set αf high intensity hollow coaxial conical beams that project from this grating high intensity aπnuli on their intersection with

the plane of the second grating. In addition there is also a central beam Cnot necessarily hollow) projected by this first grating that is blocked by the central solid part 583 of the second grating. The radii of these conical beams at the second grating far beam N is then R_ N. _s_ R • λ / R■. The first conical beam is the most intense. For Rs a_ 5 microns, the radius of this first hollow beam is then R ___ 480 microns Cabout 1/S mm) . The radial thickness of the hollow beams depends inversely on the outer radius αf the first grating. When that radius is αf order R , then the radial thickness αf the hallow beams is also of order R F.

The second grating has the configuration αf Figure lie. A favorable design for it places its slits 58S spanning the radial extent αf the high intensity anπulus created by this first Cmαst intense) hollow beam. If the second grating's slit spacing is the same as that αf the first, then the second will refocus the hollow beam into a pattern consisting αf concentric high intensity rings, centered on the third grating. The third grating again has the slit configuration of Figure lid. This grating then acts as a fringe mask.

A common features of the above configurations for interferometers is that they consist of a sequence of spaced solid sheets with each sheet having at least one aperture through which neutral particles and their associated matter waves pass. Matter-wave interference effects are especially evident when a propagation path appears to bend around a corner. This bending occurs when two αr more paths overlap and interfere. A common feature of at least one such sheet's aperture configuration that in general causes such interference effects to be thus evident is created when there is at least one imaginary straight line segment that passes through a solid portion of that sheet when drawn between two points that both lie within the geometrical plane αf that sheet and that bath lie inside an aperture of that sheet. A multiplicity of

I apertures on the same sheet satisfies this condition, as does any single aperture that is not everywhere outwardly convex, such as an anπulus.

10. DIFFERENTIAL PHASE SHIFTER 6 An alternative configuration tα that αf Figure 1 is depicted in Figure 5. Source S, slits SO, SI and SS perform the same functions as before. An adjustable differential phase shifter 30 has been inserted in one αf the matter-wave paths Pδ. A fringe mask δB is positioned in

II front αf the detector 6. The detector's dimensions span the extent αf the fringe mask. The maxima and minima of the fringes essentially form a transverse standing matter wave across the fringe mask. The fringe mask consists αf a set αf slits Dl-Dn, with a spatial periodicity matching the

16 spatial periodicity of the transverse standing matter wave. It is positioned so that the various fringe maxima all simultaneously coincide with the slit openings for some value of the inserted phase delay. The last grating in the interferometer geometries discussed above essentially forms δl such a mask.

As the inserted differential phase delay is varied, there will be a corresponding sinusoidal variation in the detected flux as a function of the delay. The offset phase

SB αf this sinusoidal variation Cas a function of delay) is a measure of the interferometer phase shift due tα rotation and acceleration plus gravity. The frequency of this variation Cas a function of delay) is related to the atomic-beam effective energy and interferometer cell area,

31 quantities which are needed to determine the C. and D. coefficients described above. If more than one species or energy is passing through the cell simultaneously, then the phase and frequency of the variation as a function αf delay for each species can be determined by a Fourier analysis αf

36 the detector current variation.

In practice, the insertion of an adjustable phase

delay αf one path relative to the other can be accomplished by various means. The beam-sag limiters discussed above perform just such a function. A differential phase shifter has additional useful functions. For example, if the inserted phase is made to rapidly alternate between 0 and 90 degrees and the interferometer phase difference is monitored synchronously with this alternation, then a two channel interferometer is created CO and 90 degree channels respectively). If the rotation rate and/αr acceleration plus gravity change, then the net interferometer phase shift will change. Monitoring both channels then will allow one tα determine the sense of the change Cplus or minus) .

Another method for operation for a system with an adjustable phase delay insertion is to repetitively sweep the delay in time through many radians and monitor the detector response as a function αf the inserted delay. If the sweep rate is rapid with respect to the rate of change αf the phase shift due to changes in rotation rate and/or acceleration plus gravity, then the invention can determine the sense C+ αr -) and magnitude of any change αf the latter from one sweep to the next. Additionally, if the inserted phase delay depends upon the beam energy, then drifts αf that energy can alsα be monitored. Moreover, if the interferometer cell's effective area depends, in turn, upon this effective energy Cas it does if electromagnetic standing-wave gratings are used) then the effective enclosed area Cand path displacement) can likewise be determined.

Another form of differential phase shifter is any device which laterally moves diffracting elements in the system, including moving the fringe mask. If slits αr multi-slit gratings are employed for matter-wave deflection, these can be physically moved in a direction perpendicular to the interferometer axis by an electro-mechanical device such as a piezoelectric element. When standing-wave electromagnetic gratings are employed, the positions αf these can be shifted by an electro-optical

I element. An advantage of this form of phase shifter is that it can respond much more rapidly tα abrupt changes in rotation rate αr changes in acceleration than can the magnetic variety discussed above, which take a particle transit time through the interferometer to act.

6

11. FRINGE-MAGNIFIER

The fringe mask 58 in Figure 5 was specified above to have its slit spacing matched to the transverse spacing of the matter-wave fringes in the superposition region, where

II the maxima and minima αf the fringes form a transverse standing matter wave. In an alternative mode of operation, the fringe mask is configured so that its slit spacing is only approximately matched to but slightly different from that αf the transverse standing matter-wave. For this mode,

16 detector 6 is replaced by a detector array such as detector screen 4 of Figure 1. The dif erence between the periodicities will yield a slow transverse periodic variation of the transmitted intensity across the detector screen Ci.e. a Mαi έ pattern is formed). The result is a

51 highly magnified transverse fringe pattern that can be monitored by ^' an array of detectors spaced much more coarsely than those of detector screen 4 in the configuration αf Figure 1. A small change in slit spacing can be produced by slightly tilting a fringe mask with a 6 slit spacing equal to that of the standing matter-wave.

IS. ELECTROMAGNETIC FRINGE DETECTOR

The last grating in a matter-wave grating interferometer, as discussed above, in addition to farming 1 a fringe mask, can become an integral part αf the detection system when electromagnetic gratings are used. In addition to the scattering of atoms at the maxima of electromagnetic standing waves, a reciprocal resonant scattering αf the electromagnetic waves occurs. This scattered radiation can

36 be imaged onto a detector array for the electromagnetic waves. For example, when the scattered electromagnetic waves have optical wavelengths, then a lens can be used to

I image them onto a detector such as a CCD array or vidicαn tube. The output signal of that detector then provides the needed measurements αf interferometer phase shift.

Alternatively, depending upon the intensity and 6 wavelength of the electromagnetic waves and upon the level structure αf the propagating atoms, particles such as ions and electrons may be produced by the interaction of the electromagnetic wave and the atoms. A suitable means for imaging and detecting the spatial distribution αf the

II emitted particles alsα will allow one to determine the interferometer phase shift.

13. MEASURING GRAVITATIONAL GRADIENTS

Gravitational gradients Cand or the position of the

16 center of rotation, in the presence of rotation) can be measured by the apparatus described above by simply building two interferometers and displacing them from each other in position. However, a simpler more accurate system utilizing the same principles can alsα be built.

SI

Matter-wave interferometers in which the two paths follow a two loop C igure-eight) structure are shown in Figures 4e and 4f. The paths are deflected at six locations Gl - G6 by diffraction gratings. Deflection at Gl performs

56 the initial wave-front division. Deflections at GS - G5 redirect the paths, while deflection at G6 provides wave-front recombination in the superposition region. The paths are composed αf straight line segments and are configured so that the two loops of the figure-eight have

31 equal areas.

