Optical manipulation of atoms or molecules

Abstract

An optical beam-forming apparatus 10 is configured to form optical beams of light for manipulating cold atoms or cold molecules in a chamber of a magneto-optical trap (MOT). The apparatus comprises a

Description

FIELD

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

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

[03] The technique of laser cooling exploits the condition in which the frequency of a laser beam is set close to resonance with an energy difference between two energy levels within the atoms of the gas. This allows transitions of the quantum states of atoms of gas being cooled. An atom of gas moving in the +x direction with a velocity vx is caused to interact with a counterpropagating laser beam of light having a frequency f which is close to resonance with one of the allowed quantum transitions of the atom: f = to + 5, in which to is the frequency of a photon required to achieve the quantum transition in the atom, and 6 « to is a small frequency detuning. As seen from the perspective (inertial frame) of the atom, the source of the laser light moves with a relative velocity (vx) towards the atom. Due to the Doppler effect, the frequency of the laser light (photon energy) is shifted to a frequency f in proportion to that relative velocity : f = f(l+v> / c) ~ a) + 6 + u) [v / c],

[04] If the value of 6 is selected so that 6 = - co [v^c], where c is the speed of light in vacuum, then f = co. Under these conditions the laser is in resonance with an atomic transition of the atoms within the gas moving in the +x direction. Thus, when a gas atom absorbs a photon from the laser, it is excited to an excited quantum state for a short period of time and subsequently returns to the original un-excited quantum state by emitting a photon spontaneously in a random direction.

[05] Each time this quantum transition cycle is repeated, a net change (Ap) in momentum of the atom occurs in the +x direction. This net change is equal to the momentum of the initially absorbed photon, which is given by: Ap = - h / A, where h is Planck’s constant and A is the wavelength of the laser light The absorption of the photon, and therefore the momentum change, is always in the -x direction. However, importantly, the momentum change experienced by atom caused by the subsequent spontaneous photon emission averages-out to zero. This is because the direction of spontaneous photon emission is random. The slowing force imposed upon atoms by the cooling laser beam, is equal to the rate of change of momentum experienced by an atom. This is given by the momentum change per absorption-emission cycle, multiplied by the rate of such cycles. Accordingly, repeated photon absorption-emission cycles generate a net slowing force in the -x direction, which reduces the velocity of gas atoms in the +x direction.

[06] However, this Doppler cooling process begins to become ineffective when the detuning required for cooling becomes comparable to the natural line width (Af) of the atomic transition in question. As a consequence, the minimum thermal energy of the atom approximately equal to hAf. This means that the minimum temperature (T) will be about: T ~ hAf / kB, where kB is Boltzmann’s constant.

[07] Laser cooling with a single laser beam is effective when the laser detuning (6) is larger than the line width (Af) of the atomic transition. However as the atoms cooled down, the necessary detuning becomes comparable to the line width and atoms moving in the -x direction then experience an accelerating force which cancels the slowing force experienced by atoms moving in the +x direction. The increased speed of the former atoms reheats the latter atoms by inter-atomic collisions. Optical Molasses

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

[09] Fx = F+ + F~

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

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

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

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

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

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

[16] The energy of a magnetic (Zeeman) sub-level of a spin state in a magnetic field B is given by the magnetic interaction energy: E = gujBMB in which gL is the Lande g-factor, and gB is the Bohr magneton and M is an integer (quantum number) for the different Zeeman sub-levels. Right-circular polarized light is able to drive atomic transitions to some split spin states when propagating in one direction along the z-axis, whereas left-circular polarized light is able to drive atomic transitions to the split spin states when propagating in the other (opposite) direction along the z-axis. This is due to the conservation of angular momentum. As a result, an atom bathed within two such counter-propagating laser beams will experience a net force pushing it towards the location z = 0 where the magnetic field is zero and where the Zeeman splitting ceases. At position z = 0, an atom feels no net force.

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

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

[19] However, the optical apparatus employed to prepare, direct and control the multiple laser beams in 2D-MOTs and 3D-MOTs is large, expensive and typically bespoke or peculiar to the experimentalist who has created the MOT in question.

[20] The invention aims to address these matters. SUMMARY

[21] In a first aspect, the invention provides an optical beam-forming apparatus configured to form optical beams of light for manipulating cold atoms or cold molecules in a chamber of a magneto-optical trap (MOT), the apparatus comprising: a first optical beam-former and a second optical beam-former; wherein each said optical beam-former is configured to receive a respective input optical beam of light and therewith to form a respective pair of optical beams of linearly polarised light for output into the chamber of the MOT; and, wherein the orientations of linear polarisation of each of the four optical beams are mutually substantially parallel.

[22] A particular benefit of producing four parallel beams of this type is that it avoids the need to use one single, large-diameter optical beam to bathe a system of multiple separate mirrors concurrently, from which to generate all of the counter-propagating optical beams required for a 3D-MOT using different reflected sections of the same one optical beam. A single such beam requires a great deal of space within which to expand to sufficient beam diameter to achieve the required uniformity (of intensity) across the advancing wave front of the beam. This is a significant obstacle to miniaturisation, which is overcome by the invention.

[23] Desirably, the first optical beam-former and / or the second optical beam-former is configured to form said respective pair of optical beams to be substantially parallel. A benefit of forming the beams to be substantially parallel is that it becomes easier to re-direct the parallel optical beams to cross each other (i.e. not parallel, but coplanar and intersecting at some location), or to be coaxial (i.e. parallel and propagating along a common axis: either in the same or opposite directions), using small and simple folding optics (e.g. simple mirrors). This reduces the space and cost required in achieving such geometries, and enables greater miniaturisation. Preferably, the first and / or second optical beam formers are configured to direct the two optical beams of the pair of optical beams, in respective directions that are both substantially parallel and pointing / propagating in the same direction. The two optical beams of the pair of optical beams are preferably laterally separated (i.e. substantially parallel but not collinear).

[24] Desirably, the first optical beam-former and the second optical beam-former are configured to form mutually substantially parallel said optical beams, thereby providing four substantially parallel optical beams. A benefit of forming all four of the optical beams to be substantially parallel is that it becomes easier to re-direct any number of the beams (e.g., two, three or four of them) to cross each other (i.e. not parallel, but coplanar and intersecting at some location), or to be coaxial (i.e. parallel and propagating along a common axis: either in the same or opposite directions), using small and simple folding optics (e.g. simple mirrors). This is particularly advantageous in tetrahedral mirror (three mirror surfaces) or pyramidal mirror (four mirror surfaces) structures that may be advantageous in 2D-MOT and / or 3D-MOT applications. This reduces the space and cost required in achieving such geometries, and enables greater miniaturisation.

[25] The first optical beam-former and / or the second optical beam former may comprise a dedicated mounting plate (e.g. rigid) configured to hold the optical elements of the optical beamformer in the required optical configuration / communication. Some or all optical elements of the optical beam-former may be rigidly fixed to the mounting plate. The optical elements of both the first optical beam-former and the second optical beam former may share the same mounting plate. The provision of a mounting plate has the advantage that the optical beam former may be attached and detached from a greater assembly / apparatus of which it forms a part, without disrupting the careful optical alignments of the optical elements of the beam former in question. This permits ease of servicing of the greater assembly / apparatus in question (e.g. a cold atom source, an accelerometer etc.) and modular design.

[26] The first and / or second optical beam former may comprise a respective polarising beamsplitter configured to receive an input optical beam and to split the input optical beam in to two separate optical beams. The polarising beam splitter is preferably arranged to impose a first linear polarisation state upon one of the two separate optical beams, and to impose a second linear polarisation state upon the other of the two separate optical beams in which the first polarisation state differs from the second polarisation state. Preferably the first polarisation state is perpendicular (i.e. in polarisation position angle) to the second polarisation state.

[27] The polarising beam splitter may comprise a beam-splitter cube. The first and / or second optical beam former may comprise a respective pair of mirrors configured to receive one of the two separate optical beams from the polarising beam-splitter and redirect the received separate optical beam through a first angle of 90 degrees by reflection from a first mirror of the pair of mirrors, and subsequently through a second angle of 90 degrees by reflection from a second mirror of the pair of mirrors. Preferably the first angle of 90 degrees lies in a plane perpendicular to the plane containing the second angle of 90 degrees. Preferably, the first mirror is substantially planar. Preferably, the direction of the polarisation transmission axis (e.g. polarisation position angle of the polarised light transmitted through it) of the polarising beamsplitter is parallel to the plane surface of first mirror, when projected upon that plane surface. Preferably, the second mirror is configured to redirect the received separate optical beam in a direction which is substantially perpendicular to the plane containing the first 90 degree angle. Preferably, the polarising beam splitter and the second mirror are configured to direct the two separate optical beams in respective directions that are both substantially parallel and pointing / propagating in the same direction. This arrangement has the benefit of compactly permitting the two separate polarised optical beams output by the polarising beam splitter with non-parallel linear polarisations, to be formed into the pair of optical beams output by the optical beam former having substantially parallel linear polarisations.

[28] Preferably, the first optical beam-former includes a polarisation controller configured to adjustably impose an orientation of linear polarisation upon said input optical beam thereby to form a linearly polarised input optical beam, and a polarising beam-splitter configured to split the linearly polarised input optical beam into a pair of optical beams of linearly polarised light of relative optical intensities adjustable according to said imposed orientation of linear polarisation, and therewith the first optical beam-former is configured to form said respective pair of optical beams.

[29] The polarisation controller may comprise a linear polarising optical element (e.g. a polarising filter, or a half-wave plate, or a rotatable output end of a polarisation-maintaining optical fibre) via which the input beam is received into (or passed to or passed through) the optical beam former. Adjusting the polarising properties of the input optical beam allows the effects of the polarising beam-splitter to be optimised. For example, the orientation / position-angle of linearly polarised input light provided by the polarisation controller may be adjusted controllably to control the intensity of the component of the optical beam transmitted through the polarising beam-splitter, e.g. in accordance with Malus’ Law. Accordingly, the reciprocal change is achieved in the intensity of the component of the optical beam reflected by polarising beamsplitter is achieved. In this way, the relative intensities of the two beams in the pair of optical beams output by the optical beam former, may be easily and accurately controlled in a compact way.

[30] Preferably, the second optical beam-former includes a polarisation controller configured to adjustably impose an orientation of linear polarisation upon said input optical beam thereby to form a linearly polarised input optical beam, and a polarising beam-splitter configured to split the linearly polarised input optical beam into a pair of optical beams of linearly polarised light of relative optical intensities adjustable according to said imposed orientation of linear polarisation, and therewith the second optical beam-former is configured to form said respective pair of optical beams. Desirably, the polarisation controller is controllable to adjust the imposed orientation of linear polarisation thereby to controllably adjust said relative optical intensities of the optical beams of the said respective pair of parallel optical beams to be substantially the same. The polarisation controller may comprise a linear polarising optical element (e.g. a polarising filter, or a half-wave plate, or a rotatable output end of a polarisation-maintaining optical fibre) via which the input beam is received into (or passed to or passed through) the optical beam former. Adjusting the polarising properties of the input optical beam allows the effects of the polarising beam-splitter to be optimised. For example, the orientation / position-angle of linearly polarised input light provided by the polarisation controller may be adjusted controllably to control the intensity of the component of the optical beam transmitted through the polarising beam-splitter, e.g. in accordance with Malus’ Law. Accordingly, the reciprocal change is achieved in the intensity of the component of the optical beam reflected by polarising beamsplitter is achieved. In this way, the relative intensities of the two beams in the pair of optical beams output by the optical beam former, may be easily and accurately controlled in a compact way.

[31] Preferably, the optical beam-forming apparatus includes a circular polariser configured to receive an optical beam of the four parallel optical beams to convert the polarisation thereof from a state of linear polarisation to a state of circular polarisation. The provision of circular polarisation has the advantage of permitting control over the relative rates of atomic / molecular transitions occurring in atoms / molecules by absorption of circularly polarised photons of light from the optical beam in question. This may be advantageous in 2D-MOT and 3D-MOT processes. The circular polariser may comprise a quarter-wave plate configured to receive the optical beam and to impose upon it a circular polarisation.

[32] The circular polariser may be configured to receive each optical beam of the four parallel optical beams simultaneously thereby simultaneously to convert the polarisation thereof from a state of linear polarisation to a state of circular polarisation. This allows for greater compactness and miniaturisation.

[33] The optical beam-forming apparatus may comprise a mounting plate bearing one or both of the first and second optical beam formers, e.g. as described above, wherein the mounting plate defines one of more through-openings positioned in register with the optical path defined by one or both of the first and second optical beam formers thereby to permit an optical beam of the pair of optical beams formed by one or both of the first and second optical beam formers to pass through the mounting plate. Preferably, the one or more through-openings are configured such that each of the optical beams formed by one or both of the first and second optical beam formers passes through the mounting plate. A benefit of this arrangement is that optical elements of the beam former may be located on the reverse side of the mounting plate thereby permitting access to those optical elements without having to dismount the mounting plate from a greater structure (e.g. cold atom source, accelerometer etc.) to which it is mounted, and into which the beams of the optical beam forming apparatus may be directed / injected, in use. This permits greater versatility and ease of use of the optical beam-forming apparatus.

