Beam splitters

Abstract

A temporally continuous matter wave beam splitter (14) comprising a plurality of intersecting and interfering laser beam (k.sub.r, k.sub.b), which act as waveguides for a matter wave beam. The laser beams of the waveguides each have a frequency detuned below a frequency of an internal atomic transition of the matter wave. The matter wave has a wavevector which is an integral multiple of the wavevector of the laser beams within a region of intersection of the laser beams. There is also provided an atomic interferometer (200) comprising such a continuous matter wave beam splitter, and a solid state device comprising such a continuous matter wave beam splitter, which may be part of an atomic interferometer. A cold atom gyroscope, a cold atom accelerometer or a cold atom gravimeter comprising such a solid state device are also provided. There is further provided a quantum computer comprising such a solid state device, wherein atoms of the matter wave beam are in an entangled quantum state. There is also provided a method of splitting a matter wave beam, comprising introducing the matter wave beam into a first temporally continuous laser beam, the frequency of which is detuned below a frequency of an internal atomic transition of the matter wave beam; intersecting and interfering the first continuous laser beam with a second temporally continuous laser beam, the frequency of which is also detuned below the frequency of the internal atomic transition of the matter wave beam; providing the matter wave beam with a wavevector which is an integral multiple of the wavevector of the first and second laser beams within a region of intersection of the laser beams, whereby the laser beams act as waveguides for the matter wave beam.

Claims

1. A continuous matter wave beam splitter comprising a plurality of intersecting and interfering laser beams wherein the laser beams have at least one common frequency and a matter wave beam, the laser beams being arranged to act as waveguides for the matter wave beam, wherein: the laser beams have a frequency detuned below a frequency of an internal atomic transition of the matter wave beam; and the matter wave beam has a wavevector which is an integral multiple of the wavevector of the laser beams within a region of intersection of the laser beams.

2. A continuous matter wave beam splitter according to claim 1, wherein a splitting ratio of the beam splitter is determined by at least one of a respective polarization, intensity, or diameters of at least one of the laser beams, or velocity of atoms in the matter wave beam.

3. A continuous matter wave beam splitter according to claim 1, wherein a splitting ratio of the beam splitter is substantially equal to 50:50.

4. A continuous matter wave beam splitter according to claim 1, wherein a splitting ratio of the beam splitter is substantially equal to 100:0, whereby the beam splitter can act as a mirror.

5. A continuous matter wave beam splitter according to claim 1, wherein at least one of the intersecting and interfering laser beams is bichromatic.

6. A continuous matter wave beam splitter according to claim 5, wherein the bichromatic laser beam has a first frequency which is red-detuned below a frequency of the internal atomic transition of the matter wave beam and a second frequency which is blue-detuned above the frequency of the internal atomic transition of the matter wave beam.

7. A continuous matter wave beam splitter according to claim 5, wherein the bichromatic laser beam circulates in a circular planar waveguide and intersects orthogonally and interferes with two counter-propagating laser beams, the latter having mutually orthogonal polarisations.

8. A continuous matter wave beam splitter according to claim 1, wherein at least one of the laser beams has a waveguide that is curved.

9. A continuous matter wave beam splitter according to claim 1, comprising more than two of said intersecting and interfering laser beams, the laser beams having waveguides arranged in a non-planar configuration.

10. A continuous matter wave beam splitter according to claim 1, comprising first, second, and third laser beams, wherein at least one of the first and second laser beams intersects the third laser beam, and the third laser beam having a frequency detuned above the frequency of the internal atomic transition of the matter wave beam, whereby the third laser beam provides a mirror for the matter wave beam.

11. An atomic interferometer according to claim 10, comprising at least one of a Michelson, Fabry-Perot, Mach-Zehnder or Sagnac interferometer.

12. A continuous matter wave beam splitter according to claim 1, further comprising a surface upon which the wave matter beam is situated.

13. The continuous matter wave beam splitter of claim 12, wherein the surface on which the matter wave beam splitter is situated comprises a cold atom gyroscope, a cold atom accelerometer, or a cold atom gravimeter.