Because the circuits about the two loops are oppositely directed, the net area that the matter waves circuit is zero. As a result, the interferometer will be 36 insensitive to rotation, at least to the extent that one can neglect centrifugal acceleration. If the gravitational field acting on one of the loops is slightly different from

I that acting on the other loop, then the phase shifts due to gravity in the two loops will not exactly cancel each other. There will result a phase shift that will be proportional to this difference. Such will be the case when a gravitational gradient is present, and the difference

6 between the gravitational fields acting an the two loops will be the gradient times the effective loop spacing. Thus, a neutral atom matter-wave interferometer with a figure-eight geometry will measure gravitational gradients.

II Since a centrifugal force acts like a gravitational field with a gradient, and since the Coriαlis force produces no phase shift in these configurations because of the interferometers' zero effective area, these configurations will measure the magnitude αf the

16 centrifugal force. Since the rotation rate can simultaneously be determined by an interferometer with non-zero area, the radius vector of the rotation can alsα be determined by a set αf such devices.

1 Interferometers with three αr more loops will correspondingly measure the second derivative of the gravitational field, etc.

14. USE OF GRATINGS FOR FOCUSING 6 Applicant is first to teach the use of gratings consisting αf a multiplicity αf slits in a solid sheet as beam-splitters for matter-wave interferometry. An extension of this invention is to use such gratings as focusing elements also as is done in the field αf physical optics, 1 e.g. the use of a Fresnel zone plate grating for focusing light and microwaves. This component αf applicant's invention can be configured tα form a Fresnel zone plate to act as a lens that focuses the diverging output of the applicant's velocity adapter and provides a more nearly 6 parallel input beam to an interferometer, thus further reducing the spread αf atomic velocity vectors. As such, it acts further as a velocity adapter.

I Such focusing elements are shown in Figures llf and llg. As with the discussion of Figure lie given above, they also rely on the mathematics of Fresnel far wave propagation. Figure llf shows a circular ring structured focusing grating. Figure llg shαws an astigmatic focusing

B grating with elliptical ring shaped slits 585, useful for correcting Car creating) beam astigmatism. In distinction with the annular slits 5B0 of Figure lid, the slits 584 of Figure llf have suitably graded spacings and widths. A propagation path through one annular aperture from a point

II on a preceding focal plane to a point on a subsequent focal plane is approximately an integral number of deBroglie wavelengths longer than a path between the same two points that threads an adjacent ring-shaped slit. Radial arms 581 Cor other structure not necessarily in the plane αf the

16 grating) provide mechanical support for the annular ring structure of Figures llf.g. When the subsequent focal plane is moved to infinity and the preceding plane is at a virtual focal point αf the source, then a roughly parallel output beam is created from a diverging one.

51

15. MASS TOMOGRAPHY WITH A GRAVITATIONAL GRADIOMETER

Tomography is a methodology by which the internal three dimensional structure of an inaccessible volume is determined via a sequence of measurements performed with an

56 apparatus located remotely from the volume. A familiar application that has revolutionized medical radiography is the CAT scan. With it, the three dimensional internal structure of a patient is mapped by passing a sequence of x-ray beams through his body. A computer then uses the

31 x-ray transmission measurements to construct the desired three dimensional image.

Use of tomography is by no means limited to medicine, nor to x-ray transmission measurements. Applicant's

36 invention teaches a new application of tomography. It exploits the weak gravitational attractive force αf all bodies towards each other, and uses this force, along with

4B

I applicant's sensitive gravity gradiometer or accelerometer, to map the mass distribution αf an inaccessible volume. If the gradiometer Cor accelerometer) is placed in a sequence of positions near the volume and measurements αf the resulting gravitational gradient Cor field) are performed, B then, knowing the gradiometer's response to a given mass, it is straight forward to use the results to mathematically reconstruct the mass distribution within the volume. Nondestructive, non-intrusive inspection of inaccessible volumes Csuch as cargo containers) is then facilitated by

II applicant's invention.

An important inaccessible volume needing inspection is the earth itself. A neutral-atom interferometer employing applicant's gradiometer configuration may be transported by

16 a surface vehicle, such as a ship, a submarine αr a truck, an above surface vehicle such as an aircraft, spacecraft or earth orbiting satellite and then may be used to map the distribution of mass in the earth's crust, αr even sense the approach of other vehicles or spacecra t. The motion of

51 the gradiometer facilitates performing a sequence of measurements at different gradiometer positions, which, in turn, allows solution of the tomography problem. In cases wherein the vehicle provides an unsteady platform, vibratiαnal isolation for the device is facilitated by the

56 use of a gradiometer instead of an accelerometer. A properly designed suspension system for the apparatus will then provide a degree αf isolation between it and vehicle vibrations.

31 A sequence of measurements allowing, at least, a partial solution tα the mass tomography problem is afforded by lowering applicant's gradiometer into a hole bored into the earth, such as one bared in anticipation of locating natural resources such as petroleum αr minerals. Figures

36 15a,b show applicant's invention employed in this application. A pair of figure-eight interferometers whose long axes are parallel to the bore hole provides azimuthal

I information concerning the location αf density variations in the local earth surrounding the hole, such as those produced by narrowly missed pockets of gas. An embodiment that is simpler to construct but more cumbersome to operate contains only one gradiometer-coπfigured interferometer,

B and provides azimuthal information by rotating it within the hole about its axis. Another embodiment, shown in Figure lδb, combines the two orthogonal interferometers of Figure lδa into a single axi-symmetric interferometer through the use αf axi-symmetric gratings. A sequence of

II gradient measurements is performed for various positions of the apparatus within the bore hole. The variation αf the gradient signal as a function αf interferometer position within the hole is then analyzed to provide density distribution information about the surrounding nearby

IB earth.

IB. MEASURING AN ELECTRIC CURRENT WITH A NEUTRAL ATOM INTERFEROMETER Magnetic fields and/or their gradients can affect the δl phase difference detected in a matter-wave interferometer, via the interaction of the neutral particle's magnetic moment with the field. When a current passes through a conductor near the propagation paths, it creates a magnetic field whose gradient affects the observed interferometer

56 phase shif t . This effect is exploited in various embodiments of the invention to create a differential phase shifter. It is also straight forward to turn this process around and to use the interferometer to infer the current that generates the field from the observed phase shift.

31 Especially in configurations wherein the current actually threads an interferometer's enclosed area, a very sensitive ammeter is then created.

B. PREFERRED EMBODIMENTS 36 Any number of embodiments of the invention can be produced which employ matter-wave interferometry αf neutral atoms and/or molecules. They can be used far sensing

rotation and acceleration plus gravity, and/or gravitational gradients. Three basic configurations and variants of these are presented here which are illustrative preferred embodiments of the invention, and which encompass many of the elements αf the invention. Configurations involving interchange and/or substitution of components from those indicated in the Figures provide additional preferred embodiments. It is recognized that additional embodiments are possible which employ simultaneously some or all of the elements αf one or more of these embodiments, other species, and/or elements αf conventional sensors. In view of the extreme sensitivity of matter-wave interferometers, configurations augmented by conventional sensors may be useful for extending the dynamic range of the invention as may be desirable, for example, in inertial guidance and navigation system applications. It is also recognized that even though each depicted embodiment describes a single interferometer, configurations involving a multiplicity of such units will be required for many applications.