[34] The optical beam-forming apparatus may comprise a mirror (e.g. plane mirror) disposed upon a mounting plate of the first and / or second optical beam formers at a position between the first optical beam former and the second optical beam former on a side of the mounting plate which is opposite (reverse side) to that upon which the first and / or second optical beam formers are mounted. Preferably, the mirror is a plane mirror the plane of which is perpendicular to the direction of propagation in which the first and / or second optical beam formers are configured to direct the respective pair of optical beams. The mirror may thereby ‘face towards’ the direction in which the pair of optical beam of the first and / or second optical beam formers will propagate in use. This may be a direction towards a 2D-MOT chamber or a 3D-MOT chamber. A further optical beam may be directed towards the mirror in a direction emanating from the 2D-MOT chamber or the 3D-MOT chamber permitting it to retro-reflect (e.g. counter-propagate, e.g. antiparallel) from the mirror back into the 2D-MOT chamber or a 3D-MOT chamber. This is very useful and compact arrangement for providing an additional optical beam (or beams) for use in 2D-MOT or 3D-MOT processes. For example, the four optical beams produced by the optical beam-forming apparatus may be complemented by two additional beams (e.g. a counterpropagating pair), resulting in six beams. The six beams may be directed substantially parallel to each other for insertion into a 2D-MOT chamber or a 3D-MOT chamber.

[35] In a second aspect, the invention may provide a magneto-optical trap (MOT) comprising an optical beam-forming apparatus as described above.

[36] The magneto-optical trap (MOT) may comprise the chamber of the MOT, in which the chamber of the MOT comprises a pyramidal mirror assembly for receiving the optical beams of light and for reflecting the received optical beams of light into one or more pairs of counterpropagating optical beams of light for manipulating cold atoms or cold molecules.

[37] The magneto-optical trap (MOT) may include a magnetic field apparatus configured to provide a magnetic field arranged to concentrate gas atoms or molecules cooled or manipulated using the optical beam-forming apparatus.

[38] In a third aspect, the invention may provide a cold atom source comprising a magnetooptical trap (MOT) as described above.

[39] In a fourth aspect, the invention may provide an accelerometer comprising a magnetooptical trap (MOT) as described above, and / or comprising a cold atom source as described above.

[40] In a fifth aspect, the invention may provide a cold atom source comprising a magnetooptical trap (MOT) configured to form optical beams of light for manipulating cold atoms or cold molecules in a chamber of the MOT, the apparatus comprising: a chassis comprising an optical beam-former configured to form the optical beams of light; a cartridge comprising the chamber of the MOT; wherein the chassis comprises a compartment into which the cartridge is removably insertable via an opening in the chassis to position the chamber of the MOT in optical alignment with the optical beam-former. This arrangement permits easy removal and insertion of a cartridge into the chassis of the MOT without requiring disassembly or movement of precisely-aligned optical components mounted upon the chassis of the MOT. As s result, different MOT chamber configurations, sample “cold atom” materials may be easily and quickly changed by simply removing an existing cartridge and replacing it with another cartridge, or replacing it with the same cartridge in adjusted form (e.g. replenished with sample “cold atom” materials).

[41] The cold atom source may comprise a three-dimensional magneto-optical trap (3D-MOT) configured to form optical beams of light for manipulating cold atoms or cold molecules in a chamber of the 3D-MOT, and a two-dimensional magneto-optical trap (2D-MOT) configured to form further optical beam of light for manipulating cold atoms or cold molecules in a chamber of the 2D-MOT. The cartridge preferably comprises the chamber of the 2D-MOT arranged in communication with the chamber of the 3D-MOT to supply cold atoms or cold molecules to the 3D-MOT for manipulation. The cartridge is preferably removably insertable via the opening in the chassis to position the chamber of the 2D-MOT in optical alignment with the optical beamformer.

[42] In the cold atom source, preferably the chassis comprises one or more abutment lugs which protrude from the chassis into the hollow of the chamber such that the cartridge when fully inserted into the chamber abuts against the one or more abutment lugs, wherein the depth of protrusion of each abutment lug is configured to position the abutted cartridge in said optical alignment with the optical beam-former. Abutment lugs may be arranged such that at least one abutment lug projects into the compartment in a direction transverse to the direction in which at least one other abutment lug projects. These directions may be coplanar. The chamber may present a chamber floor, a chamber ceiling separated by chamber walls upon which the abutment lugs are disposed. The chamber floor and / or the chamber ceiling may bear upon (e.g. extending over / across) a respective abutment gasket adapted to protrude from the chassis floor / ceiling surface into the hollow of the chamber such that the cartridge when fully inserted into the chamber abuts against the one or more abutment gasket, wherein the depth of protrusion of each abutment gasket is configured to position the abutted cartridge in said optical alignment with the optical beam-former. Respective abutment gasket upon the chamber floor and / or the chamber ceiling preferably oppose each other. The opposing abutment gaskets may be aligned in register such that the peripheral outer edges thereof are aligned in mutual register. One or each abutment gasket may comprise through-openings arranged to be aligned in register with a corresponding optical opening in the cartridge when the cartridge is in said optical alignment with the optical beam-former.

[43] Desirably, one or more of the abutment lugs comprises a convex surface and the cartridge comprises one or more substantially flat abutment surfaces against which the convex surface of a respective abutment lug is arranged to abut when the cartridge when fully inserted into the chamber.

[44] Preferably, the chamber of the 3D-MOT comprises a pyramidal mirror assembly for receiving the optical beams of light and reflecting the received optical beams of light into one or more pairs of counter-propagating optical beams of light.

[45] Desirably, the MOT comprises a two-dimensional magneto-optical trap (2D-MOT) in which the chamber of the 2D-MOT comprises a mirror assembly for receiving the further optical beam of light and reflecting the received further optical beam of light into a pair of counterpropagating further optical beams of light.

[46] Desirably, the chamber of the 2D-MOT comprises a mirror assembly for receiving the further optical beam of light and reflecting the received further optical beam of light into a pushbeam of light for pushing cold atoms or cold molecules in the chamber of the 2D-MOT towards the chamber of the 3D-MOT.

[47] Desirably, the MOT comprises a three-dimensional magneto-optical trap (3D-MOT) in which the cartridge comprises an interferometry chamber arranged in communication with the chamber of the 3D-MOT for receiving cold atoms or molecules therefrom as a moving optical molasses.

[48] Desirably, the cold atom source comprises optical access ports configured for admitting one or more beams of light into the interferometry chamber for manipulating and interrogating the atoms therein.

[49] In a sixth aspect, the invention may provide an accelerometer comprising a cold atom source as described above.

[50] In a seventh aspect, the invention may provide a vehicle comprising an accelerometer as described above.

[51] Desirably, the vehicle is an aircraft, or a sea-going vessel, or a land vehicle, or a spacecraft.

[52] In an eighth aspect, the invention may provide amethod to form optical beams of light for manipulating cold atoms or cold molecules in a chamber of a magneto-optical trap (MOT), the method comprising: providing a first optical beam-former and a second optical beam-former; by each said optical beam-former, receiving a respective input optical beam of light and therewith forming a respective pair of optical beams of linearly polarised light, and outputting each pair of optical beams into the chamber of the MOT; and, wherein the orientations of linear polarisation of each of the four optical beams are mutually substantially parallel.

[53] Desirably, the method includes, by the first optical beam-former and / or the second optical beam-former, forming said respective pair of optical beams to be substantially parallel.

[54] The method may include, by the first optical beam-former and / or the second optical beam-former, forming the first optical beam-former and the second optical beam-former are configured to form mutually substantially parallel said optical beams, thereby providing four substantially parallel optical beams.

[55] The method may include, by said first optical beam former, adjustably imposing an orientation of linear polarisation upon said input optical beam thereby to form a linearly polarised input optical beam, and splitting the linearly polarised input optical beam into a pair of optical beams of linearly polarised light, and adjusting the relative optical intensities thereof according to said imposed orientation of linear polarisation, thereby forming said respective pair of optical beams.

[56] Desirably, the method includes, by said second optical beam-former, adjustably imposing an orientation of linear polarisation upon said input optical beam thereby to form a linearly polarised input optical beam, and splitting the linearly polarised input optical beam into a pair of optical beams of linearly polarised light, and adjusting the relative optical intensities thereof according to said imposed orientation of linear polarisation, thereby forming said respective pair of optical beams.

[57] Preferably, the method includes adjusting the imposed orientation of linear polarisation thereby controllably adjusting said relative optical intensities of the optical beams of the said respective pair of optical beams to be substantially the same.

[58] Desirably, the method includes converting the polarisation of an optical beam of at least one of, or each of, the four parallel optical beams from a state of linear polarisation to a state of circular polarisation.

[59] Preferably, the method includes simultaneously converting the polarisation of each of the four parallel optical beams from a state of linear polarisation to a state of circular polarisation.

[60] According to additional aspects of the invention, there is provided an optical beamforming apparatus, or a magneto-optical trap (MOT), or a cold atom source, or an accelerometer, each of which is described above, in which the magneto-optical trap (MOT) comprises a three-dimensional magneto-optical trap (3D-MOT) and / or comprises a two-dimensional magneto-optical trap (2D-MOT).

[61] Typically the velocity of a “cold atom” would be 'thermally distributed' around a target velocity according to the temperature of the atom cloud. The term “cold atom” when used in this specification, includes a reference to the temperature of the “cold atoms” in question being less than 1 (one) Kelvin (K), or preferably not greater than about 100 pK. Desirably, the temperature of the “cold atoms” in question is not greater thanlO pK. The term “cold molecule” may also be understood in this way. For example, an atom or molecule, respectively, which has a kinetic energy (E) sufficiently small that the equivalent thermal temperature (7) of the atom or molecule (i.e. according to: E=(3 / 2)kT, where k is Boltzmann’s constant) has a value which is less than 1 (one) Kelvin (K), or preferably not greater than about 100 pK, or more preferably not greater thanlO pK. However, the disclosures herein are not limited to this interpretation of the term “cold atom’” and the term “cold molecule”, unless otherwise indicted. The optical beam forming apparatus may be configured to manipulate (e.g. as part of a cooling process or otherwise) atoms or molecules in or for a ‘cold atom apparatus’.

[62] An “inertial atom source” is a source of “cold atoms” with a suitably well-defined velocity such that the population is appropriate for use in a “cold atom inertial sensor”. The well-defined velocity' may, for example, be as close as practicable to 0 m / s (zero m / s) for stationary atoms coming from a stationary molasses phase, or ‘x’ m / s for atoms which are moving in unison in a controlled direction as would be the case after a 'moving molasses phase'. The term “inertial atom source” when used in this specification, may be understood to include reference to a source of such atoms, and to a source that provides atoms which cooled to have thermal velocity distributions with characteristic temperature not greater than 100 pK.

[63] For example, a thermal distribution of rubidium (Rb87) atoms at a temperature of 100 pK will cause the “cold atoms” to have a velocity standard deviation (velocity spread) of about 66.0 mm / s. A typically velocity that may be used to launch the “cold atoms” collectively through an MOT may be about 1 m / s. Thus, a typical velocity of a group of “cold atoms” collectively would be about 1.0 ± 0.07 m / s.

[64] The invention, in a further aspect, may provide an “inertial atom source” comprising an optical beam-forming apparatus, or a magneto-optical trap (MOT), ora cold atom source, or an accelerometer, each of which is described above, as described above. Other words, the invention may provide a cold atom source for a so-called “atomic inertial sensor”, to use a terminology known in the art. In a yet further aspect, the invention may provide an “atomic inertial sensor” comprising such a cold atom source.

[65] In relation to the term “substantially parallel”, when used in this specification, it is to be understood that this term may be interpreted purposively to mean: as close to exactly parallel as reasonably and practicably possible for achieving the purpose at hand. An example of the term “substantially parallel” is: within the angular range from exactly parallel (no angular deviation / divergence) to about “0” degrees deviation / divergence from exactly parallel. Here, the angle “0” is preferably five (5) degrees, or more preferably four (4) degrees, or yet more preferably three (3) degrees, or even more preferably two (2) degrees, or yet more preferably one (1) degree.

[66] The term “expand” may be understood to mean, for example, to increase the cross-sectional area of an optical beam whilst substantially providing collimation in / of the expanded optical beam (e.g. in at least one dimension thereof transverse to the beam axis), optionally with a small degree of convergence (e.g. in at least one dimension thereof transverse to the beam axis) such as towards a notional focal point or the like. However, the disclosures herein are not limited to this interpretation of the term ‘expand’, unless otherwise indicted.

