[0001] This present application provides disclosures relating to apparatus for detecting a position of a movable object, in particular by the use of squeezed light.

BACKGROUND

[0002] The position of a laser beam that has been reflected off of an object can be measured to understand the displacement and modulation of the object.

[0003] For example, in Atomic Force Microscopy (AFM) a probe may be arranged as a microcantilever with a tip that surveys the surface of a specimen via atomic forces and a mirror that can be interrogated to measure the position of the cantilever as the specimen deflects the tip. The cantilever may be driven to vibrate by a piezoelectric transducer, and as the cantilever moves due to changes in atomic forces (a consequence of changes in mechanical properties) between the tip and the surface as the height of the surface changes, the vibration frequency of the cantilever changes. A laser beam is reflected off of the cantilever mirror and the measurement of the reflected beam can reveal information, such as the vibration frequency of the cantilever, for understanding the displacement and modulation of the vibrating cantilever mirror and, consequently, understanding the topography and mechanical properties of the specimen. The reflected beam position is typically measured using a split detector to detect one-dimensional modulations of the cantilever, and a quadrant detector for two-dimensional modulations.

[0004] However, the laser beam power and radiation pressure force can cause heating of the cantilever which impairs the precision of the cantilever, and consequently the accuracy of the height information, limiting the accuracy and the sensitivity of the AFM and can also cause damage to the specimen being surveyed. To reduce the overheating of the cantilever, a very weak beam could be used. However, here the quantum noise of the very weak beam is a limiting factor for achieving a signal to noise ratio (SNR) sufficient to detect weak signals for example due to small variations in the cantilever position.

[0005] It is in the above context that the present disclosure has been devised.

BRIEF SUMMARY OF THE DISCLOSURE

[0006] Viewed from one aspect, the present disclosure provides apparatus for detecting a position of a movable object. The apparatus comprises a nonlinear medium to receive a photon beam, the beam and medium interacting in use to output a probe beam and a conjugate beam having a photon position in continuous-variable entanglement with the probe beam; beam guiding means to cause the probe beam and entangled conjugate beam to overlap in use to form a composite beam in at least a region of the movable object such that the quantum fluctuations of the spatial intensity of the composite beam are squeezed to be symmetric with respect to the composite beam centre, the beam guiding means to cause the composite beam to be incident in use on a movable object and to be reflected therefrom; photodetection means for measuring the power of first and second portions obtained from the light of the reflected composite beam being split, wherein the apparatus is configured such that movement of the movable object varies the location of the centre of the composite beam such that the proportion of the power of the light of the composite beam being split into the first portion and the second portion is varied, the photodetection means being arranged to provide a signal indicative of the variation in the proportion of the measured power of the first and second portions, the proportion of the measured power of the first and second portions being indicative of the position of the movable object, wherein the symmetrical quantum fluctuations of the spatial intensity of the first and second portions cancel each other out, reducing the shot noise floor of the signal.

[0007] As will now be explained, in accordance with the presently disclosed apparatus, a high SNR is achievable for a weak beam as the use of entangled probe and conjugate beams having squeezed spatial intensity distribution allows the photon shot noise to be suppressed by being balanced in the two beam portions detected at the photodetection means, while the use of the beam direction means to provide a composite beam of the overlapping probe and conjugate beams both incident on the moveable object and responsive to the motion thereof in their beam pointing gives a high signal strength. This allows smaller variations of the object position to be detected against a lowered noise floor, giving a high sensitivity and high accuracy.

[0008] The sources of quantum noise in the position measurement system which dominate the classical noise sources at low beam intensity are:

[0009] (a) the back action noise which arises from the fluctuations in the position of the object (e.g. microcantilever) due to the variability of the radiation pressure applied to the object from random quantum nature of photon emission in the beam, and

[0010] (b) the photon shot noise which is a result of quantum fluctuations of the spatial intensity of the beam due to variations in photon count across the profile of the beam spot. This apparent variation in beam position at low beam energy converts into background noise in the detector due to it contributing to non-signal variation (i.e. not due to the position modulation of the object) as the energy absorbed in the different sectors of split or quadrant detectors varies due to the varying spatial intensity distribution of the photon beam, contributing to a noise background and resulting in a reduced SNR.

[0011] At a low beam intensity, the back action noise increases with increasing beam strength and comes to dominate the photon shot noise. However, the relative contribution of photon shot noise increases with decreasing beam strength and so for sufficiently weak beams, photon shot noise is the dominant noise source. In this regime, for an AFM trying to sense small features with a small position modulation on the microcantilever, this shot noise background can completely mask the contribution of the position modulation to the detected signal, limiting the sensitivity of the AFM.

[0012] The present inventors have realised that, in accordance with the presently claimed subject matter, a position detection apparatus can be provided in which the photon shot noise limit is suppressed using squeezed light while the signal strength from the position modulation is at the maximum available, allowing even weak signals due to small position modulations to be detected.

[0013] The shot noise is suppressed by providing a photon beam to interact with a nonlinear medium to produce a probe beam and a conjugate beam having a photon position in continuous-variable entanglement with the probe beam. This entanglement of the probe and conjugate beams gives a squeezing of the beam “wandering” to have spatially correlated intensity fluctuations in small corresponding areas or “locales” of the beams, such that their spatial intensity distributions match each other with the difference between the two beams is subtracted (e.g. using a split or a quadrant detector), the resulting noise is lower than the shot noise of a beam with the same total power.

[0014] Consequently, by reducing the shot noise, the SNR of squeezed light can be increased. By increasing SNR, smaller displacement and weaker modulations of a movable object can be detected.

[0015] For entangled beams having correlated intensity fluctuations, it may be viewed as advantageous to reflect only one of the beams from the movable object and use the other as a reference. In this arrangement, the beams overlap at a split detector such that at no object modulation the signal is zero. When the object position is modulated, the detector photocurrent is non-zero and the signal is proportional to the amplitude of the modulation. This setup is seemingly advantageous as back action noise due to radiation pressure is 3dB lower when reflecting only one of the probe and conjugate beam on the object because only half of the light energy received at the photodetector is incident on the moveable object. This is the case provided that the power of the single beam is already the highest tolerable.