While the descriptions presented herein describe what at present are considered preferred embodiments for the invention, it will be obvious to those skilled in the art that various changes, substitutions, modifications, and refinements may be made therein without departing from the invention.

Components for an embodiment of a matter-wave interferometric inertial sensor include the following: CA) A suitable choice Cor set of choices) αf low-energy atomic/molecular species; CB) A cαllimated atomic beam source;

CO A velocity adapter capable of slowing down the beam atoms without severely reducing their flux in a given velocity interval;

CD) A cαprαpaQatioπ deflector;

CE) An atomic-beam polarization adapter;

I CF) An enclosed-area/displaced-path neutral atom Cand/or molecule) matter-wave interferometer configuration, in which the matter-wave propagation paths enclose a finite area and/αr are displaced from each other's position, comprising, an entrance collimator and/or beam divider,

6 path redirectαrs, and a phase sensitive beam-recombiner or superposition region;

CG) An alternative configuration to CF), above, for measuring gravitational gradients, in which the propagation paths sequentially enclose independent areas Cor positional

II displacements) with such enclosures displaced from each other's position, between the entrance collimator Cand/or beam divider) and the phase sensitive beam-recombiner or superposition region;

CH) A detector or detectors; 16 CI) A means for limiting or stabilizing the free-fall of a slow atomic beam Cbeam-sag limiter);

CJ) A differential phase shifter;

CK) A high-vacuum system enclosing all paths for atomic/molecular-beam propagation; 51 CL) Servo controlled gimbals;

CM) Associated monitors for any of the above;

CN) Suitable electronic circuitry and data processing hardware and software for analysis of the results for the desired application. 56 Some of these components are optional, depending upon the desired system sensitivity, accuracy, cast and complexity.

1. CHOICE OF ATOMIC OR MOLECULAR SPECIES.

From Eqs. CD and Cδ), an interferometer's sensitivity

31 to rotation and acceleration plus gravity is a function of particle mass and kinetic energy. Thus, employing matter waves associated with low energy, high mass atoms and/αr molecules will provide high sensitivity. Also a plurality αf atomic species can be used simultaneously to extend the

36 dynamic measurement range αf the invention. Depending on the choice for other system components Ce.g. upon the use of an electromagnetic standing wave as a grating, the use

5S

I of laser cooling and slowing in the velocity adapter, etc.) another desirable feature is that the chosen species have an energy level with allowed electromagnetic resonance transitions to it from the ground state. Moreover, the wavelength of the associated electromagnetic radiation

6 should be as short as passible Cto provide a fine grating periodicity, thereby maximizing the enclosed cell area), yet still within the range αf presently available electromagnetic radiation sources such as lasers.

II Cesium, rubidium, thallium, mercury and sodium atoms, and Cs 2, CsRb and I2 molecules are among the suitable choices for use in this invention. Mercury is especially attractive in that it is a very heavy atom CA-lS8-504) and simultaneously has short wavelength resonance transitions

16 C5537 and 1B50 A), although suitable lasers at these wavelengths may be difficult tα obtain and/αr expensive. Atomic sodium and rubidium have the advantage that laser cooling of these species has already been demonstrated. When crystal surfaces are used in a Bragg reflection mode

51 for matter - wave path deflection, division and recombination, a heavy noble gas atomic species such as krypton or xenon may be used to prevent adsorption an the crystal faces.

SB S. COLLIMATED ATOMIC-BEAM SOURCE.

The atαmic-beam source depends upon the species employed. A suitable source for the species examples given above is an effusive oven similar to that commonly used in an atαmic-beam apparatus. Effusive oven 3, containing

31 species 1, is shown behind collimating slits 5 and 11 in Figures 6a, 6b, behind collimating slits 5 and 71 in Figure 7a and behind collimating slits 5 and 163 in Figure 8a, with the combination producing a cαllimated atomic Cor molecular) beam. Source 5 and collimating slits 10 Car slit

36 SO) function similarly in Figures 1, 3, 4a - 4f, and 5.

Such ovens can be fabricated from a suitable

I refractory metal such as tantalum αr molybdenum and heated with embedded wire coils insulated from the oven by ceramic sleeves. Ramsey (. Molecular Beams, Oxford, London, 1969) describes applicable atomic and molecular beam methodology. The source and associated collimating slits should provide

6 a well collimated beam. A supersonic jet type source of the type described by English and Zorn Cin Me thods of Experimental Physics Vol . 3, Cδnd Edition), D. Williams, ed., Academic Press, New York. 1975) as well as the flowing of a gas such as Argon through the jet may also be used far

II an i ncreased flux and a narrower resulting velocity distribution.

Heating the slits and/or apertures will help prevent their clαgging by a buildup of condensed beam-particles.

16 Indeed, down-stream beam defining elements within the system such as slits 17 and 19 and mirror 15 in Figures 6a and 6b, and slits 71 and 81, mirror 15 and lens 105 in Figure 7a, and crystals 167, 169, 179, 181, 183, and 185 and slits 163, 155 and 157 in Figures θa and 8b may also

51 benefit from such heating. Alternatively, cooling such elements with liquid nitrogen will prevent re-emission αf adsorbed beam particles on them.

3. BEAM-VELOCITY ADAPTER.

56 Methods for generating nearly mono- energetic and, more importantly, slow atomic beams have recently been demonstrated. When the species is a molecule, it can be slowed and cooled by similar techniques. Low velocity is desirable for high sensitivity. An important feature of

31 such slow beams is that the de Broglie wavelength of the species varies inversely with its momentum. A long de Broglie wavelength is desirable for other reasons as well. Achieving acceptable fringe visibility with short wavelengths requires extremely small slit dimensions and

36 extreme mechanical rigidity αf the interferometer geometry, while longer wavelengths significantly ease these requirements and simplify the construction. Additionally,

54

if diffraction is used for redirecting the beam, the enclosed area of the interferometer that can be incorporated increases with decreasing wavelength, further increasing the sensitivity to both rotation and acceleration plus gravity.

The embodiment of Figures 6a and 6b, uses a variant of the pulsed technique by Ertmer et al. In it, the velocity adapter is configured tα produce two different velocities, each with a narrow velocity spread. The narrowness is desirable tα yield a high fringe visibility Cfriπge contrast) . These two velocities are produced one at a time in rapid alternation. Although either the pulsed or continuous velocity adaptation technique can be used here, the pulsed technique was selected for the embodiment of Figures 6a and 6b since rapid velocity change of the beam is readily accomplished by this technique via electro-αptically tuning the laser pulse characteristics an alternate pulses.

In Figures 6a and 6b, a ribbon shaped laser beam 13 is reflected by mirror 15, passes through the interferometer entrance slit 11 and interacts with the atomic beam from oven 3 in region 7. The atomic beam is thereby slowed and cooled. The laser beam is pulsed and its wavelength changes during the pulse C'chirped"), thereby coaling and slowing a group of atoms. Alternate laser pulses have different intensities and/or durations so that the associated slow atomic-beam pulses have different velocities upon passing through slit 11.

An alternative embodiment for the configuration of Figures 6a and Bb is to have the velocity adapter and source produce two different masses simultaneously. Tα do sα, oven 3 is loaded with a mixture of the two species. The associated laser beam then alternates between two chirped pulses with different wavelengths, each appropriate tα its respective species.