[67] The term “about” when used in this specification refers to a tolerance of ±10%, of the stated value, i.e. about 50% encompasses any value in the range 45% to 55%, In further aspects or embodiments “about” refers to a tolerance of ±5%, ±2%, ±1%, ±0.5%, ±0.2% or 0.1% of the stated value. BRIEF DESCRIPTION OF DRAWINGS

[68] There now follows a detailed description of certain examples and preferred embodiments of the invention which are presented as an aid to understanding the broader general concept of the invention, by way of example and with reference to the following drawings of which:

[69] Figure 1 presents a perspective view of a “moving molasses” cold atom source configured for use as an inertial atom source (e.g. in an accelerometer);

[70] Figure 2 presents a plan view of the cold atom source presented in figure 1;

[71] Figure 3 presents a perspective view of the cold atom source illustrated in figure 1, with certain component parts removed in order to reveal internal components within the cold atom source;

[72] Figure 4 presents a magnified view of the view presented in figure 3;

[73] Figure 5 presents the view presented in figure 4, with certain component parts further removed in order to further reveal internal components within the cold atom source;

[74] Figure 6 presents a perspective view of the cold atom source presented in figure 1 with yet further certain component parts removed in order to yet further reveal internal components within the cold atom source;

[75] Figure 7 presents the perspective arrangement presented in figure 6 in which detachable components of the cold atom source are detached, in normal use;

[76] Figure 8 presents a side perspective view of the arrangement presented in figure 7;

[77] Figure 9A presents an underside perspective view of the arrangement presented in figure 7;

[78] Figure 9B presents a perspective view of the arrangement of selected parts of the apparatus of Figure 9A;

[79] Figure 10 presents a side perspective view of the arrangement presented in figure 8 with certain components removed in order to reveal internal components of the cold atom source;

[80] Figure 11 presents a side perspective view of the specific elements of the cold atom source as they are arranged within the cold atom source illustrated in figures 1 to 10, but with the majority of the components of the cold atom source removed from the view in order to improve clarity;

[81] Figure 12 presents a side perspective view of specific elements of the arrangement illustrated in figure 11, with certain components removed in order to improve clarity;

[82] Figure 13 presents a further side perspective view of the arrangement illustrated in figure 11;

[83] Figure 14 presents a yet further side perspective view of the arrangement illustrated in figure 12 and figure 13 in which the trajectory of 3D MOT transverse cooling beams input into the cold atom source are indicated;

[84] Figure 15 illustrates a perspective view of elements of the 3D MOT transverse cooling beam delivery optics of the cold atom source, as illustrated in figures 1 to 14;

[85] Figure 16 illustrates an underside view of the 3D MOT transverse cooling beam delivery optics in which the trajectory of 3D MOT delivered transverse cooling beams within the cold atom source are indicated;

[86] Figure 17 illustrates the chassis of a cold atom cell cartridge employed within the cold atom source illustrated in figures 1 to 16, in which six optical beams delivered to the 3D MOT cooling chamber are schematically illustrated;

[87] Figure 18 schematically illustrates the optical beam delivery components for delivery of the six optical beams illustrated in figure 17;

[88] Figure 19A illustrates a plan view of the underside of the cold atom source illustrated in figure 1;

[89] Figure 19B illustrates a magnified perspective view of the cold atom source as illustrated in figure 19A;

[90] Figure 20A illustrates a perspective side view of the underside of the cold atom source illustrated in figure 19A, with certain components removed from the apparatus to aid clarity;

[91] Figure 20B illustrates a magnified perspective view of the cold atom source as illustrated in figure 20A;

[92] Figure 21 illustrates a perspective side view of the underside of the cold atom source illustrated in figure 19A with yet further components removed from the apparatus to aid clarity;

[93] Figure 22A illustrates a perspective side view of the cold atom source illustrated in figure 1, with the majority of the chassis of the apparatus removed, to aid clarity, leaving the principal optical components of the apparatus in situ with the relative positions preserved;

[94] Figure 22B illustrates a perspective view of the underside of the cold atom source optical components illustrated in figure 22A;

[95] Figure 23A illustrates a side view of the cold atom source of figure is 22A and 22B with yet further chassis components removed, to aid clarity, leaving the principal optical components of the apparatus in situ and indicating the trajectory of optical light beams formed by these principal optical components, in use;

[96] Figure 23B illustrates a perspective side view of the cold atom source as illustrated in figure 23A;

[97] Figures 23A and 23D show schematic views of principal optical components in a beam forming apparatus of the cold atom source for use in conjunction with a 2D MOT chamber for producing an initial 2D MOT cooling of atoms;

[98] Figure 23E schematically illustrates the expansion of a laser line of light input to an optical beam expander of the beamforming apparatus shown in figures 23A and 23B, to produce a forwardly propagating wall of light;

[99] Figure 23F graphically illustrates the distribution of light intensity across the advancing face of the forwardly propagating wall of light illustrated in figure 23E;

[100] Figures 24A, 24B and 24C each schematically illustrate the process of delivery of “optical molasses” cold atoms within the cold atom cell cartridge illustrated in figure 17, by a process of initial 2D MOT cooling of atoms followed by a 3D MOT cooling of those atoms, and subsequently the provision of “moving molasses” from the 3D MOT cooling chamber of the cold atom cell cartridge;

[101] Figure 25 shows a flow diagram of steps in performing cold atom inertial measurement using the inertial atom source according to preferred embodiments of the invention;

[102] Figure 26 schematically shows the atomic transitions driven by circularly polarised photons at locations within an anti-Helmholtz magnetic field for the purposed of a 2D-MOT and a 3D-MOT. DESCRIPTION OF EMBODIMENTS

[103] In the figures, like items are assigned like reference symbols for consistency. In the following, the terms “light beam” are preferably synonymous with “laser beam” in that the source of the light beam in question is preferably a laser light source.

[104] Referring to figure 1 and figure 2, there is illustrated a cold atom source apparatus (1) configured for use in generating so called “moving molasses” cold atoms for use as inertial atoms in a so-called cold atom inertial measurement exploiting the Bose-Einstein condensation effects in the cold atoms produced by the apparatus in use. To this extent, the cold atom source apparatus (1) will hereafter be interchangeably referred to as an inertial atom source. The inertial atom source comprises a two-dimensional magneto-optical trap (2D-MOT) configured to form optical beams of light for manipulating cold atoms or cold molecules in a 2D-MOT chamber, and arranged in communication with a three-dimensional magneto-optical trap (3D-MOT) configured to form optical beams of light for manipulating in a 3D-MOT chamber the cold atoms or cold molecules received from the 2D-MOT chamber, as described in more detail below. The inertial atom source also comprises an inertial measurement chamber arranged in communication with a 3D-MOT chamber and configured to receive “moving molasses” cold atoms from the 3D-MOT chamber and to receive optical beams of light for manipulating the “moving molasses” cold atoms for the purposes of making inertial measurements.

[105] The inertial atom source apparatus (1) comprises a chassis (2, 3) comprises optical beam-former apparatus configured to form optical beams of light, and a cartridge (4) comprising the 3D-MOT chamber. The chassis comprises a compartment (see figures 7 to 10, item 41) into which the cartridge is removably insertable via an opening chassis to position the 3D-MOT chamber in optical alignment with appropriate optical beam-former apparatus, as is described in more detail below.

[106] The chassis is formed in two parts including a chassis base part (2) and a chassis top part (3) which, between them, define the compartment (41) into which the cartridge is removably insertable via an opening in a side of the chassis. A cartridge clamp piece (5) is also detachably attachable to the chassis and is configured to concurrently embrace the side of the cartridge exposed at the side of the chassis when the cartridge is inserted into the compartment of the chassis, thereby to secure the cartridge in a fixed position within the compartment so as to maintain the aforementioned optical alignment.

[107] In particular, the optical beamforming apparatus includes a first optical beam former (6A, 7A, 8A, 9A, 10 [items 10A, 10B, 10C: see figure 15] and 420 [see figures 18, 23A-23B]) and a second optical beamformer (6B, 7B, 8B, 9B, 10 [items 10D, 10E, 10F: see figure 15] and 420 [see figure 18, 23A-23B]). Each of the first and second optical beamformers is configured to receive a respective optical input beam of light and therewith to form a respective pair of parallel optical beams of linearly polarised light for output into the 3D-MOT chamber (45, see figure 14: see figure 14 and figure 17). The parallel optical beams formed by the first optical beamformer are each substantially parallel to the parallel optical beams formed by the second optical beamformer thereby providing for substantially parallel optical beams (101, 102, 103, 104: see figure 14). The orientations of linear polarisation of each of the four parallel optical beams are mutually substantially parallel (see figure 18). Accordingly, the four parallel optical beams have the desired optical properties for manipulating cold atoms within the 3D-MOT chamber (45), and this will be discussed in more detail below with reference to figures 14 to 20.

[108] A third optical beam former (23, 300, 310, 320, 330: see figure 19A, 19B, 23A, 23B) which is configured to receive and optical input beam of light and to direct the received beam of light for input to the 3D-MOT chamber in conjunction with the light beams input to the 3D-MOT chamber from the first and second optical beam formers. Collectively, the first, second and third optical beam formers are configured to enable the formation of “optical molasses" of cold atoms in the 3D-MOT chamber.

[109] A fourth optical beamformer (11, 12, 13, 14, 15, 16, 17 and 410: see figure 22A) is configured to receive and optical input beam of light and therewith to form a forwardly-advancing sheet of light (item 650: see figure 23E) and to input the sheet of light into the 2D-MOT chamber (item 40: see figure 11) to enable the formation of cold atoms confined in two dimensions, ready for injection into the 3D-MOT chamber.

[110] A fifth optical beamformer (20, 21,22) is configured to receive a beam of optical light and therewith to form a so-called “push beam” of light directed into the inertial measurement chamber (46: see figure 8 and figure 22A) for use in controlling the movement of “optical molasses” injected into the inertial measurement chamber from the 3D-MOT chamber.

[111] Similarly, a sixth optical beam former (400, 410, 420, 430: see figure 20A) is configured to receive a beam of light and therewith to form a further so-called “push beam” of light directed into the 2D-MOT chamber for controlling the movement of cold atoms within that chamber. In particular, the further “push beam” is directed to push cold atoms within the 2D-MOT chamber towards the 3D-MOT chamber to inject them therein.

[112] A seventh optical beam former (24, 25) is configured to receive a heating beam of light and to direct that light beam into the 2D-MOT cell in order to be incident upon pellets of sample material disposed within the 2D-M0T cell. The pellets of sample material are arranged to respond to the incidence of the heating beam by releasing atoms of the sample material into the 2D-MOT chamber for manipulation by the sheet of light and the further “push beam” to form a packet of trapped cold atoms pushed towards the 3D-MOT chamber. The simple material may be formed from rubidium, such that the cold atoms are cold atoms of rubidium.

[113] Each of the first, second, third, fourth, fifth, sixth and seventh optical beam formers comprises a respective optical input port comprising an optical fibre coupler arranged to receive the output end of a respective optical fibre. Subsequent optical elements in each of these optical fit beam formers are arranged in optical communication with the respective optical fibre coupler to direct a beam of light output from the respective optical fibre end into the appropriate one of the 2D-MOT chamber, the 3D-MOT chamber and the inertial measurement chamber.

[114] Each of the first, second, third, fourth, fifth and sixth optical beam forms comprise respective mounting plates (27, 28, 29A-D) upon which the optical elements of the respective beam formers are securely mounted in the necessary and appropriate relative optical alignment necessary to permit them to achieve their function. This provision of dedicated, modular mounting plates for respective optical beam former optical elements, permits the manufacture of the optical beam formers separately and independently of one another, subject only to the requirements imposed by the function of the optical beamforming question relative to the function of the inertial atom source as a whole.

[115] In particular, once the optical requirements of an optical beam former are specified, the relative orientation position and configuration of optical elements the respective mounting plate can be carefully and precisely defined within the constraints of the structure of the mounting plate in question, according to the specified requirements. Examples include the alignment of mirror faces and lens optical axes and optical fibre couplers so as to ensure the correct mutual optical communication between the optical elements necessary to produce the desired overall optical output from the optical beamformer question. Once this has been achieved, the resulting mounting plate, with optical elements fixed upon it, may then be connected to the body of the inertial atom source (1) as necessary. Furthermore, disassembly of the inertial atom source (1) for the purposes of repair or servicing of component parts thereof, may be more easily achieved by simply disconnecting the necessary mounting plates from the structure of the inertial atom source, as required, without requiring the disassembly or disconnection of the optical elements upon the mounting plates. The mounting plates for the first, second, fourth, fifth and seventh optical beam formers are mounted upon the upper chassis part (3) of the inertial atom source, while the mounting plates for the third and sixth optical beam formers are mounted upon the lower chassis part (2).

[116] The first optical beam former includes a mounting plate (28) upon which is mounted a train of collimating optical lenses (7A) configured to collimate light output from the associated optical fibre coupler, followed by a first right-angle prism mirror (8A) and a subsequent second right-angle prism mirror (9A) in optical communication with the first right-angle prism mirror and with a subsequent 3D-MOT beam delivery optical system (10) in optical communication with the second right-angle prism mirror (9A) and comprising a first polarising beam splitter followed by a pair of right-angle prism mirrors (10A, 10B, 10C: see figure 15).

[117] Similarly, the second optical beam former is also mounted upon the same mounting plate (28) carrying the first optical beam former, and includes a train of collimating optical lenses (7B) configured to collimate light output from the associated optical fibre coupler, followed by a first right-angle prism mirror (8B) and a subsequent second right-angle prism mirror (9B) in optical communication with the first right of an angle prism mirror, and with a subsequent 3D-MOT beam delivery optical system (10) in optical communication with the second right-angle prism mirror (9B) and comprising a first polarising beam splitter followed by a pair of right-angle prism mirrors (10D, 10E, 10F: see figure 15).