[0016] The present inventors have realised that, despite this perceived advantage, it is advantageous for both beams to be incident on the movable object. This is because, the back action noise due to radiation pressure is only lower if the power of the single beam incident on the object is already the highest tolerable. Operating the apparatus with light incident on the moveable object at powers higher than the highest tolerable (in respect of back action noise) means that the contribution of the back action noise takes over and acts to reduce SNR. Operating the apparatus with light incident on the moveable object at powers lower than the highest tolerable (in respect of back action noise) may result in a lowered shot noise floor, but proportion of the power of the detected light contributing to the received signal is half compared to that of the classical (non-squeezed) arrangement described above, which thus has the effect of reducing the SNR by 3dB. This effectively reduces, and in some circumstances eliminates, any advantage of the shot noise floor reduction achieved using squeezed light.

[0017] In contrast, the present disclosure provides an apparatus that includes beam direction means that cause the entangled probe and conjugate beams to overlap to form a composite beam such that the quantum fluctuations of the spatial intensity of the composite beam are squeezed to be symmetric with respect to the composite beam centre (and therefore matched on opposite sides of the beam centre) to allow the shot noise to be suppressed when portions of the composite beam are detected. In accordance with the present disclosure, the composite beam as a whole is incident on a movable object and reflected therefrom, such that all of the power of the detected light from the composite beam carries signal from the position modulation within it. Thus, as both probe and conjugate beams are incident on the movable object, the movement of the object is imparted on both beams resulting in twice the signal strength (i.e. a 3dB boost in signal compared to the arrangement where only one of the probe or the conjugate beam is modulated) for the same achievable suppression in the photon shot noise floor.

[0018] Thus, in such an apparatus, SNR is 3dB higher than if one beam was modulated for the same total detected power. As SNR is higher, smaller amplitude displacements in the position of the movable object can be detected.

[0019] Thus, there is provided an apparatus that can detect smaller amplitude displacements in a position of a movable object due to reducing the shot noise and consequently improving SNR. In AFM, this allows for more precise measurements to be received and consequently a more detailed indication of the topography and mechanical properties of a specimen. This apparatus can also be used in measuring the precise position of other objects such as MEMS sensors (e.g. gravity sensors) or for measuring any deflection in terms of distance or by modulation of the object at a suitable frequency.

[0020] The composite beam may be arranged to be incident on a movable object in the near field with respect to the medium and the reflected composite beam may be arranged to be split in the far field with respect to the medium, the quantum fluctuations of the spatial intensity of the composite beam in the far field being symmetric with respect to the composite beam centre.

[0021] The modulation is imparted on both beams in the near field (by guiding the composite beam onto the movable object) and the beams are split in the far field. In the near field, the correlated locales of the overlapped probe and conjugate beams appear on top of each other whereas in the far field the correlated locales of the overlapped probe and conjugate beams are symmetric with respect to the beam centre. This enables a measurement of a position of an object to have a reduced shot noise because, in the near field, the modulation of the object displaces the beams in the same direction and, in the far field, when the beams are split the correlated locales are symmetric such that the intensity fluctuations in the correlated locales of the probe and conjugate beams subtract but the modulation from the object remains.

[0022] The nonlinear medium may have third order nonlinear susceptibility and may receive a second photon beam in addition to the photon beam and the second photon beam, photon beam and medium may interact in use by four wave mixing to output the probe beam and conjugate beam.

[0023] Four wave mixing is a very robust method of producing squeezed light and advantageously doesn’t require aligning cavities or stabilizing. Thus, four wave mixing is preferable for processing of optical beams with quantum characteristics (squeezed light) in high order spatial modes.

[0024] The nonlinear medium may comprise hot Rubidium vapour.

[0025] The first portion may be a first split beam and the second portion may be a second split beam and the photodetection means may comprise a splitter to split the reflected composite beam into the first split beam and the second split beam, wherein movement of the movable object varies the location of the centre of the composite beam on the splitter and the proportion of the composite beam being split into the first split beam and the second split beam; and a balanced photodetector for receiving the first and second split beams, wherein the symmetry of the quantum fluctuations of the spatial intensity of the composite beam may cause the shot noise to be balanced in the measured first and second split beams detected by the balanced photodetector.

[0026] A technical limitation of the split detector is that it has a common electrode, which removes the possibility to connect the two photodiodes in current-subtracting configuration when reverse biased, resulting in a higher sensitivity to optical saturation. The currents of the detectors need to be independently trans-impedance amplified, which increases the electronic noise floor and possibly reduces the detector bandwidth. A balanced photodetector overcomes such limitations.

[0027] The balanced detector may be a differential photodetector having a first eye and a second eye, the first eye to receive the first split beam and the second eye to receive the second split beam.

[0028] The splitter may split the reflected composite beam into the first and second split beam in the far field.

[0029] The splitter may comprise two D-shaped mirrors.

[0030] The beam guiding means may cause the probe and conjugate beam to overlap only in the region of the movable object and to be incident on the movable object and reflected therefrom, wherein, on reflection, the reflected probe and conjugate beams diverge, and wherein the photodetection means is to measure the power of first and second portions obtained from the reflected probe and conjugate beams being split.

[0031] The photodetection means may comprise a first and a second split detector, the reflected probe beam being incident on the first split detector and the reflected conjugate beam being incident on the second split detector, wherein the reflected probe and conjugate beams are split further by the split detectors into the first portion and the second portion, the first portion comprising a first portion of the reflected probe beam and a first portion of the reflected conjugate beam and the second portion comprising a second portion of the reflected probe beam and a second portion of the reflected conjugate beam.

[0032] The first portion may be a first split probe beam of the reflected probe beam and a first split conjugate beam of the reflected conjugate beam and the second portion may be a second split probe beam of the reflected probe beam and a second split conjugate beam of the reflected conjugate beam and wherein the photodetection means may comprise: a first splitter to split the reflected probe beam into the first split probe beam and the second split probe beam, wherein movement of the movable object varies the location of the centre of the reflected probe beam on the splitter and the proportion of the reflected probe beam being split into the first split probe beam and the second split probe beam; a second splitter to split the reflected conjugate beam into the first split conjugate beam and the second split conjugate beam, wherein movement of the movable object varies the location of the centre of the reflected conjugate beam on the splitter and the proportion of the reflected conjugate beam being split into the first split conjugate beam and the second split conjugate beam; and a balanced photodetector for receiving the first and second split probe beams and the first and second split conjugate beams, wherein the symmetry of the quantum fluctuations of the spatial intensity of the composite beam causes the shot noise to be balanced in the measured beams detected by the balanced photodetector.

[0033] The photodetection means may be a split detector having a first eye and a second eye, the first eye to receive the first portion and the second eye to receive the second portion.