In the embodiment of Figure 7a, the associated interferometer cell produces its own additional velocity Cand matter-wave de Broglie wavelength) selection, which can be even more selective than that αf the velocity adapter. It does so by using standing-wave laser beam 153 to form electromagnetic diffraction gratings B7, B9, 91, 93, 97, 99 and 101. Similarly, the embodiment of Figure Ba,b, produces its own additional velocity selection, by using Bragg reflection by the faces αf crystals 167, 169, 179, 1B1, 183, and 185. In these embodiments the velocity adapter functions to match the peak of the input velocity distribution to the interferometer cell to that selected by the cell itself in order to maximize throughput. Suitably configured, it eliminates overlapping diffraction orders in the interferometer cell.

The velocity adapters in the embodiments of Figures 7a and Ba employ the continuous technique by Prodan et al. Cooling and slowing occurs by radiation pressure from laser beam 155 acting on the atoms. Figure 7a shαws reflection αf this laser beam by mirror 15, and its subsequent passage through center slit BI, and slit 71. In Figure Ba it enters by passing through a hole in crystal 179 and then through slit 163. In both Figures it then passes into tapered solenoid 115 where it interacts with the atomic beam produced by oven 3 and slit 5. As atoms propagate through solenoid 115, they are slowed and cooled by radiation pressure from laser beam 1S5. As their velocity Cand correspondingly their Dαppler shift) decreases, they advance to regions with an increasing magnetic field corresponding to the taper of solenoid 115. The resulting increased Zeeman energy shift maintains their resonance, and hence their interaction with laser beam 155.

The laser coaling and decelerating elements αf the beam velocity adapter used by the embodiments of Figures

15a,b produce a diverging and/αr astigmatic velocity distribution. Most interferometer configurations work best

with a parallel input beam velocity distribution. To correct the divergence and astigmatism in the embodiment αf Figure lδa, focusing grating δ65 is employed. It has a slit configuration similar tα that shown in Figure llg. Correspondingly, in the embodiment αf Figure 15b, focusing grating 365 performs a similar function. Since the source in this latter embodiment has negligible astigmatism, a slit configuration similar to that shown in Figure llf is employed for the focusing grating.

4. COPROPAGATION DEFLECTOR.

A velocity adapter that uses radiation pressure requires a laser beam that propagates cαaxially Cat least approximately) with the associated atomic beam. In the configurations of Figures 6a,b, 7a,b, and Ba,b, the various downstream slits are sufficiently wide tα permit the velocity adapter laser beams tα be injected via small mirrors 15 that do not disrupt the atomic beams so that the laser beams then propagate unobstructed tα the interaction region Ce.g. region 7 in Figures 6a and 6b) where they are Cat least approximately) collinear with the atomic beams.

In alternative embodiments, various apparatus components may obstruct the injection of the velocity adapter laser beam. As a result, either the laser beam, the atomic beam, or both must be deflected to allow counter-propagation of the laser beam and the atomic beam. Thus tα avoid obstructions, in Figures 6a and 6b, mirror 15 deflects laser beam 13, and likewise in Figure 7a, it deflects laser beam 155. These laser beams are incident on the mirrors 15 from a direction that is perpendicular to the interferometer cell plane. As an alternative, when the slits are too narrow to allow injection through them, the laser beam may be injected by reflecting it off the front surface of the interferometer cell entrance slit Cslit 11 in Figures 6a and 6b and slit 71 in Figure 7a) . Another alternative is to allow the laser beam Cor beams) to impinge on the atomic beam diagonally at an acute angle.

In situations in which deflection of the laser beam is either unfeasible or insufficient, then the atomic beam may be deflected away from the laser beam tα permit the injection αf the latter. Various methods for deflecting the beam are possible. An inhomαgεneous magnetic field will provide an appropriate deflecting force when it interacts with the atom's magnetic moment. Such a field can be produced by a Stern-Gerlach type of magnet, a two-wire magnet, or a multipαle focusing magnet. Suitable examples of these configurations are described by Ramsey . ibid. . . Another means for deflecting the beam is to allow resonant laser light to impinge perpendicularly on the beam and allow the radiation pressure of the light to provide the deflecting force.

The embodiment αf Figure 8a uses a beam deflection method that is due to I. Rabi C loc. c i t . Ramsey, p395) . Atomic beam 189 is deflected by the magnetic field gradient that it experiences as it passes from magnetic field 166 to magnetic field 165. Uniform magnetic field 166 is generated by solenoid 150, while uniform magnetic field 165 is generated by solenoid 15S. Laser beam 155, passes though a hole in crystal 179 , through one of the slits 163 and is collinear with atomic beam 189 in solenoid 115.

5. ATOMIC-BEAM POLARIZATION ADAPTER

The means for differential phase-shifting and/αr that for beam-sag limitation may require that the magnetic moments αf the atomic-beam particles be polarized or aligned in a specific direction. In embodiments that employ laser cooling and slowing, the velocity adapter and/or deflector will usually produce a polarized beam. For alternative embodiments in which the velocity adapter does not produce a polarized or aligned beam, a magnetic state-selector similar tα one αf those described for use as an atαmic-beam deflector can be employed for this purpose

5S

also .

In the embodiment αf Figures 6a and 6b, the velocity adapter produces a beam whose polarization is parallel to the long direction of slits 11, 17 and 19. This direction is already suitable for the atαmic-beam sag limiter, so that a constant background magnetic field 41 prevents precession αf this polarization.

In the embodiment of Figure 7a, the velocity adapter produces a beam polarized parallel to the beam axis, whereas the beam-sag limiter and differential phase shifter require a beam that is polarized perpendicular to the cell plane. The polarization shift is accomplished in this embodiment by configuring the externally applied magnetic fields to slowly rotate along the propagation path into the cell so that the atomic magnetic moments adiabatically readjust themselves to the new applied field direction. The conditions for such an adiabatic precession are described by Rαbiscoe CAmer. J. Phys. 39, pl46, 1971). In Figure 7a the required slowly rotating field is produced as the fringing fields αf solenoid 115 diminish, and the dominant field becomes uniform magnetic field 41. Similarly, in Figure 8a the required slowly rotating field is produced as the fringing fields of solenoid 115 diminish, and the dominant field becomes uniform magnetic field 166. Magnetic fields 165 and 166, although of different magnitudes, are in the same direction and serve tα maintain the beam polarization.

In the embodiments of Figures lδa.b the atomic beam is polarized parallel to the interferometer axis throughout. This polarization is maintained by the magnetic field produced by solenoid 537. The quarter-wave plates 551 produce circularly polarized light for cooling and deceler a tio . Thus , the polarization adaptation is performed an the laser light instead.

I 6. INTERFEROMETER CELL FOR MEASURING ROTATION AND

ACCELERATION PLUS GRAVITY. A neutral atom interferometer cell for measuring rotation and acceleration plus gravity is comprised of the fallowing set of components: a path geometry that encloses 6 a finite area so that it is sensitive to rotation; a path geometry with the paths displaced from each other so that it is sensitive to acceleration plus gravity; an entrance collimator; a beam divider; path redirectors; a phase sensitive beam-recombiner or recombination Csuperpositiαn)

II region.