[118] The third optical beam former (23, 300, 310, 320, 330) includes a mounting plate (29B) upon which is mounted a pair of collimating optical lenses configured to collimate light output from the associated optical fibre coupler, followed by the first right-angle prism mirror (310) for receiving the collimated light beam from the collimating optical lenses and for reflecting the collimated light beam to a second right-angle prism mirror (320) which is, in turn, configured to reflect the collated light beam to a third right-angle prism mirror (330). The collimating lens is, and the first and second right-angle prism mirrors (310, 320) configured to restrain the collimated light beam in the horizontal plane (i.e. the X-Z plane), whereas the third right-angle prism mirror (330) is configured to reflect the collimated light beam in a direction perpendicular to the horizontal plane and towards the 3D-MOT chamber within the body of the inertial atom source (1) for use conjunction with light beams from the first optical beam former and the second optical beam former concurrently in generating so-called “optical molasses” within the 3D-MOT chamber. This is described in more detail below.

[119] The fourth optical beam former (11) includes a mounting plate (29A) upon which is mounted an optical train configured to receive an optical beam output from the optical fibre coupler of the beam former, and to expand that received optical beam in a first dimension which is transverse to the axis of the received optical beam thereby to generate a sheet of light, and subsequently to expand the sheet of light in a second dimension which is transverse to the plane of the sheet of light thereby to form a forwardly-advancing wall of light. In particular, a plano-convex cylindrical lens (12) is arranged in optical communication with the optical fibre coupler and is arranged to collimate the output light beam received from the optical fibre coupler in only one of the two dimensions transverse to the axis of the received light beam. That is to say, the light beam output by the optical fibre coupler has the form of an expanding cone of light which expands in each of the two orthogonal dimensions (X and Y axes) transverse to the propagation direction (Z-axis).

[120] The plano-convex cylindrical lens (12) presents a plane surface to the optical fibre coupler and presents a convex curved surface in a direction away from the optical fibre coupler, the radius of curvature of the convex curved surface being confined to the plane which is perpendicular to both the plane of the mounting plate to which the lens is fixed and the plane surface of the lens (i.e. the Y-Z plane, a ‘vertical’ plane). The effect of the plano-convex cylindrical lens (12) is to collimate the expanding cone of light such that the beam of light ceases to expand in the dimension perpendicular to the plane of the mounting plate (e.g. the Y-axis) but continues to expand in the horizontal dimension (e.g. the X-axis). A series of three mirrors (13, 14,15) are arranged in optical communication with the plano-convex cylindrical lens (12) and, successively, with each other. These three mirrors are arranged to fold the optical path of the expanding sheet of light output by the plano-convex cylindrical lens to increase the optical path length of the sheet to permit the desired extent of expansion of the sheet of light in the horizontal plane.

[121] Accordingly, a first of the series of three mirrors (13) comprises a right-angle prism mirror in optical communication with a subsequent second right-angle prism mirror (14) presenting a reflective surface having a horizontal width exceeding that of the first right-angle prism mirror in order to accommodate the increased horizontal expansion of the sheet of light received by from the first right-angle prism mirror. Subsequently, a third plane mirror (15) is arranged in optical communication with the second right-angle prism mirror and presents a reflective surface having a horizontal width exceeding that of the second right-angle prism mirror in order to accommodate the further increased horizontal expansion of the sheet of light received from the second right-angle prism mirror.

[122] Subsequently, a second plano-convex cylindrical lens (16) is arranged in optical communication with the third plane mirror (15) and defines a plane lens surface presented towards the third plane mirror, and a cylindrical curved convex surface presented in a direction away from the third plane mirror. The horizontal width of the second plano-convex lens exceeds the horizontal width of the third plane mirror (15) thereby accommodating further expansion of the sheet of light received by it from the third plane mirror. The radius of curvature of the curved convex surface is confined to the plane of the mounting plate (i.e. the X-Z plane, a ‘horizontal’ pane), and the effect of this lens is to collimate the expanding sheet of light received by it such that further expansion of the sheet in the horizontal plane ceases, and the sheet of light output by the second plano-convex cylindrical lens (16) is substantially fully collimated (e.g. see figure 23D, discussed below).

[123] A linear array of three right-angle prisms (17), abutted one after the other, define an elongated right-angle prism which is arranged in optical communication with the curved output surface of the second plano-convex cylindrical lens (16). The larger (hypotenuse) surface of each of the three right-angle prisms of the linear array are arranged plane-parallel in the same plane (i.e. the X-Y plane, a ‘vertical’ plane perpendicular to the mounting pate) and facing towards the convex surface of the second plano-convex cylindrical lens (16) for receiving the collimated light sheet into the array of three prisms. Accordingly, the elongated right-angle prism presents a plane rectangular optical input surface (hypotenuse) for receiving the collimated sheet of light directed into the body of the elongated right-angle prism for internal reflection successively at the two plane rectangular and orthogonal internal surfaces of the elongated prism, and subsequent output from the prism through the hypotenuse surface. The effect of the elongated prism is to fold the optical path of the collimated sheet of light in a way which laterally displaces the optical path in a direction towards the 2D-MOT chamber and also reverses the path of the collimated light sheet such that it is parallel to the long axis of the 2D-MOT chamber and passes in a direction extending over that chamber.

[124] The lateral displacement and direction reversal is such that the collimated light sheet is directed towards an optical beam expander optic (item 410: see figure 22A, 22B, 23A-E) comprising a plane-rectangular block arranged to receive the first expanded light beam (640) and to expand the cross-sectional area of the first expanded light beam asymmetrically in a second dimension (i.e. the Z-dimension) which is transverse to the first dimension, and to output the result as a second expanded light beam (650) in a direction (i.e. the Y-dimension) which is transverse to both the first dimension and the second dimension thereby to provide an output light beam having a cross-sectional area expanded in two transverse dimensions of the output light beam. The second expanded light beam is directed into the 2D-MOT chamber.

[125] The fifth optical beam former (20, 21, 22) includes a mounting plate (27) upon which is mounted a first right-angle prism mirror (21) placed in the optical path of an output beam of light from the optical fibre coupler of the fifth optical beam former, for diverting the output light beam through 90° whilst maintaining the diverted light beam in the horizontal plane (i.e. the X-Z plane). This is followed by a pair of collimating optical lenses configured to collimate the diverted light beam, and the optical lenses are followed by a subsequent second right-angle prism mirror (22) in optical communication with the collimating lens is (21). The second right-angle prism mirror (22) is configured to divert the received optical beam through 90° in a direction perpendicular to the plane of the mounting plate upon which it is mounted, and into a ‘vertical’ plane (i.e. the X-Y plane) to direct the light beam into the inertial measurement chamber (46) as a so-called “push beam” of light for use in controlling the movement of “optical molasses” injected into the inertial measurement chamber from the 3D-MOT chamber, in use.

[126] The sixth optical beam former (400, 410, 420, 430, 440, 450, 460: see figures 20A, 22A) includes a mounting plate (29D) upon which is mounted a train of collimating optical lenses (410) configured to collimate light output from the associated optical fibre coupler (400), followed by a first right-angle prism mirror (420) and a subsequent second right-angle prism mirror (430) in optical communication with the first right-angle prism mirror and with a subsequent beam delivery optical system (440, 450, 460: see figures 20A, 22A) in optical communication with the second right-angle prism mirror (430) and comprising a triplet of rightangle prism mirrors (440, 450, 460) configured to divert the optical beam received from the second right-angle prism mirror (430) to the 2D-MOT chamber (40) for use as a so-called “push beam” of light for pushing cold atoms within that chamber towards the 3D-MOT chamber (45).

[127] The seventh optical beam former (24, 25; 440, 450, 460: see figure 22A) includes a mounting plate (29C) upon which is mounted a train of collimating optical lenses and subsequent right-angle prism mirrors configured to receive light output from the associated optical fibre coupler of the seventh optical beam former. Subsequent to the collimating optical lenses, which function to collimate the received beam of light output from the optical fibre coupler to form a collimated heating light beam, the right-angle prism mirrors function to divert the heating light beam into the body of the inertial source so as to be incident upon the aforementioned pellets of sample material disposed within the 2D-MOT cell.

[128] An inertial measurement optical input port (26) comprising an optical fibre coupler is arranged to receive the output end of an optical fibre and, with appropriate inertial measurement optical elements (not shown) to direct a light beam output from that optical fibre end into the inertial measurement chamber in whatever appropriate way is required by the user for making desired inertial measurements upon the inertial atoms injected into the inertial chamber. Details of the inertial measurement optical elements are not disclosed here, but would be readily apparent to the skilled person in the art according to the desired inertial measurements required by the skilled person.

[129] Referring to figures 3 and figure 4 there is illustrated an overview of the inertial atom source (1) already shown in figure 1 and figure 2, but in which the fifth optical beam former (20, 21, 22) together with the mounting plate (27) upon which the optical elements of the optical beam former are mounted, is removed from the view in order to aid clarity. This reveals in better detail the first optical beam former, the second optical beam former and the mounting plate (28) upon which both are securely mounted. In particular, it can be seen that the optical elements of the 3D-MOT beam delivery optics (10) are mounted upon the mounting plate of the first and second optical beam forms, over and in register with four separate through-openings (280) which pass through the mounting plate thereby placing the optical elements of the 3-D-MOT beam delivery optics (10) in optical communication with the 3D-MOT chamber of the inertial atom source via an upper anti-Helmholtz coil (30) mounted upon the upper chassis part (3) of the inertial atom source.

[130] Figure 5 illustrates the view illustrated in figure 4 but with the mounting plate of the first and second optical beam formers removed to permit greater clarity, whilst keeping the optical elements of the first and second optical beam formers present and in their correct relative positions and orientations. Here the mounting arrangement of the upper anti-Helmholtz coil (30) within the upper chassis part (3) can be clearly seen.

[131] Figure 6 illustrates a view of the inertial atom source illustrated in figure 4, but with the mounting plate (29A) of the fourth optical beam former, and all optical elements upon it, removed to permit better clarity. This view reveals the position of the lower anti-Helmholtz coil (35) which is mounted upon the lower chassis part (2) in register with the upper anti-Helmholtz coil (30) such that the two anti-Helmholtz coils may be used to collectively generate, in use, an anti-Helmholtz magnetic field structure within the 3D-MOT chamber (45) of the inertial atom source. Each of the upper and lower anti-Helmholtz coils comprises a coil of wire, e.g. copper wire, forming an annular coil which responds to the passage of analytical current by generating a magnetic field for use, together, in the process of forming “optical molasses”, as would be readily apparent and understood by the person of ordinary skill in the art. Similarly, figure 6 illustrates the relative position of a first pair of linear permanent magnetic pole pieces (50) which are mounted within the upper chassis part (3) so as to extend above and in parallel along the longitudinal axis of the 2D-MOT chamber (40). As is shown in figure 11, figure 21, figures 22Ato 22B and figures 23A to 23B, these two linear permanent magnetic pole pieces from an upper pair of for such linear permanent magnetic pole pieces comprising an upper pair and a lower pair in which the lower pair is mounted within the lower chassis part (2) so as to extend below and in parallel along the longitudinal axis of the 2D-MOT chamber (40). Collectively, the four permanent magnetic pole pieces define a magnetic field within the 2D-MOT chamber suitable for use in generating a 2D array of cold atoms.

[132] Figure 7, figure 8 and figure 9 each show different views of the structure illustrated in figure 6 but in which the detachable cartridge (4) is shown detached from the compartment (41) defined between the lower and upper chassis parts (2, 3). In addition, the cartridge clamp piece (5) is also shown as detached from the upper and lower chassis parts thereby permitting the removal of the cartridge from the compartment, as shown. The cartridge (4) comprises a channel cell (47) within which are formed the 2D-MOT chamber (40), the 3D-MOT chamber (45) and the inertial measurement chamber (46), and an ion pump attached to channel cell in fluid communication with the 3D-MOT chamber and the inertial measurement chamber and configured to maintain these three chambers at a suitably low pressure.

[133] The channel cell (47) includes transparent upper cover plate (100A) and a corresponding transparent lower, plate (100B) which permit optical communication with the 2D-MOT chamber, the 3D-MOT chamber and the inertial measurement chamber from the upper chassis part (3) and the lower chassis part (2) such that optical beams formed by optical components mounted upon the upper and lower chassis parts may communicate directly with the three chambers of the channel cell. The cartridge clamp piece (5) defines a generally “U”-shaped structure defining a recess (44) between two surrounding arm portions (42, 43) adapted and configured to reciprocally fit around opposing parts of the channel cell (47) and attached ion pump (47B) of the cartridge (4). Averages are formed within the ends of the two arm portions which are accessible from either the lower or upper chassis parts (2,3) and are configured to receive retaining means from the upper or lower chassis part, such as pins or rods, with which the cartridge clamp piece may be fixed are securely (but detachably) coupled to the chassis part in question, in use.