[0034] The photodetection means for measuring the power of third and fourth portions obtained from the reflected composite beam may be split in four, wherein the apparatus may be configured such that movement of the movable object varies the location of the centre of the composite beam such that the proportion of the power of the composite beam being split into the first, second, third and fourth portions may be varied, the signal provided by the photodetection means being indicative of the variation in the proportion of the measured power of the first, second, third and fourth portions, the proportion of the measured power of the first, second, third and fourth portions being indicative of the position of the movable object, wherein the symmetrical quantum fluctuations of the spatial intensity of the first, second, third and fourth portions may cancel each other out, reducing the shot noise floor of the signal.

[0035] The photodetection means may be a quadrant detector having a first, second, third and fourth eye, each eye to receive a portion.

[0036] The beam guiding means may comprise a polarising beam splitter cube and a half wave plate for overlapping the probe beam and entangled conjugate beam.

[0037] The quantum fluctuations of the spatial intensity of the overlapped probe and conjugate beams may be intensity fluctuations in small corresponding areas of the beams, wherein in the near field the intensity fluctuations may be spatially correlated such that they have substantially identical positions within the beams and in the far field the intensity fluctuations may be symmetrically positioned with respect to the composite beam centre.

[0038] The angle between the probe and conjugate beams when output from the nonlinear medium may be between 6 milliradians and 8 milliradians.

[0039] Viewed from another aspect, the present disclosure provides an apparatus for atomic force microscopy, the apparatus comprising the apparatus as described hereinbefore and a movable object comprising a cantilever mirror. The moveable object, which may be a cantilever or microcantilever may be caused to vibrate, for example by being actuated by a piezoelectric transducer, to provide a deflection signal for detection in various imaging modes.

[0040] Viewed from another aspect, the present disclosure provides a method of detecting a position of a movable object, the method comprising transmitting a photon beam onto a nonlinear medium, the beam and medium interacting in use to output a probe beam and a conjugate beam having a photon position in continuous-variable entanglement with the probe beam; guiding the probe beam and entangled conjugate beam to cause the beams to overlap in use to form a composite beam in at least a region of the movable object such that the quantum fluctuations of the spatial intensity of the composite beam are squeezed to be symmetric with respect to the composite beam centre, the guiding of the beam to cause the composite beam to be incident in use on a movable object and to be reflected therefrom; measuring the power of first and second portions obtained from the light of the reflected composite beam being split, wherein movement of the movable object varies the location of the centre of the composite beam such that the proportion of the power of the light of the composite beam being split into the first portion and the second portion is varied; and providing a signal indicative of the variation in the proportion of the measured power of the first and second portions, the proportion of the measured power of the first and second portions being indicative of the position of the movable object, wherein the symmetrical quantum fluctuations of the spatial intensity of the first and second portions cancel each other out, reducing the shot noise floor of the signal.

[0041] The composite beam may be guided to be incident on a movable object in the near field with respect to the medium and the reflected composite beam may be guided to be split in the far field with respect to the medium, and the quantum fluctuations of the spatial intensity of the composite beam in the far field may be symmetric with respect to the composite beam centre.

[0042] The method may further comprise transmitting a second photon beam onto the nonlinear medium, wherein the nonlinear medium may have third order nonlinear susceptibility and the second photon beam, photon beam and medium may interact in use by four wave mixing to output the probe beam and conjugate beam.

[0043] The nonlinear medium may comprise hot Rubidium vapour.

[0044] The first portion may be a first split beam and the second portion may be a second split beam, the method may further comprise splitting the reflected composite beam into the first and second split beam, the first split beam having substantially the same power as the second split beam, wherein the measuring of the power of first and second portions may be by a balanced detector that the first and second split beams are arranged to be incident on.

[0045] The balanced photodetector may be a differential photodetector having a first eye and a second eye, the method may further comprise receiving the first split beam at the first eye and the second split beam at the second eye.

[0046] The splitting of the reflected composite beam may be in the far field.

[0047] The first and second portions may be received at a split detector for measuring the power of the first and second portions, the split detector having a first eye and a second eye, the method may further comprise receiving the first portion at the first eye and the second portion at the second eye.

[0048] The method may further comprise measuring the power of third and fourth portions obtained from the reflected composite beam being split in four, wherein movement of the movable object varies the location of the centre of the composite beam such that the proportion of the power of the composite beam being split into the first, second, third and fourth portions may be varied, wherein the signal provided may be indicative of the variation in the proportion of the measured power of the first, second, third and fourth portions, the proportion of the measured power of the first, second, third and fourth portions being indicative of the position of the movable object, and wherein the symmetrical quantum fluctuations of the spatial intensity of the first, second, third and fourth portions cancel each other out, reducing the shot noise floor of the signal.

[0049] The measuring of the power of first, second, third and fourth portions may be by a quadrant detector that the first, second, third and fourth portions are arranged to be incident on, the quadrant detector having four eyes, each eye to receive a portion.

[0050] The probe and conjugate beams may be guided to cause the beams to overlap only in the region of the movable object and to be incident on the movable object and reflected therefrom, wherein, on reflection, the reflected probe and conjugate beams diverge, and wherein measuring the power of the first and second portions comprises measuring the power of first and second portions obtained from the reflected probe and conjugate beams being split.

[0051] The method may further comprise receiving the reflected probe beam at a first split detector and receiving the reflected conjugate beam at a second split detector, and splitting, by the first and second split detectors, the reflected probe and conjugate beams into the first portion and the second portion, the first portion comprising a first portion of the reflected probe beam and a first portion of the reflected conjugate beam and the second portion comprising a second portion of the reflected probe beam and a second portion of the reflected conjugate beam.

[0052] The first portion may be a first split probe beam of the reflected probe beam and a first split conjugate beam of the reflected conjugate beam and the second portion may be a second split probe beam of the reflected probe beam and a second split conjugate beam of the reflected conjugate beam, the method may further comprise: splitting the reflected probe beam into the first split probe beam and the second split probe beam, wherein movement of the movable object varies the location of the centre of the reflected probe beam on the splitter and the proportion of the reflected probe beam being split into the first split probe beam and the second split probe beam; and splitting the reflected conjugate beam into the first split conjugate beam and the second split conjugate beam, wherein movement of the movable object varies the location of the centre of the reflected conjugate beam on the splitter and the proportion of the reflected conjugate beam being split into the first split conjugate beam and the second split conjugate beam, wherein the measuring of the power of first and second portions is by a balanced detector that the first and second split probe beams and the first and second split conjugate beams are arranged to be incident on, wherein the symmetry of the quantum fluctuations of the spatial intensity of the composite beam causes the shot noise to be balanced in the measured beams detected by the balanced photodetector.