One embodiment αf such an interferometer cell is shown in Figures 6a and 6b. This configuration is a straightforward extension αf that of Figure 1. The cell

16 entrance collimator slit 11 also acts as a beam divider. The path redirectors are slits 17 and 19. The slits deflect the incident atomic beam by the matter-wave equivalent of diffraction of light by a slit, as is familiar in the study αf the physical optics of light. The superposition region

51 is on the surface of hot wires SI. The matter-wave paths 9 pass from slit 11, through slits 17 and 19, and terminate an hat wires 51. Two hot wire detectors are used, staggered laterally about the cell axis sα that they each sample a slightly different matter-wave phase shift. Monitoring both

SB signals from the two electron multipliers 55 allows the sense αf any change in the inertially induced phase shift to be determined.

Since the de Broglie wavelength of the atoms is on the 31 order αf Angstroms A , in order to achieve acceptable fringe visibility, the necessary slit widths Cand/or transverse spacings) for the embodiment of the interferometer cell shown in Figures 6a and 6b will be on the order of microns when the spacing between the entrance 36 collimating slit 11 and redirecting slits 17 and 19 and between slits 17 and 19 and detector surfaces 51 is on the order of meters. Such slits may be readily fabricated using

techniques currently common in the micro-electronics and semiconductor industries. For example, a sheet αf metal or other suitable material may be selectively milled via a plasma-etch or other suitable process tα thin dimensions and then slits cut through the thin portions also by an electron-beam or plasma-etch process. Alternatively, one can cut holes in a sheet of metal or other suitable material, deposit into these holes a material such as crystalline salt, thereby filling them back up to a flush surface. A metallic film can then be deposited by an evaporation process onto the surface, except at points where the slits are desired tα be which are covered by a mask. Finally, the salt can be removed by dissolution. Another, method for fabricating the slits is to use carefully sharpened and lapped metal knife edges, as was done by Leavitt and Bills . ibid. . .

An alternative means for fabricating a slit or sequence αf slits is tα farm a grid αf very fine wires or fibers.

Artificially grown pure crystalline silicon is an especially useful base material for slit fabrication. Currently available techniques allow it to be milled to sub-micron dimensions. A silicon structure can be αvercαated with a thin film of high nuclear charge Chigh Z) refractory metal to provide it with opacity to soft x-rays.

Figure lib shαws an alternative arrangement for the slits 17 and 19 in the embodiment αf Figures 6a,b, allowing the embodiment to utilize a geometry similar to that of Figure 4b. The two slits groups of grating 18 selected by preceding two-slit collimator 15 are then combined with those collimating slits, allowing all such slits to be formed by the same sheet.

Figure 11a shαws an alternative arrangement for slit 11 in the embodiment of Figures 6a,b, allowing it to

I utilize a geometry similar tα that of Figure 4b. The slits αf grating 16 selected by the last slit αf collimator 10 are combined with that slit so that all such slits are formed by the same sheet. In addition, to allow the embodiment αf Figures 6a,b to utilize the geometry of

B Figure 4b, the slit arrangement αf Figure 11a is inserted in the path geometry of Figures 6a,b immediately in Front αf hαt-wire detectors 51 to act as a fringe mask.

Figure lie shows an alternative slit arrangement to

II that of Figure lib that focuses the paths in the long direction of the slits. A detailed description of its structure and function is provided above. Each αf the two slit groups αf Figure lib has been replicated end-tα-end, with each such replicated group decreased in length from

16 that of an interior group. The spacings and lengths of the slits themselves within each group also decrease slightly as one proceeds from an inner slit tα an outer one. The additional slit groups and uneven slit spacing allow focusing αf the paths to increase flux throughput.

51 Moreover, for the same outer most slit end tα αuter most slit end length, the ladder-like cross members ΞB6 allow the configuration of Figure lie to be mechanically stronger than that of Figure lib. A simpler construction method for the configuration of Figure lie maintains equal slit

56 spacing and slit width within the slits of each group. This end-to-end replication technique may alsα be applied tα the grating of Figure 11a with similar focusing resulting there.

31 Another embodiment of an interferometer cell is shown in Figure 7a. It uses standing-wave laser beams as electromagnetic diffraction gratings. These gratings are configured to produce three cells simultaneously. Gratings 87, B9, 91 and 97, and gratings 87, 93, 91 and 101 each

36 produce a laterally asymmetric .grating interferometer cell, while gratings 87, B9, 93 and 99 produce a laterally symmetric grating interferometer cell. The entrance

I collimator is slit 71, while the extensions of gratings B9, 91 and 93 are limited by the set αf three slits 81. The beam divider is grating 87, that operates order zero and a high αrder _; n. The path redirectors are gratings 89, 91 and 93. Gratings 89 and 93 operate in orders n and Sn, while

B grating 91 operates in orders zero and n. The superposition region is on gratings 97, 99 and 101, each of which acts simultaneously as a fringe mask, a fringe magnifier and a fluorescent detector screen. These three gratings Cextensions αf the same grating) are tilted at a small

II angle relative tα the interferometer axis, while gratings 87, 89, 91 and 93 are perpendicular to this axis.

The embodiment of Figure 7a uses a matter-wave beam with a narrow velocity spread and only one mass at a time.

16 The velocity adapter is configured to produce a continuous very low velocity atomic beam. The velocity is low enough that the natural atomic-resonance width is comparable tα or less than the Doppler shift αf laser beam 153 that is due to the atomic beam's velocity.. Thus, depending upon the

51 species choice, Doppler velocity selection by the gratings may not occur. Additional velocity selection Cover and above that produced by the velocity adapter), however, does occur by the action αf the gratings and the slits 71 and 81. With no Dαppler velocity selection, a single laser beam

56 153 serves to create all of the electromagnetic gratings 87, 89, 91, 93, 97, 99, and 101. It is generated by narrow bandwidth laser 117 that is tuned to a wavelength near that αf an electromagnetic resonance of the chosen species. Lenses 154 focus it into a parallel ribbon-shaped beam. The

31 laser beam 153 is split into three beams by partially reflecting mirrors 75, and then reflected back upon itself by mirrors 69 to form the standing-wave gratings.

Another embodiment of an interferometer cell for

36 simultaneously measuring rotation and acceleration plus gravity is shown in Figure Ba. It uses crystal surfaces for wavelength selective reflection of atomic beam 189. The

I entrance collimator is slit 163. The beam divider is crystal 179, that reflects the beam simultaneously in two different directions that correspond to different diffraction orders, and/or reflections from a different set of crystal planes. The directions are selected by slits

6 195. The path redirectors are crystals 1B1 and 1B3. The superposition region is an the face αf crystal 1B5. The embodiment of Figure 8a uses a beam with a narrow velocity spread and only one mass at a time. Additional velocity selection Cover and above that produced by the velocity

II adapter), however, occurs by the action of the diffracting crystals. Matter-wave paths 191 are displaced from each other and enclose a finite area so that the embodiment is sensitive to bath rotation and acceleration. This embodiment has the feature that large enclosed areas can be

16 obtained with a compact device via the narrow lattice spacing of the crystal, which yields large diffraction angles.

7. INTERFEROMETER CELL FOR MEASURING GRAVITATIONAL δl GRADIENTS

An embodiment of an interferometer cell for measuring gravitational gradients is created by simply replacing the path geometry of the interferometer shown in Figure 7a by that shown in Figure 4e and/or 4f. Gratings Gl - GB in δ6 Figures 4e and 4f can be driven by the same standing-wave laser beam as was done in the embodiment of Figures 6a,b by splitting the laser beam into four rather than three parts as was done in the embodiment of Figure 7a. Since the two loops of the figure-eight geometries of Figures 4e,f

31 enclose equal areas, but are circuited in apposite directions, the interferometer is insensitive to rotation and acceleration plus gravity, but sensitive to gravitational gradients.