[134] An upper mounting gasket (49) is attached to the upper chassis part (3) upon the ceiling of the compartment (41) formed between the upper and lower chassis parts, and an opposing lower mounting gasket (48) is attached to the lower chassis part (2) within the compartment aligned in register with the upper mounting gasket. The upper and lower mounting gaskets are substantially identical in shape, size and structure and are configured to each form a respective interference fit against, respectively, the upper cover plate (100A) and the lower cover plate (100B) around the periphery of the channel cell (47) without obstructing or obscuring optical communication with any of the 2D-MOT chamber, 3D-MOT chamber and inertial measurement chamber. This interference fit assists in family securing the cartridge in position within the compartment when the cartridge is inserted into the compartment in use so as to prevent undesired movement of the inserted cartridge. To achieve the interference fit, the separation between the opposing upper and lower mounting gaskets closely matches the separation between the outermost faces of the upper cover plate and the lower cover plate, whether cover plates and mounting gaskets meet, in use.

[135] The lower chassis part (2) comprises three abutment lugs (41 A) which protrude from the walls of the lower chassis part defining the inner periphery of the compartment, into the hollow of the compartment (41) such that the cartridge (47) when fully inserted into the chamber (as shown in Figure 9B) abuts against the abutment lugs. The depth of protrusion of the abutment lugs (41 A) is configured to collectively position the abutted cartridge in optical alignment with the optical beam-formers adapted to communicate optically with the 2D-MOT and 3D-MOT chambers of the cartridge.

[136] The abutment lugs (41 A) each comprise a convex hemi-spherical surface and the cartridge (47) comprises substantially flat abutment surfaces (47B) against which the convex surface of a respective abutment lug is arranged to abut when the cartridge when fully inserted into the chamber, as shown. The advantage of these abutment lugs is that each one can be easily finely adjusted in shape to adjust its respective depth of protrusion, e.g. by simply removing (e.g. abrading / filing-away) a small but sufficient part of the convex protruding surface of the lug to which the cartridge surface will abut. It is not necessary to change the overall shape and position of the inner walls of the compartment from which the lugs protrude.

[137] Figure 10 illustrates a perspective view of the assembly illustrated in figure 8 and figure 9 but in which the upper and lower cover plates, and the ion pump, are removed to permit a clearer view of the structure of the channel cell (47). In particular, the 2D-MOT chamber presents three inclined walls (62) each being optically reflective and angled at 45° to the to the plane of the channel cell. The three reflective walls comprise two opposing inclined side walls which extend in a direction along the longitudinal axis of the channel cell, and one inclined end wall adjacent to source pellets (66) at a distal end of the channel cell within (and in communication with) the 2D-MOT chamber. Consequently, a ‘vertically’ incident light beam (i.e. directed perpendicular to the plane of the channel cell) is deflected by 90° upon reflection at a respective inclined wall so as to be directed towards the opposite wall of the chamber. The optical beam (650) input to the 2D-MOT chamber by the fourth optical beam former is in direct optical communication with both of the opposing inclined side walls.

[138] A beam expander (410) of the fourth optical beam former bears a A / 4-plate (“quarterwave” plate: 41 OB or Fig.23A, 23C, 23D) extending over its optical output surface and configured to receive the optical beam (640) of linearly-polarised light from the beam expander (410) and to convert it into circularly-polarised light for onward transmission into the 2D-MOT chamber. A through-opening is formed at the base of the channel cell coincident with the base of the 2D-MOT chamber, to permit those parts of the circularly-polarised optical beam (640) from the fourth optical beam former which have not impinged upon a reflective inclined side wall, to pass through the through-opening and out of the 2D-MOT chamber and the channel cell via the lower cover plate (100 B). A return mirror (430, figure 22A-22B; figure 23A-23B) is positioned in register with the through-opening and configured to retro-reflect those parts of the light beam from the fourth optical beam former that pass through the through-opening in a direction directly back towards the through-opening and back into the 2D-MOT chamber. The return mirror bears a A / 4-plate (“quarter-wave” plate) extending over its reflective surface and configured to receive the optical beam (650) of circularly-polarised light and to convert it into linearly polarised light for reflection at the reflective surface of the return mirror. The returned linearly polarised optical beam then passes back through the A / 4-plate (“quarter-wave” plate) and which converts the linearly polarised light back into circularly-polarised light which passes upwardly in counter-propagation back into the 2D-MOT chamber.

[139] As a result, the input of a single optical beam (650) from the fourth optical beam former interacts with the aforementioned reflective elements to generate a pair of light beams which counter-propagate in the plane of the channel cell, via the inclined side walls (62), and a concurrent pair of light beams which counter-propagate in the plane perpendicular to the plane of the channel cell and which all intersect within the volume of the 2D-MOT chamber (40), as required for the purposes of a 2D-MOT process.

[140] Similarly, the inclined end wall of the 2D-MOT chamber is in optical communication with the sixth optical beam former (400-460) so as to receive a so-called “push-beam” generated by the sixth optical beam former and to reflect received push-being in a direction parallel with and along the longitudinal axis of the channel cell within the 2D-MOT chamber. This push beam serves to push cold atoms formed within the 2-D-MOT chamber in a direction towards a transfer passage (65) which places the 2D-MOT chamber (40) in communication with the 3D-MOT chamber (45) thereby to permit the transfer of cold atoms from the 2D-MOT chamber to the 3D-MOT chamber.

[141] The 3D-MOT chamber (45) defines a pyramidal mirror system formed by four plane reflective side walls of the chamber each inclined at 45° to the plane of the channel cell and each defining a respective one of the four internal faces of a recess an inverted pyramidal frustum. Each side-wall resides at an angle of 45° to the plane of the channel cell. The four reflective walls comprise two pairs of opposing inclined side walls which extend in a direction oblique to the longitudinal axis of the channel cell. Consequently, an incident light beam directed perpendicular to the plane of the channel cell, is deflected by 90° upon reflection at a respective inclined side wall of a given pair of sidewalls so as to be directed towards the opposite side wall of the pair. The four optical beams (101, 102, 103, 104) input to the 3D-MOT chamber by the first and second optical beam formers are in direct optical communication with both pairs of the opposing inclined side walls. In particular, each one of the four optical beams in question is in direct optical communication with a respective one of the four inclined side walls of the 3D-MOT chamber, and indirectly with the opposite side wall which forms the respective pair of sidewalls. Consequently illumination of the four inclined sidewalls by the respective four optical beams, concurrently, permits the forming of two co-planar pairs of paraxial and counter-propagating light beams in which one paraxial pair intersects (110) the other paraxial pair at an angle of 90°, as is schematically illustrated in figure 14.

[142] A distal end of the inertial measurement chamber (46) possesses plane reflective end wall (60) of the chamber inclined at 45° to the plane of the channel cell and adapted for receiving a light beam from the fifth optical beam former and to deflect the received light beam through 90° to direct the deflected light beam along the longitudinal axis of the channel cell in a direction towards the 3D-MOT chamber. Consequently, this deflected light beam may serve as a “push beam” for the purposes of controlling motion of “optical molasses” inserted into the inertial measurement chamber by a insertion passageway (67) which places the 3D-MOT chamber in communication with the inertial measurement chamber. Furthermore, an ion pump duct (63) is formed within the channel cell in communication with the inertial measurement chamber to permit the pumping action of the ion pump (47B) to reduce the pressure within the inertial measurement chamber. In addition, a pumping passageway (64) formed within the channel cell places the 3D-MOT chamber in fluid communication with the ion pump duct to similarly permit the pumping action of the iron pump to reduce the pressure within the 3D-MOT chamber.

[143] It is to be noted that each of the inclined reflective surfaces within the channel cell are inclined so as to face obliquely towards the upper chassis part (3) upon which associated optical beam formers are mounted for the purposes of directing light beams to the relevant inclined reflective surfaces.

[144] Figures 11, 12, 13 and 14 show views of the channel cell in conjunction with the optical elements of the first and second optical beam formers, wherein figure 11 also shows these components in conjunction with the upper and lower anti-Helmholtz coils (30, 35) disposed in register above and below, respectively, the 3D-MOT chamber, and the four linear permanent magnets (50) arranged around the 2D-MOT chamber as discussed above. This configuration and relative positioning of the anti-Helmholtz coils and the permanent magnets, as well as the optical elements of the first and second optical beam formers, around the channel cell, and relative to each other, is the same as their configuration and relative positioning within the inertial atom source (1) within which they are mounted (or inserted, in the case of the channel cell), in use.

[145] Referring particularly to figure 14, in conjunction with figure 15 and figure 16, the 3D-MOT beam delivery optics are shown in position relative to the channel cell (47). The path of respective light beams through the first and second optical beam formers is shown in figure 14 (perspective view) and the subsequent path of the four optical beams formed by the first and second optical beam formers is also shown together with its interaction with the pyramidal mirror assembly defined by the 3D-MOT chamber (45) of the channel cell (47). Figure 16 shows a view as seen from the 3D-MOT chamber, in which the four optical beams (101, 102, 103 and 104) are directed out of the plane of the paper of figure 16.

[146] In particular, the first optical beam former comprises a first polarising beam-splitter cube (10A) arranged in optical communication with the second right-angle prism mirror (9A) so as to receive at an optical input face thereof an optical beam which has been input to the first optical beam former, by the optical fibre coupler thereof, and which has subsequently been directed to the first polarising beam-splitter by the second right-angle prism mirror (9A). The internal reflecting surface of the first polarising beam-splitter serves to reflect the component of the received optical beam which has a linear optical polarisation orientation coplanar with the plane of the internal reflecting surface, and to transmit the component of the received optical beam which has a linear optical polarisation orientation perpendicular to the polarisation of the reflected component.

[147] Consequently, a first optical output beam (101) is output to a first optical output face at the underside of the first polarising beam-splitter cube and represents a first optical beam output by the optical beam former towards the 3D-MOT chamber. The transmitted component of the optical beam received at the internal reflecting surface of the first polarising beam-splitter is transmitted through a second optical output face at the back of the first polarising beam-splitter cube (10A) and through an abutting plane face of an intermediate right-angle prism mirror (10B) which is coupled to the second optical output face of the first polarising beam-splitter cube. The transmitted component of the optical light beam is transmitted to an internal reflecting plane surface (hypotenuse) of the intermediate right-angle prism mirror where it is diverted through an angle of 90° in a direction parallel to the plane of the internal reflecting surface of the first polarising beam-splitter (10A), and subsequent output from a plane output face of the intermediate right-angle prism and immediately input through a plane face of a final right-angle prism (10C) abutting the plane output face of the intermediate right-angle prism.

[148] The transmitted component of the optical light beam is subsequently transmitted to an internal reflecting plane surface (hypotenuse) of the final right-angle prism mirror (10C) where it is diverted through an angle of 90° output from the final right-angle prism mirror as a second optical beam (103) in a direction parallel to the direction of the first optical output beam (101) output by the first polarising beam-splitter cube (10A). It is to be noted that the polarisation vector (electric field vector) of the transmitted component of the optical light beam is parallel to the plane of the internal reflecting surface of the intermediate right-angle prism mirror, whereas the plane of the internal reflecting surface of the final right-angle prism mirror is oblique to that polarisation vector. Consequently, while the intermediate right-angle prism mirror preserves the polarisation vector of the light beam reflected from it, the final right-angle mirror re-projects the polarisation vector of the light beam into a plane parallel to the plane of the internal reflecting surface of the first polarising beam-splitter cube (10A).

[149] In this way, the first optical beam former is able to produce to parallel and linearly polarised light beams, which have parallel linear polarisation position angles (i.e. parallel electric field vectors of respective electromagnetic waves) for insertion into the 3D-MOT chamber.

[150] Similarly, the second optical beam former comprises a second polarising beam-splitter cube (10D) arranged in optical communication with its second right-angle prism mirror (9B) so as to receive at an optical input face thereof an optical beam which has been input to the second optical beam former, by the optical fibre coupler thereof, and which has subsequently been directed to the second polarising beam-splitter by the second right-angle prism mirror (9B). The internal reflecting surface of the second polarising beam-splitter serves to reflect the component of the received optical beam which has a linear optical polarisation orientation coplanar with the plane of the internal reflecting surface, and to transmit the component of the received optical beam which has a linear optical polarisation orientation perpendicular to the polarisation of the reflected component.

[151] Consequently, a first optical output beam (102) is output to a first optical output face at the underside of the second polarising beam-splitter cube and represents a first optical beam output by the second optical beam former towards the 3D-MOT chamber. The transmitted component of the optical beam received at the internal reflecting surface of the second polarising beam-splitter is transmitted through a second optical output face at the back, of the second polarising beam-splitter cube (10D) and through an abutting plane face of an intermediate right-angle prism mirror (10E) which is coupled to the second optical output face of the second polarising beam-splitter cube. The transmitted component of the optical light beam is transmitted to an internal reflecting plane surface (hypotenuse) of the intermediate right-angle prism mirror where it is diverted through an angle of 90° in a direction parallel to the plane of the internal reflecting surface of the second polarising beam-splitter (10D), and subsequent output from a plane output face of the intermediate right-angle prism and immediately input through a plane face of a final right-angle prism (10F) abutting the plane output face of the intermediate right-angle prism.