[0053] The quantum fluctuations of the spatial intensity of the overlapped probe and conjugate beams may be intensity fluctuations in small corresponding areas of the beams, wherein in the near field the intensity fluctuations may be spatially correlated such that they have substantially identical positions within the beams and in the far field the intensity fluctuations may be symmetrically positioned with respect to the composite beam centre.

[0054] The angle between the probe and conjugate beams when output from the nonlinear medium may be between 6 milliradians and 8 milliradians.

[0055] The apparatus may be as described hereinbefore.

BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Examples of the invention are further described hereinafter with reference to the accompanying drawings, in which:

[0057] Figure 1 provides a schematic diagram of an apparatus for detecting a position of a movable object according to an example;

[0058] Figure 2 provides an example flowchart of a method of detecting a position of a movable object;

[0059] Figures 3A to 3D provide schematics of entangled probe and conjugate beams undergoing manipulation by an example apparatus

[0060] Figure 4 provides an example illustration of an apparatus for detecting a position of a movable object;

[0061] Figures 5A and 5B provide plots of example signals illustrating the detection of a position of a movable object by the example apparatus of Figure 4;

[0062] Figures 6A and 6B provide examples of apparatus for detecting a position of a movable object.

DETAILED DESCRIPTION

[0063] The performance of an optical system may be limited in some modes of operation by shot noise. Shot noise originates from the random manner in which photons are distributed within a light beam. Shot noise is caused by quantum fluctuations in the amplitude of light arriving at the photodetector due to the photons randomly impacting on the photodetector. When a photodetector measures the intensity of a beam to produce a signal, the photodetector measures such fluctuations and they appear on the measured signal as background noise. Thus, for photodetection, shot noise can be a limiting factor for achievable signal to noise ratio (SNR) of the beam. Shot noise can result in a reduced SNR and possible complete masking of a weak signal preventing signal detection.

[0064] In quantum mechanics, there is a theoretical limit imposed in the simultaneous measurement of a pair of physical properties known as canonically conjugated variables. The more precisely one of the pair of the variables is determined, the less precisely the other of the pair of variables can be determined, and vice versa. This is known as Heisenberg’s uncertainty principle. Example canonically conjugated variables are position and momentum. The more precisely the position of a particle is determined, the less precisely its momentum can be determined, and vice versa. The uncertainty of the variables can be illustrated as a circle, and squeezing is where the circle is “squeezed” to an ellipse having the same area. Thus, whilst one of the variables has a reduced uncertainty, the other variable has an increased uncertainty. Squeezing of high order modes of light involves the modes which exhibit the quantum noise having the quantum noise reduced below the shot noise level. Squeezing can be a precursor to continuous variable entanglement. Squeezed light can be referred to as nonclassical light, which is light that has characteristics that are described by quantum mechanics. This is in contrast to classical light, which is light that can be described by classical electrodynamics.

[0065] Squeezing the beam “wandering” is equivalent to squeezing the intensity fluctuations in the high order spatial modes of the laser light. Squeezing can be achieved by any process that uses a nonlinear medium to produce a beam pair in continuous variable entanglement. The beam pair produced has entangled spatial modes. The energy and momentum entanglement of the quantum state of the generated beam pair are seen as a consequence of the fundamental indistinguishability of the time and the position in which the pair is created inside the nonlinear medium. For some processes, the nonlinear medium may have a second order nonlinear susceptibility. For other processes, the nonlinear medium may have a third order nonlinear susceptibility.

[0066] In an example, squeezing can be achieved by a nonlinear optical process called four wave mixing (FWM). FWM induces correlations of photons across two beams. FWM requires a nonlinear medium such as hot Rubidium (Rb) vapour. In FWM, a weak input probe beam interacts with a strong pump beam in the hot Rb vapour, which is contained in a vapor cell, preferably of approximately 1cm in length. The Rb atoms mediate the interaction resulting in amplification of the probe and generation of a conjugate beam. The output probe and conjugate beams have spatially correlated intensity fluctuations in small corresponding areas or “locales” of the beams, such that when their intensities are subtracted, the resulting noise is below the shot noise of a beam with the same total power. The probe and conjugate beams are also called twin beams. Preferably, non-degenerate FWM is used to generate the probe and conjugate beams. In another example, squeezing can be achieved by a process called parametric down-conversion. In parametric down- conversion, a single pump beam interacts with a nonlinear medium to generate a probe and entangled conjugate beam.

[0067] The term “quantum fluctuations of the spatial intensity of the composite beam are squeezed to be symmetric with respect to the composite beam centre” can be understood to mean that that l(x, y) is squeezed so that the fluctuations in the intensity of the composite beam at l(x, y) and l(-x, -y) are identical for all x and y where position (0,0) is the centre of the beam.

[0068] Figure 1 provides a schematic diagram of an apparatus 100 for detecting a position of a movable object 114 according to an example. The apparatus 100 comprises a nonlinear medium 104, beam guiding means 110 and photodetection means 118. The nonlinear medium 104 is to receive a photon beam 102, the beam 102 and medium 104 interacting in use to output a probe beam 106 and a conjugate beam 108 having a photon position in continuous-variable entanglement with the probe beam 106. The beam guiding means 110 cause the probe beam 106 and entangled conjugate beam 108 to overlap in use to form a composite beam 112 in at least a region of the movable object 114 such that the quantum fluctuations of the spatial intensity of the composite beam 112 are squeezed to be symmetric with respect to the composite beam centre. The beam guiding means 110 cause the composite beam 112 to be incident in use on a movable object 114 and to be reflected therefrom. The photodetection means 118 are for measuring the power of first and second portions obtained from the light of the reflected composite beam 116 being split. The apparatus 100 is configured such that movement of the movable object 114 varies the location of the centre of the composite beam 112 such that the proportion of the power of the light of the composite beam 116 being split into the first portion and the second portion is varied. The photodetection means 118 are arranged to provide a signal 120 indicative of the variation in the proportion of the measured power of the first and second portions, the proportion of the measured power of the first and second portions being indicative of the position of the movable object 114. The symmetrical quantum fluctuations of the spatial intensity of the first and second portions cancel each other out, reducing the shot noise floor of the signal 120.