36 Another embodiment of an interferometer cell for measuring gravitational gradients is created by simply replacing the path geometry αf the interferometer shown in

Figure Ba by that shown in Figure Bb. In this alternative geometry, the matter-wave paths circuit two equal areas in opposite directions, so that the interferometer is insensitive to rotation and acceleration plus gravity, but sensitive to gravitational gradients. In the embodiment αf Figure Bb the matter waves are reflected by crystals 167 and 169, while the path geometry is fixed by slits 197.

Figure 15a shαws an embodiment of the invention that is suitable for use in petroleum Cor mineral) exploration when lowered into a bore hale. It consists of two orthogonally oriented, gradiometer-cαnfigured interferometers, whose axes 561 and 563 are each parallel to the axis 540 of the bore hale. Atoms such as potassium, cesium, or rubidium effuse from dual-port oven SOI, through collimating slits 505 and 503 creating two ribbon shaped beams 559 and 531 that propagate along interferometer axes 561 and 563, respectively. The thin directions of these beams are perpendicular to each other. Salid-state lasers 519 provide frequency chirped cooling and decelerating ele c trαmagne tic radiation that is given a circular polarization by quarter-wave plates SSI, and focused by astigmatic lenses 553. Mirror 557 reflects the light from one αf these lasers, while partially silvered mirror SΞ5 combines the two laser beams. This source of cooling decelerating radiation is similar to one described by Watts and Weiman Coptics Lett. 11, 591 C19B6)_1. The radiation is reflected by mirror 533 to cαpropagate in a direction anti-parallel with atomic beam 559 and focus on the collimating slit 503. Radiation from a second such source Cnot shown) is reflected by mirror 505 to cαpropagate anti-parallel to atomic beam 531. Mirrors 505 and 533 thus act as copropagation deflectors and have thin slits, 554 and 553 respectively, cut in them tα allow passage of the cooled decelerated atomic beam. Perpendicularly oriented astigmatic focusing gratings S65 improve the beam velocity parallelism.

I Coaled beam 559 propagates through grating 507, consisting αf a set αf slits configured as per Figure 11a, with the slit long direction oriented to allow passage and diffraction of the beam. Grating 507 splits beam 5S9 onto two sets αf paths which propagate through the various slits

B αf grating 509, collimator 511, the various slits αf grating 513, thereby traversing a figure-eight path 550 and recombining on grating 515. One set αf paths threads through differential phase shifting solenoid S39. Gratings 509 and 513 contain slit configurations similar to those of

II Figures lib or lie, while the slit configuration of grating 515 is configured as per Figure 11a. Detector 517 is similar tα hot-wire pair 51 of Figures 6a,b and its associated components. The passage of beam 531 is similar to that of beam 559, with the path defining components δOδ,

16 505, 50B, 510, 515, 514, 51B, 518, and 539 similar to their respective counterparts 503, 533, 507, 509, 211, 513, 215, 217, and 551, but rotated 90 ^* about the parallel) interferometer axes, corresponding tα the perpendicular ribbon shaped atomic beam orientation.

51

Figure 15b shows an alternative embodiment to that of Figure lδa. It consists αf a single gradiometer-configured interferometer, and contains many components common tα the embodiment of Figure ISa. Oven 301 has one exit port.

56 Collimator 303 produces a conical shaped atomic beam 359, and lenses 353 correspondingly produce a conical beam of cooling decelerating radiation. The interferometer utilizes the axi-symmetric grating configuration shown in Figure lid for gratings 307 and 315, and that of Figure lδe for

31 gratings 309 and 313. Collimatαrs 303 and 311 each has a circular aperture Crather than a slit) while mirror 333 has an elliptical aperture 353 that appears circular when viewed by oven 301 or by the incident laser radiation. Focusing grating 3B5 has the axi-symmetric configuration of

36 Figure llf and diminishes the transverse spread αf beam velocities. Gratings and apertures are symmetric about axis 361.

I The multiplicity αf paths for the embodiment of Figure lδb is a set of coaxial hollow conical shaped paths that form a "figure-eight of revolution" 350 Crevαlved about the figure-eight's long axis), rather than the set αf ribbon shaped figure-eight paths S50 used by the embodiment of 6 Figure 12a. It will be seen, however, that any plane containing the interferometer axis in the axi-symmetric interferometer αf Figure 12b reproduces the two dimensional slit arrangement geometry αf either of the interferometers αf the embodiment of Figure 15a. The number αf possible

II conical-shaped particle paths depends upon the number αf circular slits in gratings 307, 309, 313, and 315. Preferred dimensions for these are discussed above. Detector 317 contains four hot wires and can detect particle flux gradients in both directions transverse to

16 the interferometer axis.

B. DETECTO S).

The choice of atomic-beam detector will depend upon the species 1, chosen. If the species choice is an alkali

51 metal such as sodium, cesium αr rubidium, a molecule containing such an alkali metal, or from among some of the alkaline earths, it can be detected by surface ionization on a hot wire followed by measuring the resultant emitted ion current. This current is easily measured with an

SB electron multiplier or other means. Hot-wire contaminants can be rejected, if necessary, by focusing the ions thus produced through a mass spectrometer.

The embodiment αf Figures 6a and 6b detects the atomic 31 beam in the superposition region by surface ionization an hat wires 51, followed by acceleration through negatively biased slits 53. A mass spectrometer is produced by allowing the ions to propagate along paths 57 in the presence of magnetic field 41. The ions are then detected 36 by electron multipliers 55. Hot wires 39 and biased ion collector plates 37 are used far coarsely detecting atomic beam sag in the direction parallel to the long direction of

the slits. The signals from these are used far coarse servo control of the atomic beam sag-limiting magnetic fields. Fine control is obtained from the signals from an orthogonal interferometer whose acceleration sensitive axis is in this direction.

The embodiment of Figure Ba and Bb detects the atomic beam in the superposition region by surface ionization on hat wire 175, fallowed by acceleration through negatively biased slit 173. A mass spectrometer is produced by allowing the ions tα propagate in the presence of magnetic field 165. The ions are then detected by electron multiplier 177.

An alternative means for detecting the atoms is to monitor resonance fluorescence light from the beam that is due to an incident resonant laser beam. Multi-photon ionization of the beam by laser excitation followed by monitoring the emitted ion or electron current by suitable means such as an electron multiplier is another means far detecting the atoms. Such techniques are now standard in atαmic-beam experimentation. Many of them are discussed by Ramsey C ibid. ) .

A fringe mask may be placed in the superposition region. It consists of a series of slits formed from a solid material, and is followed by a detector with large dimensions. Alternatively, the fringe mask, itself, can act as a fluorescent screen, by forming it from a standing-wave electromagnetic grating. The resulting emitted light Cor particles if photo-ionization or molecular photo-dissociation occurs) can be detected by a detector. Suitable detectors are a photomultiplier in the case where light is emitted, and an electron multiplier when charged particles αr etastable atoms are emitted. Alternatively the emitted light αr charged particles can be imaged onto an image sensing detector such as a CCD

Csolid-state charge-coupled-device) or silicon diode array

BB

I in the case where light or electrons are emitted, or a vidicαπ when light is emitted.

In the embodiment of Figure 7a, electromagnetic gratings 97, 99 and 101 each act simultaneously as an 6 electromagnetic fringe mask, as a fluorescent detector screen and as a fringe magnifier. The light emitted at these gratings by resonance fluorescence of laser beam 153 and the atoms in the matter-wave beam is focused by lens 105 onto an optical image sensing CCD detector array 107 at I locations 109, 111 and 113.