[152] The transmitted component of the optical light beam is subsequently transmitted to an internal reflecting plane surface (hypotenuse) of the final right-angle prism mirror (1 OF) where it is diverted through an angle of 90° and output from the final right-angle prism mirror as a second optical beam (104) in a direction parallel to the direction of the first optical output beam (102) output by the second polarising beam-splitter cube (10D). It is to be noted that the polarisation vector (electric field vector) of the transmitted component of the optical light beam is parallel to the plane of the internal reflecting surface of the intermediate right-angle prism mirror, whereas the plane of the internal reflecting surface of the final right-angle prism mirror is oblique to that polarisation vector. Consequently, while the intermediate right-angle prism mirror preserves the polarisation vector of the light beam reflected from it, the final right-angle mirror re-projects the polarisation vector of the light beam into a plane parallel to the plane of the internal reflecting surface of the second polarising beam-splitter cube (10D).

[153] In this way, the first optical beam former is able to produce to parallel and linearly polarised light beams, which have parallel linear polarisation position angles (i.e. parallel electric field vectors of respective electromagnetic waves) for insertion into the 3D-MOT chamber.

[154] Furthermore since the plane of the internal reflecting surface of the first polarising beamsplitter cube (10A) is parallel to the plane of the internal reflecting surface of the second polarising beam-splitter cube (10D), the result is that the four parallel and linearly polarised light beams (101,102, 103,104) concurrently produced by the first and second optical beam former is, all have parallel linear polarisation position angles. This is an important feature for the purposes of controlling photon angular momentum and exciting appropriate atomic transitions within cold atoms contained within the 3D-MOT chamber, at the point (110) of intersection of the four optical beams, for the purposes of achieving atomic cooling and manipulation to generate “optical molasses”.

[155] As discussed above a fifth optical beam (120) is directed into the 3D-MOT in a direction that is anti-parallel to the mutually parallel four light beams output by the first and second optical beam formers, and that is directed to intersect the same point of intersection (110) at which those four light beams intersect within the 3D-MOT. The fifth optical beam is linearly polarised, and the linear polarisation position angle (i.e. electrical field vector orientation of the EM wave) of the fifth optical beam is parallel to the four mutually parallel linear polarisation position angles of each of the mutually parallel four light beams output by the first and second optical beam formers. As a consequence, five mutually parallel beams of linearly polarised light (including one anti-parallel light beam) which will have parallel linear polarisation position angles, may be generated and directed towards the 3D-MOT chamber of the channel cell.

[156] The first and second optical beam formers and the four mirrors defined by the pyramidal mirror structure provided within the 3D-MOT chamber, mutually configured and arranged such that a respective one of the four light beams from the first and second optical beam formers is directed by its associated optical beam former so as to be incident at an angle of 45° upon a target location on the reflective surface of a respective one of the four mirrors of the pyramid mirror structure. The target location upon any one of the reflective surfaces is chosen so that it is diametrically opposed by corresponding target location upon the reflective surface of a diametrically opposing one of the four mirrors defined by the pyramidal mirror structure. The result is that a light beam incident upon a given target location of one of the four mirrors is reflected across the pyramid-shaped open volume of the 3D-MOT chamber to subsequently be incident upon the diametrically opposing target location associated with the diametrically opposing mirror. This results in the formation of a pair of anti-parallel, paraxial and counterpropagating light beams which span the open volume of the 3D-MOT chamber. Of course, the pyramidal mirror structure possesses two pairs of diametrically opposing mirrors and, therefore, two pairs of diametrically opposing target locations resulting in the formation of two pairs of antiparallel, paraxial and counter-propagating light beams which concurrently span the volume of the 3D-MOT chamber.

[157] Figure 17 schematically illustrates the four beams (101, 102, 103, 104) incident upon the pyramidal mirror structures of the 3-D-MOT chamber, together with the fifth beam (120) all intersecting at the intersection point (110). The intersection point is located upon the longitudinal axis of the channel cell of the cartridge (4) and this axis passes from the transfer passage (65) of the 2D-MOT to the insertion passage (67) of the 3D-MOT. This means that cold atoms transferred from the 2D-MOT into the 3D-MOT via the transfer passage (65) continue to move along the longitudinal axis of the channel cell towards the insertion passage (67) and in doing so they are caused to pass through the intersection point (110) at which they are acted upon by the beams (101, 102, 103, 104 120) at that point to further cool and confine those atoms into a “moving molasses” which then continues to move along the longitudinal axis of the channel cell and passes from the 3-D-MOT into the initial measurement chamber via the insertion passage (67).

[158] Polarisation Control and Atomic Transitions

[159] Referring to figure 18 and to figures 23A and 23B, a first circular polariser, in the form of a A / 4 plate (‘quarter-wave plate’; 420) is disposed between the 3D-MOT beam delivery optics (10) and the 3D-MOT chamber (45) such that the four mutually parallel optical beams (101,102, 103 and 104) delivered to the 3D-MOT chamber pass through, and are acted upon by, the first circular polariser. The effect is to convert the linear polarisation state of each optical beam of the four optical beams, which is common to all of them, into a circular polarisation state which is also common to all of them, immediately before the four optical beams (now circularly polarised) are delivered to the 3D-MOT chamber. Figure 18, upper panel, schematically illustrates the polarisation beam-splitter and subsequent right-angle prism mirrors (10A, 10B, 10C) of the first optical beam former that receive an input optical beam (100A) and from that input beam deliver the linearly polarised first and second beams (101, 103) to the first circular polariser (420). The polarisation beam-splitter and subsequent right-angle prism mirrors (10D, 10A, 10F) of the second optical beam former also deliver associated linearly polarised optical beams (102, 104) to the first circular polariser (420), but these are omitted from the schematic illustration of figure 18, upper panel, in order to aid clarity. In figure 18, lower panel, the linear polarisation direction (i.e. the electrical field vector of the EM wave) of each of the light beams (101, 102, 103, 104) from the 3D-MOT beam delivery optics (10) is indicated in the form of a double-ended arrow transverse to the axis of the associated light beam.

[160] And a second circular polariser, in the form of a A / 4 plate (‘quarter-wave plate’; 420B), is disposed between the final right-angle prism mirror (330) of the third optical beam former (23, 300, 310, 320, 330) and the 3D-MOT chamber (45) such that the fifth optical beam (120) delivered to the 3D-MOT chamber passes through, and is acted upon by, the second circular polariser. The effect is to convert the linear polarisation state of the fifth optical beam into a circular polarisation state which is also common to all of the five beams (101, 102, 103, 104 and 120), immediately before the fifth optical beam (now circularly polarised) is delivered to the 3D-MOT chamber. In figure 18, lower panel, the linear polarisation direction (i.e. the electrical field vector of the EM wave) of the fifth light beam (120) within the 3D-MOT, is indicated in the form of a double-ended arrow transverse to the axis of the fifth light beam. Upon passing into the 3D-MOT chamber, via a lower optical access port (45A) of the 3D-MOT chamber, the circularly polarised fifth optical beam traverses the volume of the 3D-MOT chamber so as to pass through the intersection point (110) with all the other beams of light delivered to the 3D-MOT chamber, in a direction perpendicular to the longitudinal axis of the channel cell and co-axial with the axis of the pyramid frustum defined by the four mirrors (61) of the pyramidal mirror system therein. The circularly polarised fifth optical beam (120) then exits the 3-D-MOT chamber and passes through the first circular polariser (420) which acts upon the circularly polarised fifth optical beam so as to convert that optical beam back into a linearly polarised optical beam. A retro-reflecting plane mirror (490; see figures 22B, 23A, 23B) is mounted at the underside of the mounting plate (20) of the first and second optical beam formers and is disposed in optical communication with the final right-angle prism mirror (330) of the third optical beam former, and with the first circular polariser (420) and second circular polariser (420B) both which lie between the two opposing mirrors (490, 330) on either side of the 3D-MOT chamber. It is to be noted that, in order to aid clarity, the second circular polariser (420B) is omitted from the views illustrated in figures 202A and 22B, but it is to be understood that this component is indeed present in the apparatus.

[161] The function of the retro-reflecting plane mirror (490) is to retro-reflect the linearly polarised incident fifth optical beam received by it, and to return the retro-reflected beam back towards the 3D-MOT chamber in a direction which is paraxial and counter-propagating relative to the incident optical beam and which substantially exactly re-traces the path of the incident fifth optical beam assembly, of course, in the opposite direction. This opposite direction takes the retro-reflected linearly polarised fifth optical beam back through the first circular polariser (420) whereupon the retro-reflected fifth optical beam becomes circularly polarised before it enters the 3D-MOT chamber and passes through the intersection point (110). Thus, the retro-reflecting mirror (490), in conjunction with the first circular polariser (420) provides a third pair of coaxial, counter-propagating circularly polarised optical beams which pass through the intersection point (110) within the 3D-MOT chamber concurrently with, and perpendicular to the plane containing, the first and second pair of coaxial, counter-propagating circularly polarised optical beams provided by the four inclined mirrors of the pyramidal mirror system (62) of the 3D-MOT chamber. In this way, a three-dimensional orthogonal triad is generated, comprising three pairs of coaxial, counter-propagating circularly polarised optical beams suitable for use in implementing a 3D-MOT operation.

[162] Figures 19A and 19B show a plan view and a perspective view, respectively, of an underside of the inertial atom source (1) in which the third optical beam former (23, 300, 310, 320, 330) is shown mounted upon its associated mounting plate (29B). In figures 20A and 20B, similar perspective views of the underside of the inertial atom source are shown in which the mounting plate of the third optical beam former is omitted, in order to aid clarity. This omission assists in revealing the position and mounting of the lower anti-Helmholtz coil (35) and the through-opening (340) formed within the lower chassis part (2) around which the lower antiHelmholtz coil is wound and through which the third optical beam former gains optical communication with the 3D-MOT chamber within the inertial atom source. Figure 21 illustrates the inertial atom source components as illustrated in figure 20A but in which the lower chassis part, and many of the components mounted upon it, are permitted in order to aid clarity. This omission reveals the relative positioning of the optical elements of the third optical beam former and two of the four linear permanent magnet pieces (50) associated with the 2D-MOT chamber (40). Also revealed is the relative positioning of a retro-reflective mirror (400) disposed in optical communication with the fourth optical beam former via a through-opening, or window, formed in the base of the channel cell (47) between opposing inclined mirror side walls (62). Figures 22A and 22B show views of relevant components of the inertial atom source similar to the views illustrated in figure 21 but in which the upper chassis part (3) and all other mounting components of the assembly are permitted, with the exception of the mounting plate (28) of the first and second optical beam formers, in order to better assist clarity in describing the interaction between the components illustrated in these two figures. Figures 23A and 23B show additional views of the components illustrated in figures 22A and 22B but in which the mounting plate (20) of the first and second optical beam formers is omitted, again, to assist in clarity of view and explanation.

[163] Returning to figure 14 and to figure 18, particular reference is now made to linear polarisation control of the optical beams input to the first and second optical beam formers illustrated in those figures. Firstly, considering figure 14, the first optical beam former comprises a first linear polarisation control part (700A) adapted to receive and optical light beam, to control the relevant aspect of the state of linear polarisation of the received light beam, and to output the result to the subsequent optical elements (7A, 8A, 9A, 10A, 10B, 10C) of the first optical beam former. Similarly, the second optical beam former comprises a second linear polarisation control part (700B) which is similarly adapted to receive and optical light beam, to control the relevant aspect of the state of linear polarisation of the received light beam, and to output the results to the subsequent optical components (7B, 8B, 9B, 10D, 10E, 10F) of the second optical beam former. In the present embodiment, the first linear polarisation control part is identical in structure and function to the second linear polarisation control part.

[164] In more detail, the purpose of the linear polarisation control parts is to controllably adjust the position angle of the linear polarisation vector of a received optical beam (i.e. the electrical field vector of the EM wave associated with the optical beam in question) in order to consequentially control the relative optical intensities of the pair of optical beams (101, 103; or 102, 104) output by the 3D-MOT beam delivery optics (10) for input to the 3D-MOT chamber (45). It is important to note that it is highly desirable to achieve substantially the same optical intensities in each of the two parallel, concurrent optical beams output by a given one of the first and second optical beam formers. This will be explained with reference to the first optical beam former schematically illustrated in figure 18, of the panel, but it is to be understood that this explanation applies equally to the second optical beam former. Given that the first optical output beam (101) and the second optical output beam (103) produced by the 3D-MOT beam delivery optics (10A, 10B, 10C), are generated by the act of splitting a single input optical beam (100A), and parallelising the resulting split-been components, it is necessary to take steps to ensure that this process of splitting and parallelising results in a pair of “balanced” optical output beams (i.e. of equal optical intensity).

[165] The optical input beam (100A) must interact with to optical interfaces of the first optical beam former in producing the first optical output beam (101), and must interact with eight optical interfaces in producing the second optical output beam (103). The different optical properties and qualities of each of these optical interfaces may impose different optical losses on the optical beams passing through the and, of course, the second optical output beam (103) must pass through a greater number of optical interfaces than does the first optical output beam (101). As a result, either the optical properties of all of the relevant optical interfaces should be precisely controlled in a relevant way to achieve “balanced” optical beams, or other less onerous and much more versatile control means should be implemented as well now be described.