[0069] The nonlinear medium 104 may be any medium capable of interacting with a photon beam and producing a probe beam 106 and conjugate beam 108 that is in continuous variable entanglement with the probe beam 106. In another example, the nonlinear medium 104 may be any medium capable of interacting with an input photon beam 102 and a second input photon beam (not shown) to produce an output probe beam 106 and conjugate beam 108 that is in continuous variable entanglement with the probe beam 106. The two input photon beams may be known as a pump beam and a probe beam (or seed beam). The photon beam 102 and second photon beam may be incident on the nonlinear medium 104 at different angles relative to the surface of the medium. The continuous-variable entanglement of the probe beam and conjugate beam may involve two variables. For example, the conjugate beam 108 may have a photon position and tilt in continuous-variable entanglement with the probe beam 106. In another example, the conjugate beam 108 may have a photon position and direction of travel in continuous- variable entanglement with the probe beam 106. In another example, the conjugate beam 108 may have a photon position and transverse momentum in continuous-variable entanglement with the probe beam 106.

[0070] The nonlinear medium 104 may have a second or third order nonlinear susceptibility. For example, the nonlinear medium 104 may be hot Rubidium (Rb) vapour. The nonlinear medium 104 may interact to produce the entangled beams using a nonlinear process as described above, for example, FWM or parametric down-conversion. When using FWM, the produced conjugate beam 108 may have orthogonal polarization with respect to the pump beam 102. The apparatus 100 may be connected to or include a light source (not shown) to produce photon beam 102. The second photon beam may be produced by the same light source as photon beam 102 or the apparatus 100 may be connected to or include a separate second light source (not shown). The conjugate beam 108 and probe beam 106 may have continuous variables that are amplitudes of the field quadratures, which are spatially multimode. Thus, the two output beams may have a similar distribution of photons.

[0071] The beam guiding means 110 may be any means capable of guiding beams such that the probe beam 106 and conjugate beam 108 overlap. The composite beam 112 is formed from a probe beam 106 and a conjugate beam 108 that at least partially overlap in at least a region of the movable object. In an example, the composite beam is formed from overlapping probe and conjugate beams that, due to the beam guiding means 110, have the same direction of travel. In another example, the probe beam 106 and conjugate beam 108 have different directions of travel. In this example, the beam guiding means 110 may guide the probe beam 106 and conjugate beam 108 to be incident at the same point, and consequently overlap, on the movable object 114. In this example, the probe beam 106 and conjugate beam 108 are incident on the movable object 114 at different angles. In this example, the composite beam is only formed close to the movable object. For example, the composite beam may only be formed at the point of incidence of the probe and conjugate beams on the movable object. In this example, the first and second portions obtained from the reflected composite beam being split are the reflected probe beam and the reflected conjugate beam respectively. Thus, the composite beam may be split close to or at the movable object. The probe and conjugate beams are incident on the movable object 114 at different angles, and consequently are reflected from the movable object 114 at different angles, resulting in reflected probe and conjugate beams that no longer overlap. In an example, the beam guiding means 110 comprise concave or convex lenses or reflective means such as a mirror or beam splitter. In another example, the beam guiding means 110 comprises a wave plate and a beam splitter. The beam guiding means 110 may comprise a half wave plate and polarizing beam splitter.

[0072] The movable object 114 may be any object that can change the location of the centre of the beam incident on it by changing its position. The movable object may receive a composite beam 112 and reflect the composite beam to provide a reflected composite beam 116. For example, the movable object 114 may be a mirror, or a mirror attached to or forming part or a moveable object. In another example, the movable object 114 may be a vibrating cantilever mirror for use in AFM. The proportion of the measured power of the first and second portions is indicative of the position of the movable object 114. The position of the movable object 114 may refer to its position relative to its original position. For example, the position of the movable object 114 may include the distance from its original position to its current position. The position of the movable object 114 may include the direction of the current position relative to its original position. The position of the movable object 114 may include a direction and distance from current position, which may be in 3 dimensional space. In another example, the position of the movable object 114 may be an angle of tilt of an object. In another example, the position of the movable object 114 may be a frequency of the movement of an object, for example, the frequency at which the movable object 114 is vibrating, for example, by being driven at or near its resonant frequency by an actuator such as a piezoelectric transducer.

[0073] A reflected composite beam 116 may have the same properties as the composite beam 114. The location of the centre of the reflected composite beam 116 differs to the location of the centre of the composite beam 112 incident on the movable object 114 because its centre has been displaced by the movable object 114. The displacement of the location of the centre of the composite beam 112 is based on the position of the movable object 114. Both the overlapping probe and conjugate beams, as the composite beam, may deflect in the same direction due to being incident on the movable object 114.

[0074] The photodetection means 118 may be any means that can measure power of at least two portions of the reflected composite beam 116. For example, the photodetection means 118 may measure two portions of a split composite beam, the variation in power of the two portions dependent on the position of the movable object 114. The symmetry of the quantum fluctuations of the spatial intensity of the composite beam 116 may cause the shot noise to be balanced in the first and second portions when measured by the photodetection means 118. The balanced shot noise may therefore be cancelled out by the photodetection means. The photodetection means 118 may therefore provide a signal 120 indicative of the variation in the proportion of the measured power of the first and second portions, the signal 120 having reduced shot noise. Reduced shot noise may be shot noise that is lower than the shot noise floor of squeezed light. For example, the average shot noise of the signal 120 may be lower than the average shot noise of squeezed light, an example of squeezed light being the composite beam 112.

[0075] The near field and far field are distances with respect to the nonlinear medium. The near field is the region closer to the nonlinear medium where photon distribution of the probe beam and conjugate beam is identical or at least partially identical. The far field is the region further from the nonlinear medium where photon distribution of the probe beam and conjugate beam is symmetrical or at least partially symmetrical. In the near field, correlated locales may appear on top of each other and, in the far field, correlated locales may be symmetric with respect to the beam centre. The movable object may be located in the near field such that the probe and conjugate beams have substantially identical photon distribution when incident on the movable object and the movement of the object is imparted on both beams. Movement of the movable object such as a tilt leads to relative deflection at the photodetection means. The maximum deflection will be achieved when the movable object is in a Fourier plane of the photodetection means. The photodetection means may be located in the far field such that the quantum fluctuations are symmetric at the photodetection means.

[0076] The photodetection means 118 may receive the first portion and the second portion and may detect small differences in optical power between the two portions. Any small differences the spatial distribution of photons across the beam due to quantum variability would lead to fluctuations in the detected optical power giving rise to photon shot noise that would raise the noise floor and reduce SNR. However, this shot noise is reduced because the composite beam has symmetrical quantum fluctuations of the spatial intensity and so the contributions of these fluctuations to the first and second portions are equal and so cancel each other out. Thus, the main contribution to the small differences detected by the photodetection means 118 is from the movement in location of the composite beam centre which is a result of the movement of the movable object 114. When the movable object 114 moves, the centre of the composite beam 116 moves such that the beams are split differently and the portion of the reflected composite beam in each of the first and second split beams changes. This changes the intensity of each split beam. For example, when the object is at a first position, the first portion may have a larger intensity than the second portion, and when the object is at a second position, the first portion may have a smaller intensity than the second portion. The signal produced by the photodetection means 118 is based on the change in intensity of the beams which is based on the movement of the movable object. The signal produced by the photodetection means 118 is based on both the probe and conjugate beams, which are both reflected on the moveable object, meaning that all of the power measured at the photodetection means carries the signal indicative of the position modulation of the moveable object, giving an SNR 3dB higher than having only one of the probe and conjugate beams incident on the moveable object.