9. ATOMIC-BEAM SAG LIMITER.

The purpose of a beam sag limiter is to provide sufficient gradient to the component αf the magnetic field 6 that is parallel tα the atomic magnetic moments Cwhich are polarized perpendicular to the interferometer plane) to cancel curvature αf the matter-wave paths that result far the presence σf inertial forces. Such a field will alsα null out the interferometer phase shift. An additional part 1 αf the sag limiting system Cnot shown in the Figures but built according tα standard engineering practice) is an electronic feedback system that servo controls this field to maintain such a null. Its error signal provides the interferometer data output signal. That is, the error 6 signal is proportional to the sum of the rotation and acceleration plus gravity phase shifts.

Figures 9a and 9b show an embodiment of a set αf conductors that will generate the magnetic fields tα limit 1 beam sag. Discussion αf these Figures will reference coordinate system 149. The conductors in Figure 9a consist of a solenoid 147 and eight additional conducting bars 131, 133, 135, 137, 139, 141, 143, and 145, while those in Figure 5b are coils 130. Additional conductors to supply 6 the currents that flow through these conductors are not shown, but are positioned in such a manner that they generate no additional unwanted fields. In use, coils 130

I reside inside solenoid 147, with the matter-wave paths αf the interferometer fitting between them.

The conductor set shown in Figures 9a and 9b is used with both αf the embodiments of Figures 6a, and 6b and 6 Figure 7a. Coil 147 is shown both on Figure 7a and Figure 9a. A few αf the turns αf coil 147 are omitted to allow passage σf the atomic beam that exits slit 5 and laser beam 153. When used with the interferometer embodiment shown in Figures 6a and 6b, solenoid coil 147 completely surrounds

II all αf the elements shown in Figures 6a and 6b and the turns need not be omitted. When the alternative embodiment to that of Figures 6a and 6b that uses two different masses is employed, then the fields must be alternated between two different values far each mass.

16

In Figures 9a and 9b, the interferometer axis is specified tα be Capproximately) in the z-directiαn. Coil 147 creates a uniform magnetic field 41 in the embodiments of Figures 6a and 6b, and 7a, that maintains the direction

51 of the atomic magnetic moments along the y-axis.

Conductors 131, 137, 135, and 145 all carry the same current magnitude and are all parallel to the z-axis. They are spaced on a pattern that is nearly square in the x-y

56 plane. The current flow directions of conductors 131 and 145 are the same as each other, but opposite to those of conductors 137 and 135, as indicated by the arrows at their left ends. So configured, these four conductors apply a gradient in the y-directioπ tα the y-compoπent αf the

31 magnetic field. The field applied by these four conductors thus deflects the matter-wave paths in the y-direction.

Conductors 133, 135, 141, and 143 are all parallel to the z-axis and are spaced on a pattern that is a rectangle

36 in the x-y plane. The extent αf the rectangle in the x-directiαn is about forty percent of its extent in the y-directiαn. The current flow directions and magnitudes far

all four conductors are equal. So configured, these four conductors apply a gradient in the x-directioπ tα the y-cαmponent αf the magnetic field. The field applied by these four conductors thus deflects the matter-wave paths in the x-direction.

Coils 130 are wound so that successive turns span greater and greater extent in the z-directiαn. Thus they produce a field in the y direction whose magnitude varies in the z-direction. The field applied by these two coils thus deflects the matter-wave paths in the z-direction.

Figure 10 also shαws an embodiment αf a set of conductors to generate sag-limiting magnetic fields. It is similar to but more compact than that of Figures Sa and 9b. It replaces coil set 130 by four conducting bars 151, which perform the same function. Their operation is similar to that of bars 133, 135, 141 and 143. It is used with the more compact interferometer embodiment shown in Figure 8a. Solenoid call 150, shown in Figure Ba is omitted from Figure 10 tα improve Figure clarity. Coil 155 is shown in both Figure 8a and Figure 10. It surrounds the interferometer cell αf Figure 8a. Omitted turns in solenoid coil 155 allow the passage of laser beam 155 and atomic beam 189.

In the embodiments of Figures lδa,b, when the interferometer axes 561 and 563, αr 361 are not vertical then the interferometer paths will tend to sag curve) away from these axes. The sag is compensated in these embodiments by magnetic field gradients produced by current flow through bars 241, 243, 245 and 247, which are oriented parallel tα the interferometer axes. Bars 241, 243, 245 and δ47 each consist of four bars, behind each αther, thereby hiding their plurality in Figures lδa.b. They all run parallel to the interferometer axes. The eight bars δ41 and δ45 then function in a manner similar to that αf bars 131, 133, 135, 137, 139, 141, 143 and 145 in Figure 9a.

Correspondingly, the eight bars δ43 and S47 compensate for sag differential between the first and second loops of each interferometer's figure-eight path. Additional detectors Cnot shown) may be inserted immediately ahead of collimatαrs 511, 515 and 311 to sense this differential sag.

Even when the interferometer axes of Figures lδa,b are vertical, the sloping path elements will not be vertical and thus tend to curve away from a vertical direction. This curvature is compensated in two ways. First, tapered solenoid 537 provides both an axial magnetic field and an axial magnetic field gradient. To allow passage αf the laser beam, the solenoid has a small gap that is bridged by fringing fields and/or additional turns near this gap. Alternatively, the lasers and their associated components may be located inside the solenoid. The axial field maintains the atomic magnetic moment orientation parallel to the interferometer axis, while the gradient provides an upward directed force Cpotential gradient) to counteract the sag. Second, the inter-planar spacings between gratings 507 and 509, between grating 509 and collimator 511, between collimator 511 and grating 513, and between gratings 513 and 515 are not necessarily equal, but may monatαnically decrease as the paths proceed upward. The spacing variation then compensates far the particle beam's slowing down in the gravitational field it climbs. Gratings 307, 309, 313, and 315 and collimator 311 are similarly spaced in Figure lSb.

10. DIFFERENTIAL PHASE-SHIFTER.

An adjustable phase delay σf one path relative to the αther may be inserted by various means. Its usage is outlined above. One farm of a differential phase shifter is the sag limiter discussed above. This form deflects the matter-wave paths and simultaneously differentially shifts their phase. It uses magnetic field gradients to produce different magnitudes αf the magnetic field απ the two paths

75

I as well as a deflecting force on the atoms. The field, acting απ an atom's magnetic moment, shifts the energy αf the atom and thereby shifts its quantum-mechanical phase. Each path, experiencing a different field, will then exhibit a different phase shift as well as a deflection.

A second form far a differential phase-shifter is one that does not simultaneously deflect the paths. An example of this form is shown in Figures 7a, Ba and Bb. It employs a magnetic Field applied to the atoms on one path, that

II differs from that of the other path. This field has negligible gradients, and thus negligible path deflections. The appropriate magnetic field direction is parallel to the polarization of the atomic beam Cperpendicular tα the plane of the cell) in order not tα induce polarization changes in 6 the beam Cspin flips) as the beam atoms pass through the field.

In the embodiments αf Figures 7a, Ba and 8b, magnetic fields are produced by passing electric currents through 1 ribbon shaped conductors S3 and 85, parallel to an associated matter-wave path. They produce a magnetic field parallel tα the polarization of the beam Cperpendicular to the cell plane) .