14. The continuous matter wave beam splitter of claim 12, wherein the surface on which the matter wave beam splitter is situated comprises a quantum computer, wherein atoms of the matter wave beam are in an entangled quantum state.

15. A method of splitting a matter wave beam, comprising: introducing the matter wave beam into a first continuous laser beam, the frequency of which is detuned below a frequency of an internal atomic transition of the matter wave beam; intersecting and interfering the first continuous laser beam with a second continuous laser beam having at least one common frequency with as the first laser beam; providing the matter wave beam with a wavevector which is an integral multiple of a wavevector of the first and second laser beams within a region of intersection of the laser beams, whereby the laser beams act as waveguides for the matter wave beam.

16. The method according to claim 15, further comprising selecting a splitting ratio of the matter wave beam by adjusting at least one of a respective polarization, intensity or diameter of at least one of the first or second laser beams, or velocity of atoms in the matter wave beam.

17. The method according to claim 15, further comprising providing at least one of the first or second laser beams with a second frequency detuned from the frequency of the internal atomic transition of the matter wave beam, thereby making at least one of the first or second laser beams bichromatic.

18. The method according to claim 17, further comprising blue-detuning the second frequency above the frequency of the internal atomic transition of the matter wave beam.

19. The method according to claim 15, further comprising curving the waveguides of at least one of the first and second laser beams.

20. The method according to claim 15, further comprising intersecting at least one of the first and second laser beams with a third laser beam having a frequency detuned above the frequency of the internal atomic transition of the matter wave beam, thereby reflecting the matter wave beam from the third laser beam.

21. The method according to claim 15, further comprising preparing atoms of the matter wave beam in an entangled quantum state.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Embodiments of the present invention are described below, by way of example only, with reference to the accompanying drawings, in which:

(2) FIG. 1 is an isometric schematic view of a Bragg beam splitter for matter waves based on two crossed optical waveguides;

(3) FIG. 2 is a plan schematic view of a three-port waveguide beam splitter for matter waves;

(4) FIG. 3 is a plan schematic view of a waveguide Mach-Zehnder interferometer for matter waves, formed by four crossed interfering laser beams;

(5) FIG. 4 is an isometric schematic view of a waveguide Michelson interferometer for matter waves;

(6) FIG. 5 is an isometric schematic view of an atom chip waveguide Mach-Zehnder interferometer for matter waves based on two-colour evanescent light waves, which propagate along optical surface waveguide structures;

(7) FIG. 6 is a plan schematic view of a Michelson waveguide interferometer for matter waves based on two crossed Gaussian laser beams;

(8) FIG. 7 is a plan schematic view of an integrated Mach-Zehnder waveguide interferometer for matter waves;

(9) FIG. 8 is a plan schematic view of an integrated Sagnac waveguide interferometer for matter waves; and

(10) FIG. 9 is a plan schematic view of an all-optical Sagnac waveguide interferometer for matter waves based on straight laser beams.

DETAILED DESCRIPTION

(11) Referring firstly to FIG. 1, we are considering waveguides for matter waves, which are formed by focussed laser beams, both labelled k.sub.L in FIG. 1, the frequency of which is detuned sufficiently far above or below one of the internal atomic transitions of the matter waves so as not to induce such an atomic transition. Such a waveguide can be single-mode or multimode, which depends on the intensity and diameter of the laser beam.

(12) Consider two such identical waveguides, labelled 11 and 12 in FIG. 1, which intersect each other at an angle of 2 in a region labelled 13. The interference of the laser beams in the region 13 of their intersection produces a standing light wave, the angle of which with respect to the waveguides is exactly equal to and its period is equal to d=/k/sin , where k=2/ is the wave vector of the laser field. The amplitude of the standing wave depends on a degree of interference between the crossed laser beams and can be accurately tuned by their mutual polarisations or their intensities.

(13) This standing wave presents for atoms a matter wave beam splitter 13 in the form of a phase grating, which can coherently split the incident guided matter wave, labelled k.sub.dB in in FIG. 1, between the two waveguides by Bragg diffraction into reflected and transmitted components, respectively labelled k.sub.dB r and k.sub.dB t in FIG. 1 . The splitting ratio of the grating depends on the velocity of the atoms, the amplitude of the grating and its total length.

(14) It is easy to show that such a grating acts as a Bragg reflector for atoms with velocities
v=Nv.sub.r,(1)
where v.sub.r=k/m is the one-photon recoil velocity of the atom, m is the mass of the atom, and N is a whole number, which characterises the order of the Bragg diffraction.

(15) Formula (1) describes the Bragg condition for the diffraction of atoms at the light grating. The velocity v in that formula corresponds to the velocity of atoms inside the grating. In general this velocity can be different from the velocity of atoms in the waveguides. This is due to the fact that the waveguide beam splitter includes a light grating and a potential well, which is formed by the crossing laser beams.

(16) The theory of Bragg gratings is well established. According to calculations, for a grating formed by crossed laser beams of radius w=4 m and depth of the standing wave potential of 0.1E.sub.r, where E.sub.r=mv.sub.r.sup.2/2, in the case of Bragg resonance (1) at N=1, the reflectivity of Rb atoms is equal to 100%. For a depth of the standing wave potential of 0.05E.sub.r, the corresponding reflection is about 50%.

(17) In general, the intersection and interference of M laser beams forms an M-port beam splitter for guided matter waves. In that case the interference structure of the beams forms a light crystal, which splits matter waves, the wave vector of which is equal to the wavevector of light, between all the M ports of the beam splitter. Note that the intersecting light beams of such an M-port beam splitter can have any directions in 3D-space. As shown in FIG. 2, for example, the intersection and interference of 3 laser beams labelled k.sub.L forms a 3-port beam splitter labelled 23 for guided matter waves, labelled k.sub.dB.

(18) These Bragg waveguide beam splitters can be used for compact waveguide interferometers of different types. The accompanying drawings show some possible designs of Mach-Zehnder (see FIG. 3) and Michelson (see FIG. 4) waveguide interferometers, based on the beam splitters just described.

(19) In FIG. 3, the line shows the trajectory of the guided atoms labelled k.sub.dB through a Mach-Zehnder interferometer 100 and the paths of the laser beams which establish the waveguides are labelled k.sub.L.

(20) In the Michelson interferometer 200 of FIG. 4, optical potentials are formed by four non-resonant laser beams as follows: two crossed laser waveguides labelled k.sub.r, which are red-detuned from the main internal atomic transition, form an attractive (negative) potential in the region labelled 14, and two additional blue-detuned laser beams labelled k.sub.b, form a repulsive (positive) potential, serving as retro-reflective mirrors for the guided atoms in regions labelled 15 and 16.

(21) Other types of interferometers, like Fabry-Perot, Sagnac and others, can also be easily implemented.

(22) According to the condition (1) above, the waveguide interferometers use very slow atoms (v0.1-1 cm/s). Use of such slow atoms essentially increases the sensitivity of these interferometers to inertial (acceleration, rotation) and electromagnetic forces.

(23) The sensitivity of such interferometers based on Rb atoms, with a size of 1 cm by 1 cm and a flux of atoms 10.sup.6 atom/s, to gravity and accelerations can be as high as 510.sup.11 m s.sup.2 Hz.sup.0.5, and the corresponding sensitivity to rotations is expected to be about 610.sup.9 rad s.sup.1 Hz.sup.0.5. The sensitivity of such an interferometer to gradients of magnetic fields is expected to be about 410.sup.15 T m.sup.1 Hz.sup.0.5.

(24) Using bichromatic (i.e. two-colour) surface light traps and corresponding surface waveguides for matter waves, compact, integrated versions of these interferometers can be produced on a surface of a solid-state atom chip, an example of which is shown in FIG. 5. In FIG. 5, two-colour evanescent light waves, labelled k.sub.r and k.sub.b, propagate along optical surface waveguide structures 301 of an atom chip waveguide Mach-Zehnder interferometer 300 for matter waves. The arrowed line shows the trajectory of the guided atoms.