[0077] The photodetection means 118 may be any means capable of measuring small beam displacements. In an example, the photodetection means 118 is a position sensing detector. In another example, the photodetection means 118 may comprise two separate photodetectors, each photodetector to receive a split beam or a portion of the first and second portions. For example, the photodetection means may comprise two separate split detectors, a first split detector for receiving a first split beam or first portion and a second spit detector for receiving a second split beam or second portion. For example, the first split detector may receive a reflected probe beam and a second spit detector may receive a reflected conjugate beam. The data from each of the separate photodetectors may then be compared, for example by an external entity, to produce a signal indicative of the variation in the proportion of the measured power of the first and second split beams or first and second portions. In another example, the photodetection means 118 may comprise a splitter to split the reflected composite beam into the first split beam and the second split beam. Movement of the movable object 114 varies the location of the centre of the composite beam 116 on the splitter and consequently varies the proportion of the composite beam 116 being split into the first split beam and the second split beam. The photodetection means 118 may further comprise a balanced photodetector for receiving the first and second split beams from the splitter. The balanced photodetector may be external to the splitter. In an example, the balanced photodetector may be a differential photodetector. The balanced photodetector may provide a signal 120 indicative of the variation in the proportion of the measured power of the first and second split beams, which is indicative of the position of the movable object.

[0078] In another example, the photodetection means 118 may comprise a split detector having a first eye and a second eye, the first eye to receive the first portion and the second eye to receive the second portion. The variation in the position of the movable object 114 varies the position of the composite beam 116 when incident on the split detector. The movement of the composite beam 116 changes the amount of the composite beam 116 being incident on the first eye, as the first portion, and the amount of the composite beam 116 being incident on the second eye, as the second portion. The split detector may provide a signal 120 indicative of the variation in the proportion of the measured power of the first and second portions, which is indicative of the position of the movable object 114.

[0079] In another example, the composite beam 116 may be split into more than two portions. It will be appreciated that the beam may be split into any number of portions. For example, the composite beam 116 may be split into four portions. The split detector as described above may be a quadrant detector having four eyes to receive the four portions, each eye to receive a portion. Alternatively, the composite beam 116 may be split by a splitter into four split beams. The balanced photodetector as described above may be a quadrant detector having four eyes to receive the four split beams, each eye to receive a split beam, and balanced with the opposite eye such that the photon shot noise is suppressed.

[0080] The signal 120 output from the apparatus 100 may vary dependent on the relative beam displacement. The signal 120 output from the apparatus 100 may be processed to find the position of the movable object 114. For example, the remaining reduced shot noise of the signal may be filtered out. Even for weak modulations or small movements in the object, as long as magnitude of the signal from the movements is larger than the reduced shot noise, the position of the object can be detected. When the apparatus 100 is used in a system such as AFM, the signal 120 can be processed to provide details on changes in atomic forces (a consequence of changes in mechanical properties) at the surface and changes in height of the surface which enables the material under inspection to be better understood.

[0081] Figure 2 provides an example flowchart of a method 200 of detecting a position of a movable object 114. Firstly, a photon beam 102 is transmitted 202 onto a nonlinear medium 104, the beam and medium interacting in use to output a probe beam 106 and a conjugate beam 108 having a photon position in continuous-variable entanglement with the probe beam 106. Next, the probe beam 106 and entangled conjugate beam 108 are guided 204 to cause the beams to overlap in use to form a composite beam 112 such that the quantum fluctuations of the spatial intensity of the composite beam 112 are squeezed to be symmetric with respect to the composite beam centre. The guiding 204 of the beam is to cause the composite beam 112 to be incident in use on a movable object 114 and to be reflected therefrom. Next, the power of first and second portions obtained from the reflected composite beam 116 being split is measured 206. Movement of the movable object 114 varies the location of the centre of the composite beam 112 such that the proportion of the power of the composite beam 116 being split into the first portion and the second portion is varied. Next, a signal 120 indicative of the variation in the proportion of the measured power of the first and second portions is provided 208. The proportion of the measured power of the first and second portions is indicative of the position of the movable object 114. The symmetrical quantum fluctuations of the spatial intensity of the first and second portions cancel each other out, reducing the shot noise floor of the signal 120.

[0082] Figures 3A to 3D provide schematics of entangled probe and conjugate beams in the example apparatus 100. It is to be understood that these schematics are simplified and ideal illustrations to enable better understanding of how shot noise is reduced.

[0083] For each of the figures, the circle on the left represents the probe beam and the circle to the right represents the conjugate beam. The four-, five-, and six-point stars of the probe beam represent the positions of areas in the probe beam, known as “locales”, of locally increased intensity due to the random quantum fluctuations of the photon distribution within the beams. As can be seen, the locales in the probe beam correspond with entangled locales as indicated by the positions of respective four-, five-, and six-point stars in the conjugate beam. The dashed lines represent a classical axis through the centres of the beams.

[0084]

[0085] Figure 3A illustrates a schematic of the probe beam and conjugate beam in the near field, at the point at which the conjugate beam is generated by the non-linear medium to be co-incident with, and entangled with, the probe beam. In examples, the beam directing means images the near field onto the movable object, resulting in the locales also being coincident on the movable object. As can be seen, in the near field, the locales of the probe beam and corresponding locales of the conjugate beam have substantially identical positions within the beams, and as such, when imaged onto the movable object, the probe and conjugate beams substantially overlap.

[0086] Conversely, as shown in Figure 3B, in the far field, the locales of the probe beam and corresponding locales of the conjugate beam are symmetrically positioned with respect to the beam centre. The rightmost circle illustrates the overlapping probe and conjugate beams, forming the composite beam, and this shows that, in the far field, the locales beams combine to provide locales which appear symmetric with the beam centre being the centre of symmetry..

[0087] The detection means detects the light of the composite beam split into first and second portions in the far field, and so where the composite beam is split along its beam centre, generally, the symmetry of the locales about the beam centre leads to the detected power in the first and second portions of the split beam being balanced.