6 Figure 7b shows a perspective view of the matter-wave beam passing between a pair αf such ribbon shaped conductors B3 and 85. Current is fed into and out of the ribbons by wires 84 at their ends that run perpendicular to the interferometer cell plane. The current flow in a ribbon 1 85 is equal to and oppositely directed to that αf ribbon 83. A nearly uniform magnetic field is formed between the ribbon pair by these currents. Varying the currents of an associated pair of ribbons varies the phase delay of the matter-wave path that passes between them. 6

Coils 539 and 551 of an electric conductor each thread the associated interferometer path loops in Figure lδa and

provide differential phase compensation for the interferometers. Passing a current through such a conductor provides a magnetic field parallel to the looped paths and a simultaneous anti-parallel field along the unloαped paths. Since, in this embodiment, the propagating atom's magnetic moments are approximately parallel to the paths, their total energy Cand hence their associated phase advance) will differ between the looped and unloαped passible paths. Thus, the applied field will produce a detectable phase difference between the recombiniπg paths.

11

An additional application αf the apparatus is for measuring this current by measuring the phase shift produced by the current in coils 239 and 551. A simpler embodiment for thus realizing an ultra sensitive ammeter 16 instead employs a geometry similar tα that αf Figure 4a αr 4b, rather than the one shown here that is similar tα the geometry αf Figure 4f.

Differential phase cαmpeπsation is provided in the 51 configuration of Figure lδb by moving at least one of the gratings in an oscillatory Cor circular) fashion in a direction perpendicular tα the interferometer axis, and measuring the detected signal variation that is synchronous with this motion. The movement, far example, may be S6 accomplished by piezoelectric actuators.

11. HIGH-VACUUM SYSTEM

A system that produces a high quality vacuum encloses all paths for atomic-beam propagation in all of the above

31 embodiments. It is necessary to prevent scattering of the beams by residual gas in the system. Production of such a vacuum is common practice today and can use a wide variety of commercially available components and standard techniques. The vacuum chambers and components are not

36 shown in the Figures.

For example, surrounding the components αf Figure 15a

I and Figure lδb are heavy vessels. A portion δ92 of such a vessel's wall is shown in Figure 12b. They provide a suitable vacuum while simultaneously resisting the external pressure exerted by surrounding drilling mud and water 295 residing in the bore hole. Spring 291, dashpαt 293, the pendulum action of supporting cable 294, and the viscosity αf surrounding drilling mud and water 295 form portions of a vibration isolating suspension far the interferometer.

12. GIMBAL SYSTEM. I The beam sag-limiting system outlined above will not limit sag due to rotation when a variety of momenta αr masses are present. A spread αf momenta will exist when the velocity adapter Cor interferometer cell) passes a wide spread αf velocities Cas may be desired to yield high S matter-wave beam throughput), or when large deflection angles are used Cas in the case of the embodiment depicted in Figure 10) . In such cases, beam sag due to rotation can be compensated by mounting the interferometer system on gimbals that maintain it in a fixed orientation. 1

Since the interferometer systems depicted in Figures 8a and Bb employ a wide variety of path directions, they are mounted on gimbals which prevent their rotation. They do sα by servo controlling their angular positions with the 6 resulting rotation rate signals, and thereby maintain null the interferometer phase shift.

At high rotation rates, the embodiment of Figures 6a and 6b may also require gimbals if the atomic velocity 1 spread is significant. This is because a spread of areas through the interferometer, in the presence αf a spread αf beam velocities will yield a low fringe visibility at high rotation rates. Gimbals can be used to limit the rotation rate experienced by the interferometer in this embodiment. 6

The embodiment αf Figure 7a employs only a single atomic velocity and a single mass at a time. Thus, more

I than one such interferometer system is thus required tα get the data at two different velocities. However, since the momenta in this embodiment are all nearly cαllinear and contain negligible spread, it requires no gimbals and can be run in strap-down mode.

6

13. ASSOCIATED MONITORS.

Careful control and monitoring of the parameters such as beam velocities, laser wavelengths and intensities, magnetic fields, etc. is necessary if one is to achieve

II maximum sensitivity of the invention. Suitable apparatus for doing so is not always shown in the Figures, but recognized as necessary. The beam-sag detectors 37,33 are examples of such a monitor.

IS Another example αf such a monitor provides an added feature for the embodiment of Figures 6a and 6b. It consists of an in-si tu X-ray path-length stabilization scheme. Low energy X-rays are created by electron beam 29 impacting on anode 31. The material of anode 31 and energy

51 of electron beam 59 are selected so that line radiation from a or L line of this material has a wavelength that closely matches that of the atoms. The X-rays pass through a hole 36 in the oven 1. The material forming slits 5, 11, 17, 19 and 33 has a high nuclear charge Csuch as that of

26 lead) so that the slits are opaque to these X-rays. The X-rays will then travel along approximately the same paths 9 as do the atoms and alsα form an interference pattern in the vicinity of detector surfaces 21. Since the mass of the X-rays is zero, their interference will be affected

31 negligibly by rotation and/αr acceleration plus gravity. Any undesirable flexure or positional change of the slit geometry, however, will cause their interference to change. It will be detected as a change in the flux of X-rays detected by X-ray detector 35. By monitoring the X-ray

36 interference, in addition to that αf the matter-waves, the flexure of the slit geometry can be compensated.

/o

I Figure 7a shows an insi lv. X-ray interferometer for geometry monitoring. Its operation is similar to that of Figures 6a and 6b. X-ray source elements 29 and 31 and detector elements 33 and 35 function in a manner similar to that of Figures 6a and 6b. X-rays are collimated by slits SO. Diffraction αf X-rays is by gratings 92 which farm a grating interferometer with a geometry similar tα that αf Figures 4a - 4d. The gratings 92 and slits 90 and 33 are made from a material that has a high nuclear charge Csuch as that of lead) so that the slits are opaque to the I X-rays. The gratings are rigidly mounted on the mirrors 89 so that they sense positional displacements of these mirrors, which, in turn, determine the lateral positions of the electromagnetic gratings in the embodiment.

6 An in-si tu X-ray geometry monitoring system can also be used with the embodiments in Figure Ba and Bb, since X-rays will experience reflections at the crystal faces along with the atoms. Its implementation is similar tα that αf Figures Ba and 6b, but is not shown on Figures 8a nor 1 Bb.

14. ELECTRONIC CIRCUITRY AND DATA PROCESSING SYSTEM.

Suitable electronic circuitry and data processing for analysis of the results for the desired application should 6 be included. In an application αf the invention to inertial navigation and guidance, the appropriate equations for inertial guidance must be solved. A discussion of the equations can be found, far example, by Brαxmeyer ( ibid. . , O'Donnell CInert ial Navigat ion — Analysis and Design, 1 McGraw Hill. New York, 1964), Pitman ( Inert ial Guidance, John Wiley and Sons, Inc., New York, 1S62), and the NATO AGARD lecture series notes C ibid. ), which are herein incorporated by reference. Additionally, Eqs.C3), etc. must also be solved by the data system. Commercially available 6 digital computers are suitable for these and other such necessary tasks.

Changes and modifications in the specifically described embodiments can be carried out without departing from the scope of the invention which is intended to be limited only by the scope of the appended claims.

VI. INDUSTRIAL APPLICABILITY.

The invention may be used to measure acceleration, rotation, position, orientation, gravity, the mass distribution of nearby matter, and an electric current. Other important applications are mass tomography, geodesy, and petroleum exploration.