(25) The sensitivity of these interferometers makes them very attractive for different practical applications. There are several advantages of such integrated interferometers. First, the optically guided laser fields are not divergent over long distances. Second, the dipole potential of the surface optical waveguides is essentially compressed in a direction perpendicular to the surface of the substrate, which makes it possible to use these waveguides in a single mode regime without being restricted by the presence of a gravitational force.

(26) Another prospective application of these waveguide beam splitters is quantum computing based on entangled atomic states. An array of coupled atom interferometers (interferometers with common arms or beam splitters) based on such a beam splitter can be used for making a quantum computer. As soon as the depth of the light grating of the splitter depends on the internal atomic state, these splitters can be used for controlled interaction between the atoms propagating inside the optical waveguides, the strength of which depends on the internal state of the atom. The small size of the proposed waveguide beam splitter and the possibility of its integration into a solid-state chip offers a possibility to make the whole quantum processor very compact.

(27) The simplest waveguide interferometer, based on free-propagating laser beams, is a Michelson interferometer 400, as shown in FIG. 6. It is formed by two monochromatic Gaussian laser beams, labelled LB1 and LB2 in FIG. 6, which intersect each other in the region 17 of their waists. Both beams are red-frequency-detuned from the internal atomic transition, such that they trap and guide atoms.

(28) The interference between the laser beams in the crossing region produces an optical lattice, which works as a Bragg beam splitter for atoms, which propagate along the beams with corresponding velocities. Initially, the atoms propagate along one of the laser beams LB1 towards the crossing region, as indicated by the arrow labelled in in FIG. 6. At the crossing region of the laser beams, these atoms are coherently split into two partial waves, which then propagate along the LB1 and LB2 beams. These atoms are slowed down by the restoring optical dipole force along the laser beams and at some point reverse their direction of motion. After that, the two returning partial waves experience interference with each other at the Bragg beam splitter and produce the two output beams, labelled out1 and out2, which contain information about the phases of the interfering de Broglie partial waves and all corresponding information about the external electromagnetic and inertial forces.

(29) We shall now consider further the integrated version of waveguide optical interferometers for matter waves, which are based on planar optical waveguides and bichromatic evanescent light waves, as described above. One of the main advantages of such integrated waveguides for atoms is that they can be curved. This opens new very attractive opportunities. For example, the Mach-Zehnder interferometer 500 of FIG. 7 can use only two beam splitters in the regions labelled 18 and 19 in FIG. 7, instead of four beam splitters in the Mach-Zehnder interferometer 300 based on free propagating laser beams of FIG. 5 because the waveguides 501 are curved. The guided matter waves then follow the paths of the arrows labelled in1, out1 and out2 in FIG. 7.

(30) FIG. 8 shows an integrated Sagnac waveguide interferometer 600 for matter waves. The main part of it is a circular planar waveguide 20, which guides two optical running modes of different frequency. This light forms a bichromatic evanescent optical field CLW outside the waveguide, which is used to guide cold atoms along the circular waveguide. The coupling of cold atoms to the circular waveguide is performed with a special Bragg beam splitter, which is produced by three crossed laser beams, labelled LB1, LB2 and CLW. It is important that the beams LB1 and LB2 are counter-propagating and orthogonal to the circular light wave CLW. In that case, the interference of the LB1 and LB2 beams with the CLW wave produces two orthogonal optical lattices, which split the incident atoms labelled in1 into two partial matter waves, one of which propagates along the circular waveguide clockwise, and the other one anticlockwise. After a full turn of these counter-propagating partial matter waves, they interfere at the Bragg beam splitter and form the two complementary output atomic beams of the interferometer, labelled out1 and out2. Such a Sagnac atom interferometer is sensitive to its rotation with respect to its axis of symmetry, but is absolutely insensitive to linear accelerations, which is absolutely important for quantum gyroscopes. Another unique property of this Sagnac waveguide interferometer is that it is insensitive to the phase shifts of the de Broglie wave, which are generated by the trapping optical potential, because of exactly the same pass of the two partial matter waves along the same circular waveguide.