[0088] The positions of the beam locales in the far field on detection are subject to two different sources of displacement: quantum variability due to changes in the spatial distribution of the intensity locales in the probe beam; and classical motion due to movement in the moveable object (e.g. the cantilever in an atomic force microscope).

[0089] In terms of quantum variability, as can be seen in Figure 3C, when the locales in the probe beam move to different locations at a different instant, as can be seen in the central circle, corresponding locales in the conjugate beam in the far field move to symmetrically different locations. Thus, as shown in the rightmost circle, the resulting in the changes in the measured power will be balanced between the two halves or portions of the composite beam, in that they cancel each other out on either side of the detected beams. This is represented by the balanced arrow. Thus, on detection, as the changes in the positions of the locales are balanced in the far field in the reflected probe and conjugate beams, both being incident in the near field on the moveable object, there is no shot noise in the detector due to quantum variability. In terms of classical motion, as can be seen in Figure 3D, as both of the probe and conjugate beams are incident on the moveable object in the near field, motion of the moveable object changes the reflection angle and beam pointing of both the probe and conjugate beams together. This movement in the locales in the far field on detection is indicated by the arrows shown in the leftmost (probe) and central (conjugate) beams in Figure 3D. In the reflected probe and composite beams on detection, the beam centres, and thus the positions of the locales, are moved in an unbalanced way responsive to the movement of the movable object. This unbalanced, movement is shown in the rightmost beam in Figure 3D, and as indicated by the rightward arrow. This leads to an unbalancing of the power of the detected portions of the reflected probe and composite beams, leading to the detection means providing a signal that is indicative of the movement of the moveable object.

[0090] As both the beams are subject to the classical motion, the strength of the signal in the detector that is responsive to the movement in the moveable object is based on the total power of both the probe and conjugate beams. However, as the quantum variability in the locales in the probe and conjugate beams is balanced, this does not contribute to shot noise in the detector. In this way, the quantum shot noise is suppressed without the signal contribution from the classical motion being reduced, leading to a high SNR in absence of shot noise. [0091] Figure 4 provides an example illustration of an apparatus 400 for detecting a position of a movable object. The apparatus 400 is an example of apparatus 100 of Figure 1. This illustration uses a 4-f lens system. In this illustration, a probe beam 402, which is an example of photon beam 102, and a pump beam 403, which is an example of a second photon beam, are directed at hot Rb vapour 404, which is an example of nonlinear medium 104. In this example, the beams and vapour 404 interact by non-degenerate FWM to produce a probe beam 408 and a conjugate beam 406 having a photon position in continuous-variable entanglement with the probe beam 408. In this example, the angle between the probe beam 408 and the conjugate beam 406 is between 6 and 8 mrad. In this example, the beam guiding means 110 comprises convex lenses 410, 422, a polarizing beam splitter (PBS) cube 418, a half-wave-plate (HWP) 412 and a mirror 414 used to overlap the two beams efficiently to provide the composite beam 424 and to direct the composite beam to be incident on a movable object 426. In the near field, the composite beam 424 is imaged onto the movable object 426. The movable object 426 is located in the near field such that a tilt leads to relative deflection at the balanced photodetector 446. The maximum deflection will be achieved when the movable object 426 is in a Fourier plane of the balanced photodetector 446. The movable object 426 in this example is a mirror and a piezo-transducer (PZT) is to move the mirror. The position of the mirror can be modulated using an external signal applied to the PZT, resulting in beam position modulation. The modulation is applied in the near field to the composite beam 424 which comprises overlapped probe and conjugate beams.

[0092] A splitter is illustrated as two D-shaped mirrors 434, 438 configured to split the reflected composite beam 428 into two portions with substantially equal powers. The difference in powers of the portions indicates the position of the movable object 426. The split composite beams 436, 440 are detected on a balanced photodetector 446 in the far field. The balanced photodetector 446 may be located in the far field such that the quantum fluctuations will be symmetric at the balanced photodetector 446.

[0093] The first D-shaped mirror 434 deflects the first portion of the reflected composite beam 436 to one eye 444 of the photodetector 446 and the second D-shaped mirror 438 deflects the second portion 440 of the reflected composite beam to the other eye 442 of the photodetector 446. In this example, the movable object 426 is in the near field and the photodetector 446 is in the far field. The signal output from the balanced photodetector 446 may be processed to find the position of the movable object 426. In this example, the signal may be processed to find the movement or vibration of the PZT. [0094] Figures 5A and 5B provide plots of example signals illustrating the detection of a position of a movable object by the example apparatus of Figure 4. The photodetector 446 photocurrent is transimpedance amplified and the signal is observed on a spectrum analyser. Figure 5A illustrates a plot 500 of an observed signal when the PZT of movable object 426 is modulated at 2.25MHz by a comparatively large amplitude, which is larger than the amplitude of the modulation in Figure 5B. The signal of the photodetector 446 of apparatus 400 as set up in figure 4, using squeezed light, is illustrated by squeezed light trace 504. The signal of the photodetector 446 of apparatus 400 as set up in figure 4, where the composite beam 424 is replaced by a beam of coherent light (that is not squeezed light), sometimes referred to as classical light, having the same power as the composite beam 424, is illustrated by classical light trace 502. The modulation results in a peak 506 at the modulation frequency which indicates the movement of the mirror. As illustrated in the plot 500, the noise floor of the squeezed light trace 504 is reduced by an amount equal to the quantum noise reduction (QNR) due to the shot noise being suppressed, compared to classical light trace 502 and the peak 506 due to the modulated PZT is clearly visible in both traces. This illustrates that using squeezed light in the apparatus 400 of Figure 4 provides an enhancement of SNR, with an amount equal to the QNR, compared to using classical light and allows the position of the movable object to be detected. It should be noted here that the strength of the signal is the same in the classical beam as in the squeezed light apparatus of the present disclosure, but the noise floor has been reduced due to the shot noise suppression, leading to an increase in SNR.