[166] Figure 18, of the panel, describes the linear polarisation position angle of the input optical beam as being “~45°” (i.e. adjustably about 45°, but probably not exactly 45° in most circumstances). This position angle is to be considered relative to a “horizontal” plane which contains the propagation axis of the input optical beam (100A) and to which the propagation axes of both of the first and second optical output beams (101, 103) are both perpendicular (for assistance, the plane of the first circular polariser (420) shown in figure 18 is parallel to this “horizontal” plane). As a result of this position angle, the projection of the electric field vector of the EM wave of the input optical beam onto the “horizontal” plane is approximately equal (but not exactly equal) to the projection of that electric field vector onto the “vertical” plane which also contains the propagation axis of the input optical beam (100A) but is perpendicular to the aforementioned “horizontal” plane. The “horizontal” projection of the electric field vector has a projected linear polarisation component which lies within this “horizontal” plane and is also parallel to the plane of the internal reflective surface of the polarisation beam-splitter cube (10A). Furthermore, that internal reflective surface is configured and arranged to reflect this “parallel” linear polarisation component of the input optical beam, and to transmit the “perpendicular” linear polarisation component which corresponds to the projection of the electric field vector onto the “vertical” plane which has a linear polarisation direction that is transverse to the plane of the internal reflective surface and that is perpendicular to the aforementioned “parallel” linear polarisation component.

[167] The transmitted “perpendicular” linear polarisation component is subsequently incident upon the internal reflective (hypotenuse) surface of the first right-angle prism mirror (10B). The orientation of this internal reflective surface is such that the linear polarisation direction of the transmitted “perpendicular” linear polarisation component is parallel to the plane of the internal reflective surface with the result that reflection from this surface preserves the “vertical” orientation of the “perpendicular” linear polarisation component. However, the reflected “perpendicular” linear politician component is subsequently incident upon the internal reflective (hypotenuse) surface of the second right-angle prism mirror (10C) which is not parallel to the direction of linear polarisation of the incident light. Consequently, the right-angle prism mirror reprojects the direction of linear polarisation of the incident light by turning it through 90° such that it lies in the “horizontal” plane (i.e., coplanar with the first circular polariser for 420) and such that the resulting second optical output beam (103) has a direction of linear polarisation that is parallel to the direction of linear polarisation of the first output optical beam (101) output by the polarisation beam-splitter (10A).

[168] Since the internal reflective surface of the polarising beam-splitter (10A) will only reflect the “horizontal” projected polarisation component of the input optical beam (100A) that has sympathetic linear polarisation orientation, it is possible to control the proportion of input optical beam intensity that is reflected by the surface by appropriately controlling the size of the “horizontal” projected polarisation component relative to the size of the “vertical” projected polarisation component of the input optical beam thereby to control the relative intensities of the components of the input optical beam that are reflected and transmitted by the polarising beamsplitter. In this way, the linear polarisation position angle of the input optical beam (100A) may be adjusted to be slightly greater than 45° (the exact value being determined by calibration, as appropriate) such that a greater proportion of optical intensity resides in the transmitted (i.e. “vertical”) polarisation component than in the reflected (i.e. “horizontal”) polarisation component of the input optical beam. This means that the transmitted component carries with it a “sacrificial” excess budget of optical intensity was which is expected to be lost due to optical losses at subsequent optical interfaces through which the transmitted component must pass before exiting the first optical beam form. When the excess budget of optical intensity is correctly found, the result is that substantially all of the excess budget of optical intensity, but no more, is lost as the transmitted component of the input optical beam passes through the aforementioned optical interfaces and exits from the optical beam former with the same intensity as the reflected (i.e. “horizontal”) polarisation component (101).

[169] The first and second linear polarisation control parts (700A, 700B) is configured and arranged to control the orientation, or position angle, of the linear polarisation of the input optical beams (100A, 100B) for this purpose and is shown in schematic form in figure 14 because a number of different optional variants of the linear polarisation control part may be implemented according to preferred embodiments of the invention, as follows.

[170] A first option for the structure of the linear polarisation control parts is simply the provision of a rotatable linear polariser filter through which the associated input optical beam is directed and which is rotatable about an axis coaxial with the propagation axis of the input optical beam. The rotatable linear polariser filter has a polarising transmission axis perpendicular to the rotation axis of the polariser filter and which is rotatable, by physically rotating the filter, around the aforementioned axis such that the proportion of transmitted intensity passing through the linear polariser filter varies according to the rotation angle. By simply adjusting the rotation angle of the linear polariser filter to an appropriate angle, by a process of calibration, the desired result may be achieved whereby the output optical beams (101,103; or 102,104) are “balanced”.

[171] The second option may be to employ a polarisation-maintaining optical fibre as the optical delivery system by which an optical beam is delivered to the first, second, optical beam form at its associated optical fibre coupler, and to provide the linear polarisation control parts (700A, 700B) in the form of an optical fibre end rotator adapted to physically rotate the output end of the optical fibre, as received at the optical fibre coupler, about an axis coaxial with the propagation axis of the input optical beam (100A). By physically rotating the end of the polarisation-maintaining optical fibre, around the aforementioned axis, the orientation of the linear polarisation of the input optical beam is consequently rotated. The linear polarisation control parts also include, in this second option, a A / 2-plate (“half-wave plate”, or retarder) which is configured to advance by one half wavelength the component of the electrical field vector of the EM wave of the input optical beam that is projected on to the “fast axis” of the half-wave plate. Rotation of the half-wave plate serves to rotate the orientation of the “fast axis” and thereby control the proportion of the electric field vector of the input optical beam that is in advanced in this way, relative to the component that is not (i.e. the component projected onto the “slow axis” of the half-wave plate). The net effect is to controllably rotate the orientation of the linear polarisation axis of the input optical beam transmitted through the half-wave plate. By simply adjusting the rotation angle of the half-wave plate to an appropriate angle, by a process of calibration, the desired result may be achieved whereby the output optical beams (101, 103; or 102, 104) are “balanced”.

[172] As an alternative to the use of linear polarisation control parts (700A, 700B), a neutral density filter may be arranged at the output face of the polarising beam-splitter cubes (10A, 10D) which are configured to attenuate the optical intensity of the polarised optical beams (101, 102) reflected by the internal reflective surfaces of the respective polarising beam-splitter cubes, so as to ensure that the four output optical beams (101,103; or 102,104) are “balanced”.

[173] In the following discussion, reference is made to the schematic drawing of figure 26 which assists in explaining the importance of carefully controlling the linear polarisation and, ultimately, the circular polarisation state of the optical beams input into the 3D-MOT (and also the optical beams input into the 2D-MOT). This is to ensure that the photons within the optical beams possess the necessary angular momentum quantum number in order to allow them to preferentially access desired and appropriate atomic transitions to atomic energy states created, in the atoms being cooled, by the Zeeman effect.

[174] The !on-axis’ direction, is the direction which is along the symmetry axis passing through the centre of both anti-Helmholtz coils. The ‘off axis’ direction is the direction perpendicular to this, which also passes through the centre of the trapping region. Both counter-propagating beams have the same polarization. In the following discussion, it is assumed that the on-axis B-field is pointing outwards and the off-axis B-field (in the median plane between the coils) is pointing inwards (this can be reversed by changing the direction of the current).

[175] At point 'a', and ‘on-axis’, the following conditions prevail: • The photon k-vector of the left-hand optical beam and the local anti-Helmholtz magnetic ‘B-field’ point in opposite directions. The left-hand beam has a clockwise polarisation and this means that the beam drives a o~ atomic transition as schematically illustrated at the bottom of the figure (left-hand schematic). • The photon k-vector of the right-hand optical beam and the local anti-Helmhoitz magnetic ‘B-field’ point in the same direction. The right-hand beam has a clockwise polarisation and this means that this beam drives a o+ atomic transition as schematically illustrated at the bottom of the figure (right-hand schematic).

[176] Due to the Zeeman shift, the left-hand beam is closer to resonance with mF=-1 atomic transition than the right-hand beam is with mF=+1 atomic transition there. As a consequence, atoms at point ‘a’ absorb more photons from the left-hand beam than from the right-hand beam and thus tend to move towards the centre of the trap.

[177] At point 'b', and ‘on-axis’, the following conditions prevail: • The photon k-vector of the right-hand optical beam and the local anti-Helmholtz magnetic ‘B-field’ point in opposite directions. The right-hand beam has a clockwise polarisation and this means that the beam drives a a- atomic transition as schematically illustrated at the bottom of the figure (right-hand schematic). • The photon k-vector of the left-hand optical beam and the local anti-Helmholtz magnetic ‘B-field’ point in the same direction. The left-hand beam has a clockwise polarisation and this means that this beam drives a o+ atomic transition as schematically illustrated at the bottom of the figure (right-hand schematic).

[178] Again, the atoms are brought towards the centre of the trap.

[179] At point 'a', but this time ‘off-axis’, the following conditions prevail: • The photon k-vector of the left-hand optical beam and the local anti-Helmholtz magnetic ‘B-field’ are pointing in the same direction, and the left-hand optical beam has anticlockwise polarisation so that it drives a- atomic transitions. • The photon k-vector of the right-hand beam and the local anti-Helmholtz magnetic 'B-field’ point in opposite direction, and right-hand beam has a anti-clockwise polarisation so that it drives atomic transitions.

[180] At point ‘b’, again ‘off-axis’, the following conditions prevail: • The photon k-vector of the right-hand beam and the local anti-Helmholtz magnetic ‘B-field’ point in the same direction, and right-hand beam has anti-clockwise polarisation so that it drives o- atomic transitions. • The photon k-vector of the left-hand beam and the local anti-Helmholtz magnetic ‘B-field’ point in opposite direction. The left-hand beam has anti-clockwise polarisation so that it drives o+ atomic transitions.

[181] Again, the atoms are brought towards the centre of the trap.

[182] Accordingly, by controlling the circular polarisation states of photons injected into the 2D-MOT and the 3D-MOT, one is able to preferentially access appropriate atomic (Zeeman) transitions applications adjacent to the trap centre in such a way that the atoms experiencing those atomic transitions are urged towards the trap centre.

[183] The 2D-M0T: Beam Expansion

[184] Referring to figures 23A-23F the relevant optical structure and functions of the fourth optical beam former shall be described in more detail, as follows.

[185] As shown in figure 23A and 23B, the fourth optical beam former provides the functionality of a first optical expander and a subsequent second optical expander. The first optical expander (12, 13, 14, 15, 16 and 17) is arranged to receive a light beam (600) and to expand the cross-sectional area of the light beam asymmetrically in a first dimension (i.e. the X-dimension) transverse to the light beam thereby to provide a first expanded light beam (610, 620, 630, 640), and to deliver the first expanded light beam to the second optical expander. The second optical expander (410) arranged to receive the first expanded light beam (640) and to expand the cross-sectional area of the first expanded light beam asymmetrically in a second dimension (i.e. the Z-dimension) which is transverse to the first dimension, and to output the result as a second expanded light beam (650) in a direction (i.e. the Y-dimension) which is transverse to both the first dimension and the second dimension thereby to provide an output light beam having a cross-sectional area expanded in two transverse dimensions of the output light beam.

[186] The second optical beam expander (410) comprises a row of polarisation beam-splitter parallelograms. Each polarisation beam-splitter parallelogram contains a partially reflective internal surface each adapted to reflect a predetermined proportion (R) of light incident upon it internally, and to transmit the rest for input to the next polarisation beam-splitter parallelogram within the row. Thus, for example, an incident light beam (640) of intensity l0, impinges upon the partially reflective inclined surface of the first parallelogram in the row having a surface reflectivity Ri disposed therein at an angle of the parallelogram inclination. This partially reflective surface reflects a contributing part of an output beam (650) of intensity Rtlo, from an output surface of the beam-splitting parallelogram. Concurrently, a transmitted part of the incident light beam, of intensity Til0 where R^T^I, transmits through the partially reflective inclined surface of the first beam-splitter parallelogram and is transmitted into the next beamsplitter parallelogram to its partially reflective inclined surface. This next inclined surface has a surface reflectivity R2 disposed therein at the aforementioned parallelogram angle. This partially reflective inclined surface reflects a contributing part of the output beam (650) of intensity R2Til0, from an output surface of that beam-splitting parallelogram. This output beam is an additional contributing part of the overall output beam (650). Concurrently, a transmitted proportion of the incident light beam, of intensity T-iT2I0, is transmitted into the next beam-splitter parallelogram along the row to its partially reflective inclined surface having a surface reflectivity R3 disposed therein at the parallelogram angle. This partially reflective inclined surface reflects a further contributing part of the output beam (650) of intensity RsT^Iq, from an output surface of that beam-splitting parallelogram. By suitably designing the reflectivity of the partially reflective / transmissive surfaces in each successive beam-splitter parallelogram, it is possible to provide a situation in which the intensity of each of the individual beams contributing to, and collectively defining, the output beam beams (650) that are output by the successive beamsplitter parallelograms along the row of parallelograms, is substantially the same. That is to say:

[187] Ril0 = R2TiI0 = R3TiT2I0 =... etc. for subsequent beam-splitter outputs.

[188] Consequently, the optical output from each optical beam splitter parallelogram represents a component part of a greater optical beam (650) defined by the succession of partial optical beams. This is schematically illustrated in figures23C to 23E.

[189] By ensuring that the optical input face of the first, and subsequent, polarisation beamsplitter parallelograms is fully illuminated with input light light (640) one may provide that substantially the whole of each of the partially reflecting surfaces within each of the succession of polarisation beam-splitter parallelograms is also fully illuminated. A consequence of this is that there is substantially no gap between neighbouring output component optical beams of the second optical beam expander. Consequently, the output intensity transverse profile of the optical output beam (650) from the second optical expander may possess no zero-intensity null points such that the output optical beam (650) presents a usable intensity (loutPut) of light light across the whole of the second dimension (W2) in which it is expanded by the second optical beam expander.

[190] The individual beam-splitter optical elements are elongated three-dimensional optical elements possessing parallelogram-shaped cross-sectional profiles. Each is an elongated transparent body with six plane faces amongst which the two short end faces of the transparent body are each shaped as a parallelogram, while the remaining four long side faces which extend along the long axis of the transparent body are rectangular in shape. A succession of a plurality of such transparent bodies are arranged with a respective first one of the four long side faces disposed nearest to, and in optical communication with, the right-angle prism (17) for receiving light light therefrom, thereby placing a second one of the four long side faces, opposite to the first long side face, in direct contact and optical communication with the first long side face of a successive transparent body. Each such contact interface between successive transparent bodies defines a partially reflective and partially transmissive surface for use in outputting a component part of the output optical beam.

[191] The first optical beam expander may be arranged to over-expand the incoming beam before it outputs the first expanded light beam (l0) such that the cross-sectional area of the first expanded light beam fully fills the clear aperture of the optical input area / face of the second optical expander receiving it. Consequently, the second expanded light beam may provide a fully-supplied output light beam having substantially no intensity ‘nulls’ or gaps within its beam cross-section. Put another way, the cross-section beam intensity may be made free of ‘gaps’ or ‘holes’ at which the local light intensity of the beam is negligible or too small to be of practical use.

[192] Figure 23F shows a cross-sectional view of an output light beam of the optical beam forming apparatus of figures 23A-23E, that is to say, a view looking down the axis of the output light beam (650) towards the second optical beam expander (410). Beam intensity profiles are shown along the first and second dimensions (transverse) of the beam. It can be seen that the output light beam is generally rectangular in cross-section and presents a wall of light. In the example shown, the cross-sectional dimensions of the wall of light are about 25mm by about 35mm. The output light beam has a significant, non-zero light intensity over the whole of that cross-sectional area. Whereas the intensity distribution is not uniform in the example shown, a greater degree of uniformity may be achieved, if desired, by adjusting the reflectivity of the reflective surfaces within the second optical beam expander in order to achieve a desired uniformity (or at least greater agreement / similarity) as between the intensity of the reflected light output by each such surface relative to the others.

[193] Similarly, the uniformity of the cross-sectional intensity distribution of the first expanded light beam (640), produced by the first beam expander, may also impact upon the cross-sectional intensity distribution of the ultimate output light beam and factors such as the performance of the optical components of the first optical beam expander may be adjusted as desired to improve intensity uniformity, if that is desired. In addition, the cross-sectional uniformity of the light intensity initially input to the optical beam forming apparatus will influence the intensity distribution of the ultimate output light beam.

[194] A first output light beam intensity profile is illustrated in the right-hand graph / section of Figure 23F and corresponds to the intensity distribution along the ‘vertical’ line on the beam cross-section image passing from the bottom of the beam cross-section image to the top at a constant ‘horizontal’ position of about 21mm, and a ‘vertical’ position spanning from 0mm to 26mm. A second output light beam intensity profile is illustrated in the upper graph / section of Figure 23F and corresponds to the intensity distribution along the horizontal line passing from the left hand side of the beam cross-section to the right at a constant vertical position of about 12.5mm, and a horizontal position spanning from 0mm to 40mm. A series of twelve intensity peaks can be seen in the second cross-section which correspond to the peaks in reflected intensity from a second beam expander comprising twelve successive reflecting internal surfaces of the second optical beam former (410). A drop in output intensity is seen between successive intensity peaks and this arises at the region of the second optical beam expander where the bottom edge or one internal reflecting surface coincides with the upper edge of the succeeding internal reflective surface as viewed down the output axis of the output light beam. Here, greater optical losses may occur, but these optical losses are not so significant as to prevent a useful intensity of light to be present in the output light beam at the location of an intensity minimum, albeit less than that at the peak of the intensity peaks either side. Overall, the reduction in intensity at the troughs between peaks amounts to only about 5% of the overall output intensity of the beam and is not significant. The width and depth of these troughs may be reduced by adjusting the extent of the internal reflective regions so that the region where the bottom edge of one internal reflecting surface overlaps, or projects over, with the upper edge of the succeeding internal reflective surface as viewed down the output axis of the output light beam. This means that light from two neighbouring internal reflecting surfaces may be combined at the overlap region so as to boost output intensity there.

[195] It is important to note that it is not essential that the cross-sectional intensity distribution of the output light beam (650) is uniform in order to be able to manipulate cold atoms or molecules (e.g. in a 2D-MOT cooling process). This is because the optical processes (e.g. optical molasses) underpinning the manipulation induce optical forces upon an atom / molecule that saturate in value above a certain light intensity threshold, and no significant improvements in performance are achieved by employing a higher output light beam intensity at a given location of a manipulated atom / molecule. Thus, it is quite sufficient that, if one wishes to provide greater uniformity performance (optical forces) of the output light beam for manipulating cold atoms / molecules, then preferably one merely requires that there is an intensity of light across the light beam that is at or above a threshold intensity level.

[196] Referring now to figure 24 in figure 25, the process of generating cold atoms for the purposes of inertial measurements, using the initial atom source of the present embodiments, is schematically described.

[197] A first step in the process, at step (a) of figure 25, is the laser heating of sample pills located within the sample pill holders (66 : see figure 11) because to release into the 2D-MOT region (40) of the channel cell (47), atoms to be cooled (e.g. rubidium atoms).

[198] Concurrently or subsequently, at step (b) of figure 25, operation of the 2D-MOT chamber (40) is performed by injection of cooling optical beams (650) into the 2D-MOT chamber, as described above, produces generation of a lozenge (700) of cold atoms is schematically illustrated in figure 24(A). Application of a “push beam” into the 2D-MOT chamber pushes the lozenge of cold atoms into the 3D-MOT chamber.

[199] The next step, step (c) of figure 25, is to apply a 3D-MOT process to the cold atoms inserted into the 3D-MOT chamber (45) by the 3D-MOT cooling process described above, as the cold atoms traverse the volume of the 3D-MOT chamber and pass through the intersection point (110) as “moving molasses” (710) as schematically illustrated in figure 24(B).

[200] At a subsequent step in the process, according to step (d) figure 25 and schematically illustrated in figure 24(C), the moving “moving molasses” (710) generated in the 3D-MOT chamber is injected (720) into the inertial measurement chamber (46).

[201] A final step in the process, according to step (e) figure 25, the desired initial measurements are made upon the “moving molasses” (720) once it has fully entered the inertial measurement chamber (46). 21 10 24

Claims

1. An optical beam-forming apparatus configured to form optical beams of light for manipulating cold atoms or cold molecules in a chamber of a magneto-optical trap (MOT), the apparatus comprising:a first optical beam-former and a second optical beam-former;wherein each said optical beam-former is configured to receive a respective input optical beam of light and therewith to form a respective pair of optical beams of linearly polarised light for output into the chamber of the MOT; and,wherein the orientations of linear polarisation of each of the four optical beams are mutually substantially parallel.

2. An optical beam-forming apparatus according to any preceding claim wherein the first optical beam-former and / or the second optical beam-former is configured to form said respective pair of optical beams to be substantially parallel.

3. An optical beam-forming apparatus according to any preceding claim wherein the first optical beam-former and the second optical beam-former are configured to form mutually substantially parallel said optical beams, thereby providing four substantially parallel optical beams.

4. An optical beam-forming apparatus according to any preceding claim wherein the first optical beam-former includes a polarisation controller configured to adjustably impose an orientation of linear polarisation upon said input optical beam thereby to form a linearly polarised input optical beam, and a polarising beam-splitter configured to split the linearly polarised input optical beam into a pair of optical beams of linearly polarised light of relative optical intensities adjustable according to said imposed orientation of linear polarisation, and therewith the first optical beam-former is configured to form said respective pair of optical beams.

5. An optical beam-forming apparatus according to any preceding claim wherein the second optical beam-former includes a polarisation controller configured to adjustably impose an orientation of linear polarisation upon said input optical beam thereby to form a linearly polarised input optical beam, and a polarising beam-splitter configured to split the linearly polarised input optical beam into a pair of optical beams of linearly polarised light of relative optical intensities21 10 24adjustable according to said imposed orientation of linear polarisation, and therewith the second optical beam-former is configured to form said respective pair of optical beams.

6. An optical beam-forming apparatus according to claim 4 or claim 5 in which the polarisation controller is controllable to adjust the imposed orientation of linear polarisation thereby to controllably adjust said relative optical intensities of the optical beams of the said respective pair of parallel optical beams to be substantially the same.

7. An optical beam-forming apparatus according to any preceding claim including a circular polariser configured to receive an optical beam of the four parallel optical beams to convert the polarisation thereof from a state of linear polarisation to a state of circular polarisation.

8. An optical beam-forming apparatus according to claim 7 wherein the circular polariser is configured to receive each optical beam of the four parallel optical beams simultaneously thereby simultaneously to convert the polarisation thereof from a state of linear polarisation to a state of circular polarisation.

9. A magneto-optical trap (MOT) comprising an optical beam-forming apparatus according to any preceding claim.

10. A magneto-optical trap (MOT) according to claim 9 comprising the chamber of the MOT, in which the chamber of the MOT comprises a pyramidal mirror assembly for receiving the optical beams of light and for reflecting the received optical beams of light into one or more pairs of counter-propagating optical beams of light for manipulating cold atoms or cold molecules.

11. A magneto-optical trap (MOT) according to claim 9 or claim 10, and including a magnetic field apparatus configured to provide a magnetic field arranged to concentrate gas atoms or molecules cooled or manipulated using the optical beam-forming apparatus.

12. A cold atom source comprising a magneto-optical trap (MOT) according to claim 10 or 11.

13. An accelerometer comprising a magneto-optical trap (MOT) according to claim 10 orclaim 11, or comprising a cold atom source according to claim 12.21 10 2414. A vehicle comprising an accelerometer according to claim 13.

15. A vehicle according to claim 14, where in the vehicle is an aircraft, or a sea-going vessel, or a land vehicle, or a spacecraft.

16. A method to form optical beams of light for manipulating cold atoms or cold molecules in a chamber of a magneto-optical trap (MOT), the method comprising:providing a first optical beam-former and a second optical beam-former;by each said optical beam-former, receiving a respective input optical beam of light and therewith forming a respective pair of optical beams of linearly polarised light, and outputting each pair of optical beams into the chamber of the MOT; and,wherein the orientations of linear polarisation of each of the four optical beams are mutually substantially parallel.

17. A method according to claim 16 including, by the first optical beam-former and / or the second optical beam-former, forming said respective pair of optical beams to be substantially parallel.

18. A method according to claim 16 or claim 17 including, by the first optical beam-former and / or the second optical beam-former, forming the first optical beam-former and the second optical beam-former are configured to form mutually substantially parallel said optical beams, thereby providing four substantially parallel optical beams.

19. A method according to any of claims 16 to 18 including, by said first optical beam former, adjustably imposing an orientation of linear polarisation upon said input optical beam thereby to form a linearly polarised input optical beam, and splitting the linearly polarised input optical beam into a pair of optical beams of linearly polarised light, and adjusting the relative optical intensities thereof according to said imposed orientation of linear polarisation, thereby forming said respective pair of optical beams.

20. A method according to any of preceding claims 16 and 19 including, by said second optical beam-former, adjustably imposing an orientation of linear polarisation upon said input optical beam thereby to form a linearly polarised input optical beam, and splitting the linearly polarised input optical beam into a pair of optical beams of linearly polarised light, and adjusting21 10 24the relative optical intensities thereof according to said imposed orientation of linear polarisation, thereby forming said respective pair of optical beams.

21. A method according to claim 19 or claim 20 including adjusting the imposed orientation of linear polarisation thereby controllably adjusting said relative optical intensities of the optical beams of the said respective pair of optical beams to be substantially the same.

22. A method according to any of preceding claims 16 to 21 including converting the polarisation of an optical beam of at least one of, or each of, the four parallel optical beams from a state of linear polarisation to a state of circular polarisation.

23. A method according to claim 22 including simultaneously converting the polarisation of each of the four parallel optical beams from a state of linear polarisation to a state of circular polarisation.

24. An optical beam-forming apparatus according to any of claims 1 to 8, or a magnetooptical trap (MOT) according to any of claims 9 to 11, or a cold atom source according to claim 12, or an accelerometer according to claim 13, in which the magneto-optical trap (MOT) comprises a three-dimensional magneto-optical trap (3D-MOT) and / or comprises a two-dimensional magneto-optical trap (2D-MOT).

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