(31) The laser beams LB1 and LB2 ideally should not interfere with each other to avoid an additional standing light wave along these beams, which might essentially change the propagation of atoms along these beams via their Bragg diffraction. This can be achieved by mutually orthogonal polarisation of these beams or by other means. The LB1 and LB2 beams can be either bichromatic evanescent light fields, or free propagating laser beams, which are essentially overlapped with the evanescent light field of the circular resonator CLW.

(32) The coupling efficiency of the atoms to the ring waveguide can be changed by varying the light intensities of the LB1 and LB2 beams. In particular, these can be changed by a very small amount, which also means very little decoupling of atoms from the ring resonator. This means that atoms can run many turns in the ring waveguide before they are decoupled, which should increase the sensitivity of the Sagnac interferometer proportionally to the number of turns of the circular waveguide, assuming the same output flux of atoms in the matter wave beam.

(33) FIG. 9 shows the general structure of an all-optical waveguide Sagnac interferometer for matter waves. It consists of a waveguide for atoms in the form of a closed figure, e.g. a square as shown, and, which is produced by four laser beams (B1, B2, B3, B4) which propagate either clockwise or anti-clockwise. All these laser beams have the same frequency and the same polarisation. For example, all the beams can be linearly polarised, such that the direction of the polarisation is perpendicular to the plane of the ring-like waveguide. At the four regions of intersection of the beams B1, B2, B3 and B4 the interference between them leads to the formation of standing light waves, which act on guided atoms as Bragg gratings of 100% reflectivity, provided that the longitudinal velocity of the atoms satisfies the Bragg condition. Two additional counter-propagating laser beams B5 and B6 intersect one of the arms B1 of the waveguide and form a symmetric Bragg beam splitter (SBS) for guided matter waves. The beams B5 and B6 have the same optical frequency as the other beams. The beams B5 and B6 are used for guiding matter waves and also for coupling and outcoupling of them to or out of the waveguide of the Sagnac interferometer. To avoid the interference between the beams B5 and B6, they have orthogonal polarisations. For example, they can have orthogonal linear polarisations, which are at +/45 degrees to the plane of the interferometer. The partial interference of these beams to the beam B1 leads to the production of two orthogonal standing waves (Bragg gratings) at the region of intersection of the beams B5, B6 and B1. Such a crossed Bragg grating splits the atoms, which initially propagate along the waveguide B5, into two partial waves, one of which propagates along the B1 waveguide while the other propagates in the opposite direction. After full propagation around the waveguide in two opposite directions, the two partial matter waves interfere at the symmetric beam splitter (SBS), where the atoms are decoupled from the Sagnac interferometer either in B5 or B6 input/output ports of the SBS, which depends on the relative phase of the partial matter waves, and therefore on the rotational speed of the Sagnac interferometer.

(34) The coupling and outcoupling strength of the SBS can be adjusted by changing the intensity of the laser beams B5 and B6, which changes the potential depth of the corresponding Bragg gratings. To avoid decrease of the atom guiding efficiency of the B5 and B6 beams at low intensities, the beams B5 and B6 can be superimposed with an additional beam of different frequency, which provides guiding of atoms but does not form a Bragg grating at the intersection region with the B1 beam.

(35) The same principle of the waveguide Sagnac interferometer for matter waves based of straight waveguides can be applied to the integrated version of the interferometers, which were discussed earlier.

(36) The shape of the figure formed by the four waveguides in FIG. 9 may be other than a square e.g. rectangular or parallelepipedal. In a modification three laser beams define a triangular figure. Alternatively, five or more laser beams define a corresponding polygonal figure.

(37) All optional and preferred features and modifications of the described embodiments and dependent claims are usable in all aspects of the invention taught herein. Furthermore, the individual features of the dependent claims, as well as all optional and preferred features and modifications of the described embodiments are combinable and interchangeable with one another.

(38) The disclosures in British patent application number 1410298.2, from which the present application claims priority, and in the abstract accompanying this application are incorporated herein by reference.