[0095] Figure 5B illustrates a plot 550 of an observed signal when the PZT of movable object 426 is modulated at 2.25MHz by a small amplitude. The modulation results in a peak 556 at the modulation frequency which indicates the movement of the mirror. The signal of the photodetector 446 of apparatus 400 as set up in Figure 4, using squeezed light, is illustrated by squeezed light trace 554. The signal of the photodetector 446 of apparatus 400 as set up in Figure 4, where the composite beam 424 is replaced by coherent light (that is not squeezed light), sometimes referred to as classical light, having the same power as the composite beam 424, is illustrated by classical light trace 552. The noise floor of the squeezed light trace 554 is reduced by an amount equal to the quantum noise reduction (QNR), compared to classical light trace 552 and the peak 556 due to this noise reduction the motion signal from the modulated PZT is distinguishable from the noise floor in the squeezed light trace 554 but no signal is apparent in the classical light trace 552. This is because the amplitude of the signal produced from the PZT of the movable object 426 is below the shot noise floor and therefore cannot be detected by classical light in the presence of the shot noise. This illustrates that, even when the movable object is only moved by a small amount, the movement can be detected due to the apparatus 400 of Figure 4 using squeezed light providing an enhancement of SNR, with an amount equal to the quantum noise reduction (QNR), compared to using classical light which enables small modulations of a movable object to be detected. Thus, squeezed light provides enhanced SNR without having to increase power.

[0096] Thus, the apparatus 400 of figure 4 using squeezed light, as illustrated by squeezed light traces 504 and 554, allows the detection of small amplitude displacements over a reduced shot noise background of more than 3dB, which cannot be resolved with coherent light. The apparatus 100 of figure 1 can also produce similar traces and also provides the same advantages as apparatus 400 of Figure 4.

[0097] Figures 6A and 6B provide examples of apparatus for detecting a position of a movable object. Both apparatus 600, 650 comprise a nonlinear medium 604, for example hot Rb vapour 404 as described in relation to Figure 4. Both apparatuses also comprise beam guiding means 606, for example convex lens 410 as described in relation to Figure 4. Both apparatuses also comprise a movable object 608, for example, the movable object 426 of Figure 4. The nonlinear medium 604, beam guiding means 606 and movable object 608 have all been described in detail above. Both apparatus 600, 650 comprise a beam guiding means 606 arranged to provide a composite beam 620 of overlapping probe and conjugate beams only in the region of the movable object. In the apparatus 600, 650 of figures 6A and 6B, the beam guiding means 606 guides the probe beam 610 and conjugate beam 612 towards the movable object to cause the beams to overlap only in the region of the movable object 608 when incident on the movable object 608. The beam guiding means 606 is arranged to cause the probe and conjugate beams 610, 612 to be incident on the movable object 608 and to be reflected therefrom. Due to being incident on the object at different angles, on reflection, the reflected probe and conjugate beams 622, 624 diverge. In each apparatus 600, 650, the photodetection means is to measure the power of first and second portions obtained from the reflected probe and conjugate beams 622, 624 being split.

[0098] Figure 6A provides an illustration of an apparatus 600 that comprises a first split detector 616 and a second split detector 618, the reflected probe beam 622 being incident on the first split detector 616 and the reflected conjugate beam 624 being incident on the second split detector 618. The first and second split detectors 616, 618 are examples of photodetection means 118. The reflected probe and conjugate beams 622, 624 are split further by the split detectors 616, 618 into the first portion and the second portion, the first portion comprising a first portion of the reflected probe beam and a first portion of the reflected conjugate beam and the second portion comprising a second portion of the reflected probe beam and a second portion of the reflected conjugate beam. For example, the reflected probe beam 622 may be incident on the first split detector 616 such that the first portion is incident on the first eye of the first split detector and the second portion is incident on the second eye of the first split detector. The reflected conjugate beam 624 may be incident on the second split detector 618 such that the first portion is incident on the first eye of the second split detector and the second portion is incident on the second eye of the second split detector. The first portion may be formed of the first eye of both split detectors and the second portion may be formed from the second eye of both split detectors.

[0099] Figure 6B provides an illustration of an apparatus 650 that comprises a first splitter, which, in this example, is illustrated as two D-shaped mirrors 664, 666 and a second splitter, which, in this example, is illustrated as two D-shaped mirrors 668, 670. In this illustration, the first splitter splits the reflected probe beam 622 into a first split probe beam 684 and a second split probe beam 682. Movement of the movable object 608 varies the location of the centre of the reflected probe beam 622 on the splitter and the proportion of the reflected probe beam 622 being split into the first split probe beam 684 and the second split probe beam 682.

[00100] In this illustration, the second splitter splits the reflected conjugate beam 624 into the first split conjugate beam 686 and the second split conjugate beam 688. Movement of the movable object 608 varies the location of the centre of the reflected conjugate beam 624 on the splitter and the proportion of the reflected conjugate beam 624 being split into the first split conjugate beam 686 and the second split conjugate beam 688.

[00101] The apparatus 650 also comprises a balanced photodetector 672 for receiving the first and second split probe beams 682, 684 and the first and second split conjugate beams 686, 688. The symmetry of the quantum fluctuations of the spatial intensity of the composite beam 620 causes the shot noise to be balanced in the measured beams detected by the balanced photodetector 672.

[00102] Thus, in this example, the first portion is a first split probe beam 684 and a first split conjugate beam 686 and the second portion is a second split probe beam 682 and a second split conjugate beam 688.

[00103] The balanced photodetector is an example of photodetection means 118. The balanced photodetector 672 may comprise four separate eyes for receiving the four beams 682, 684, 686, 688. The balanced photodetector may be replaced by four connected photodetectors each for receiving one of the four beams 682, 684, 686, 688. The balanced photodetector 672 may comprise a pair of eyes 674 to receive split probe beams 682, 684 and the balanced photodetector 672 may subtract the signals received from the eyes 674. The balanced photodetector 672 may comprise a pair of eyes 676 to receive split conjugate beams 686, 688 and the balanced photodetector 672 may subtract the signals received from the eyes 676. The subtracted signals received from each pair of eyes 674, 676 may then be added to produce an output signal. In an example, the balanced photodetector 672 may function as two balanced photodetectors 446 of Figure 4, one balanced photodetector 446 having the pair of eyes 674 and the other balanced photodetector 446 having the pair of eyes 676, and the balanced photodetector 672 may add the outputs of the two balanced photodetectors 446.

[00104] Throughout the description and claims of this specification, the words “comprise” and “contain” and variations of them mean “including but not limited to”, and they are not intended to (and do not) exclude other moieties, additives, components, integers or steps. Throughout the description and claims of this specification, the singular encompasses the plural unless the context otherwise requires. In particular, where the indefinite article is used, the specification is to be understood as contemplating plurality as well as singularity, unless the context requires otherwise.

[00105] Features, integers, characteristics, compounds, chemical moieties or groups described in conjunction with a particular aspect, embodiment or example of the invention are to be understood to be applicable to any other aspect, embodiment or example described herein unless incompatible therewith. All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and/or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features and/or steps are mutually exclusive. The invention is not restricted to the details of any foregoing embodiments. The invention extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed.