Patent Description:
During the early development of laser cooling and trapping in the late <NUM>'s many research groups discovered that the temperature of the trapped atoms was far below the limit thought to be imposed by the Doppler cooling at the time. A careful exploration of methods to determine the temperature was carried out by Lett et al in <NUM> [<NUM>] to confirm these findings, which were referred to at the time as "supermolasses" in comparison to Doppler-limited molasses cooling as it was then understood. In the following year, two groups independently submitted theoretical explanations identifying polarization gradient cooling (also referred to a Sisyphus cooling) as the mechanism behind the additional cooling effect [<NUM>, <NUM>]. These theories relied upon the internal structure of the atoms to scatter additional energy via the polarization-dependent modulation of the atomic states. These above effects have been explored and are now fully understood. However, during this same period of uncertainty surrounding the supermolasses effect, another observation was made which has seen very little exploration. It was noted by Chu et al [<NUM>] that when the counterpropagating laser beams were slightly misaligned the number of atoms collected inside the molasses increased significantly, by well over an order of magnitude, and remained trapped for several seconds. Some aspects of this effect could be explained via "racetrack modes" [<NUM>]. However, this observation seems to have remained largely unexplored. One possible theoretical explanation was put forward [<NUM>] based around a model inspired by the Kapitza (or inverted) pendulum that involved vortex forces but has not been experimentally verified. Similar unexpected cooling and trapping of atoms in the absence of a magnetic field has also been reported elsewhere in the literature [<NUM>, <NUM>]. The traps reported in both these references have three counter-propagating beam pairs orthogonally arranged along the three Cartesian axes. The trap of reference [<NUM>] required linearly polarised light, very good vacuum, and laser beams of large diameter (≥<NUM>) to operate successfully. To produce a counter-propagating beam pair, each incident beam was reflected at a slight angle away from exact retro-reflection with misalignments in the range <NUM>° - <NUM>° providing good performance. The postulated mechanism for trapping was the dipole force [<NUM>]. Like reference [<NUM>], the trap of reference [<NUM>] also used large-diameter beams and counter-propagating beam pairs that were slightly misaligned. The trap of reference [<NUM>] operated with either linear or circular polarization. Its operation needed loading from a standard Magnetic Optical Trap (MOT) before the magnetic field was extinguished, i.e. it could not form a cooled atom cloud direct from vapour. The authors consider a number of theoretical processes that could result in such a trap and in particular suggested the process may be related to a superlattice dipole trap.

The reason why cooling and trapping of atoms with solely optical fields, i.e. without magnetic fields, is unexpected is due to the optical equivalent of the Earnshaw theorem [<NUM>] that states: <MAT> where Fs is the scattering force on a particle with scalar polarizability. In essence, the scattering force alone cannot produce a stable restoring force on a dipole in all dimensions because there are no sources or sinks of optical fields in free space. This limitation is typically overcome by manipulating the internal states of the atom via a Zeeman shift (as in a MOT) or AC Stark shifts (as in a dipole trap).

A purpose-designed all-optical trap is the optical trap developed by Bouyer et al [<NUM>], which is called the Trap Relying On Optical Pumping (TROOP). The TROOP uses uncollimated, i.e. divergent, beams of orthogonal circular polarization aligned along each Cartesian axis to produce a spatially varying, and thus positionally dependent, force via unbalanced laser power and optical pumping. Like a MOT or a dipole trap, the TROOP is also based on the manipulation of internal states.

According to a first aspect of the disclosure there is provided an optical trap for trapping and cooling atoms, the optical trap comprising:.

According to a second aspect of the disclosure there is provided a method of laser cooling and trapping atoms, the method comprising:.

With this approach it is possible to provide an all-optical trap, i.e. one that does not rely on the presence of a magnetic field. Since no magnetic field is used for the cooling effect exploited by the present invention, of course a corresponding optical trap does not require any magnetic coils or any other form of magnetic field generator to be provided, since no magnetic field needs to be generated in the vacuum chamber. A Zeeman slower is also not needed.

An optical trap embodying the invention does not need to include a magnetic field generator, since laser cooling takes place without a magnetic field being present.

In certain embodiments, the misalignment angles comply with one or more of the following conditions:.

In certain embodiments, the first, second and third alignment angles are equal to each other. In other embodiments, at least two of the first, second and third alignment angles are different from each other.

The first, second and third reflectors may be configured such that the reference axis and each pair of incident and reflected beam paths lie at least approximately in a common plane, thereby defining first, second and third such planes. The first, second and third planes may be approximately equally angularly spaced as viewed along the reference axis.

In certain embodiments, polarising components are arranged to provide the first, second and third beams with respective defined polarisation states when they enter the vacuum chamber. The first, second and third reflectors may be configured to ensure that the defined polarisation states of the first, second and third beams are preserved on reflection, e.g. circular polarisation or linear polarisation.

For certain atomic species, there is a further electronic transition, referred to as the repump transition, which is required to be excited for efficient cooling to occur. In such cases, the laser source or a further laser source is configured to generate further laser light at a further frequency tuned at the frequency of the repump transition. The optical arrangement may then further comprise a beam combiner operable to combine the laser light and the further laser light so that each of the first, second and third beams contain both the laser light and the further laser light.

Preferably, the first, second and third beams are at least approximately collimated as they cross the vacuum chamber. Approximate collimation may be characterised by the beam divergence, where a beam divergence Θ = <NUM> corresponding to a collimated beam, and approximate collimation as concerns the present invention may be a beam divergence, Θ, less than or equal to one of <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM> or <NUM> degrees.

While in principal embodiments, the first, second and third alignment angles form an angle of between <NUM>° and <NUM>° to the reference axis, other embodiments have alignment angles beyond this range. For example, the lower limit may be as low as any one of <NUM>°, <NUM>°, <NUM>°, <NUM>° or <NUM>° and the upper limit may be as high as <NUM>°, <NUM>°, <NUM>°, <NUM>° or <NUM>° to the reference axis.

This invention will now be further described, by way of example only, with reference to the accompanying drawings.

In the following the invention is described by way of example for cooling <NUM>Rb atoms. The invention is usable for any atomic species that is capable of being optically cooled. In principle any atoms from Group I or II of the periodic table are amenable to optical cooling. In practice to date, atomic species for which optical cooling has been demonstrated include: Rb, Cs, Li, Sr, Ca, K and Fr. In the case of Sr, it is further noted that a repump is not needed, so the corresponding equipment described below in connection with repump would be omitted.

<FIG> is a schematic perspective drawing showing the laser beam geometry used in an optical trap according to embodiments of the invention. The two circles represent two vertically offset planes, perpendicular to the z-axis. The various beam paths are indicated schematically by respective straight lines corresponding to their principal optical axes with arrows indicating the direction of beam propagation. For ease of representation, the finite beam cross-sections of the beams are not illustrated.

Three laser beams travel along respective incident beam paths (lines with arrows pointing down) with circular polarisation collectively to form a tripod-like arrangement. The incident beam paths are equally spaced radially about the z-axis and so form angles of γ = <NUM>° to each other as viewed along the z-axis. The three incident beam paths are aligned at an inclination angle χ away from the z-axis. A common inclination angle is shown with a value of χ = <NUM>°, but in other embodiments unequal inclination angles could be used. Each incident beam path thus lies in a plane containing the z-axis and forms an inclination angle χ to the z-axis. Each of these three planes subtends an angle of <NUM>° to the other two planes to provide equal angular spacing of the three beams. In the following description, the laser beams are assumed to be collimated. In practice, collimated, or at least only weakly diverging or converging beams, will be needed. Each beam is reflected back from its incident beam path into a reflected beam path, the reflections taking place in the plane of the lower circle. Each reflection is performed so as to maintain the polarisation state of the beam, e.g. circular or linear. Preservation of circular polarisation may be achieved by a quarter waveplate and dielectric mirror combination. The three reflected beam paths (lines with arrows pointing up) are misaligned by respective angles [α, β, K] away from retro-reflection, where retro-reflection is when the reflected beam path is coincident with its incident beam path. The inclination of the misalignment in each case is towards the z-axis, i.e. each reflected beam path lies in the same above-mentioned plane as its incident beam, but with a reduced angle of inclination to the z-axis. The angles [α, β, K] may in general be different from each other but they could be all the same, or two of them could be the same.

As a further geometrical observation, it is noted that all six beam paths cross the z-axis at respective points. <FIG> shows the incident beam paths having a common crossing point, whereas, since the misalignment angles are generally not equal, the three reflected beam paths will generally cross the z-axis at different points, each slightly above the common point where the incident beam paths cross. The misalignment angles [α, β, K] and finite beam widths result in a volume of intersection being formed which is the volume traversed by the beams both along their incident beam paths and along their reflected beam paths. The six beam components interfere with each other in the volume of beam intersection. This interference is what causes the cooled atom cloud to be formed in the volume of intersection.

For efficient operation of the an optical trap according to embodiments of the invention, it is considered to be necessary that all the beams are at least approximately collimated and that the beam diameters, inclination angles and misalignment angles are chosen collectively such that all six beam components cross in a common region (the volume of beam intersection).

In experiments performed to date with a common inclination angle of <NUM>°, for efficient cooling and trapping to form a cloud in the volume of beam intersection directly from vapour, the misalignment angles had typical magnitudes from <NUM>° to <NUM>° in combination with beam diameters around <NUM>, where beam diameter is taken as the <NUM>/e<NUM> value of a Gaussian fit, noting that the range of useable misalignment angles depends on beam diameter, with larger beam diameters allowing larger misalignment angles. For good performance, it also seems necessary for at least two of the misalignment angles to be different from each other.

In particular, very good performance is seen with the following combination of misalignment angles: a first beam path pair has a misalignment angle such that the incident and reflected beams are separated by approximately half a beam width in the volume of beam intersection. A second beam path pair has a misalignment angle set to a very small value, perhaps <NUM>-<NUM> times lower than that of the first beam pair. The third beam path pair has a misalignment angle set to approximately the same or somewhat more than for the first beam path pair, perhaps <NUM>-<NUM> times.

An important experimental observation is that formation of a cooled atom cloud from vapour is not at all sensitive to these geometric parameters or the level of detuning. Rather, it is easy to find a parameter combination that results in formation of a cloud from vapour, and, once cloud formation occurs, it is easy to optimize the parameter combination, since cooling performance gradually and monotonically improves or worsens when one of these parameters is adjusted. Consequently, it is experimentally straightforward to adjust one parameter at a time in a stepwise or continuous manner, for example, each misalignment angle in turn, or the cooling detuning level, to improve the cloud formation, e.g. in terms of its temperature, shape or density, to find an optimum parameter combination for forming a dense, cold and approximately spherically shaped cloud.

From simple trigonometry, the misalignment angle value that causes the incident and reflected beam paths to be separated by half a beam width at the crossing point is met when the misalignment angle θ is: <MAT> where.

Experiments to date show that the optical trap's performance is comparable to that of a conventional MOT in terms of atom numbers (~<NUM>°<NUM>), cloud density (<NUM><NUM> atoms/cm<NUM>) and cloud temperature (< <NUM>µK). The atom cloud formed at the volume of beam intersection is typically millimetre-sized and has a somewhat elongate (roughly ellipsoid) shape with the long axis of the ellipse aligned along one of the beam paths. The cloud shape and cloud volume can be manipulated experimentally by incrementally adjusting the magnitude of one or more of the misalignment angles [α, β, K]. This effect can be exploited to find an optimum combination of misalignment angles by incrementally reducing both the size of the cloud and its aspect ratio, so as to form a small, dense cloud with a near-spherical shape, as is usually desired.

<FIG> are schematic drawings showing various parts of a system used to demonstrate optical trap operation experimentally with a vapour of <NUM>Rb atoms.

<FIG> and <FIG> show optical setups for providing stabilised cooling and repump laser beams respectively. It is noted that both these stabilisation schemes are known, and also that the skilled person knows of other stabilisation schemes that would be suitable. <FIG> shows the system setup around the optical trap's vacuum chamber.

With reference to <FIG>, the cooling setup <NUM> is based on a laser source <NUM>, which is a distributed feedback diode (DFB) laser. The DFB has a centre wavelength of <NUM>, linewidth of ~<NUM> and output power range <NUM>-<NUM> mW. The cooling laser is stabilised to the <NUM>Rb transition:.

<NUM><NUM>S<NUM>/<NUM> F=<NUM> → <NUM><NUM>P<NUM>/<NUM> F'=<NUM>.

using modulated transfer spectroscopy [<NUM>]. The beam from the cooling laser <NUM> is initially passed through an optical isolator <NUM> and half-wave plate <NUM>. A polarising beam splitter (PBS) <NUM> is arranged in the beam to divide it into two branches. One branch, having a small fraction of the beam power, is used as input to control a laser stabilisation system (vertical branch), whilst the remainder of the optical power, referred to as the main beam, ultimately provides the incident beams to the trap (straight-through branch). The stabilisation branch is supplied via a mirror <NUM> to a further PBS <NUM> which again divides the beam into two. The straight-through branch from the PBS <NUM> leads directly to a vapour cell <NUM> and forms the probe beam of a pump-probe scheme, the probe beam having the frequency of the laser <NUM>. The probe beam thus traverses the vapour cell <NUM> from right-to-left in the drawing. The branch deflected from the PBS <NUM> is used to generate the pump beam. The pump beam branch is directed by further mirrors <NUM> and <NUM> to an acousto-optical modulator (AOM) <NUM>. The AOM <NUM> diffracts the input beam to output zeroth and two first order diffraction beams. These three beams are reflected back from a mirror <NUM> and on their passage back through the AOM <NUM> are recombined into a single beam. A quarter-wave plate <NUM> is arranged between the AOM <NUM> and the mirror <NUM> to provide the desired circular polarisation. The combined, reflected beam passes via mirrors <NUM> and <NUM>, straight-through passage through the PBS <NUM>, further routing with mirrors <NUM> and <NUM> and a further PBS <NUM>, as well as via passage through a half-wave plate <NUM>, to traverse the vapour cell <NUM> as the pump beam from left-to-right in the drawing, i.e. in the opposite direction to the probe beam. These components thus collectively form a saturated absorption spectroscopy arrangement to generate an error signal from four-wave mixing in the rubidium atoms contained in the vapour cell. In the vapour cell, each of the pump and probe beams traversing the vapour cell <NUM> generates a sub-Doppler spectrum, slightly shifted in frequency relative to the other. By subtracting the resultant spectra, an error signal is generated from the photodiode output. The first order diffracted beam used for the laser stabilisation is composed of the main carrier of frequency ωc = ω<NUM> + ωAOM with sidebands of frequency ωs = ωc ± ωmod. The double-pass through the AOM <NUM> further modulates the main carrier beam, which now has a frequency of ω = ω<NUM> + 2ωAOM with sidebands offset by ±ωmod. In the experimental set-up, the pump beam has a frequency shift of ωshift = <NUM> with an additional modulation of ωmod = 2π x <NUM>. Considering that the atoms move inside the vapour cell with velocity v, they interact with the probe beam at the frequency of ωprobe = ω<NUM> - kv. In the case of the pump beam, the atoms interact at a frequency of ωpump = ω<NUM> + 2ωAOM + kv, where ±k are the pump and probe beams wavevectors. A spectrum is generated only when the atoms resonate with both beams simultaneously. Therefore, the only atoms that interact are those that are travelling towards the probe beam with a velocity of v = ωAOM / k. Since the error signal is generated from two sidebands of the first order diffracted beam, the feedback from the error signal will stabilise the laser <NUM> at an output frequency of ω<NUM> + ωAOM, i.e. shifted by ωAOM from what is required. In order to reverse this shift, a further AOM <NUM> is arranged in the path of the main laser beam. The first order diffraction beam output from the AOM <NUM> at frequency ω<NUM> is then supplied via mirrors <NUM> and <NUM> to an optical fibre coupler <NUM> to couple the light into an optical fibre <NUM>, which is used for convenient delivery of the cooling laser beam to the trap. The amount of laser detuning, δ, below the resonant frequency (i.e. so-called red detuning), in this case from the <NUM>Rb cooling transition, is conveniently represented in units of Γ, where Γ = 2π x <NUM> is the natural decay rate of <NUM>Rb. For the example system, the detuning δ = -<NUM>. The error signal is extracted from the left-hand-side output of the vapour cell <NUM> via a PBS <NUM> (straight-through path), focusing lens <NUM> and photodiode <NUM>. The electrical signal output from the photodiode <NUM> is then amplified and demodulated with suitable demodulation electronics <NUM> to generate the error signal. The error signal is then fed back in a feedback loop via a proportional-integral-derivative (PID) controller to control the laser <NUM> by adding the error signal as a modulation to the laser's drive signal.

With reference to <FIG>, the repump laser set up <NUM> is based on a laser source <NUM>, which is matched to form a pair with the cooling laser source <NUM>, i.e. in this example being another DFB with the same specifications. The repump laser is stabilised to the following <NUM>Rb transition:.

<NUM><NUM>S<NUM>/<NUM> F=<NUM> → 5P<NUM>/<NUM> F'=<NUM>.

using carrier modulation spectroscopy [<NUM>]. The repump laser <NUM> is stabilised using a similar approach to the cooling laser, but without the need for dedicated demodulation electronics for demodulating the signal [<NUM>]. The repump laser beam is passed through an optical isolator <NUM> and a half-wave plate <NUM>. Then a PBS <NUM> is used to separate the repump laser beam in two. One beam, having a small fraction of the beam power, is used as input to control a laser stabilisation system (vertical branch), whilst the remainder of the optical power, referred to as the main beam, ultimately provides the incident beams of the trap (straight-through branch). The branch for laser stabilisation is supplied via a mirror <NUM> to an AOM <NUM>, the AOM <NUM> having an additional modulation applied on top of its native frequency, as described above in the cooling laser stabilisation set-up. The modulation added to the AOM <NUM> is in the form of a square wave of frequency ωmod = <NUM>. This causes the first order diffracted beam from the AOM to split into two components of frequencies ω<NUM> = ω<NUM> + ωAOM + ωmod and ω<NUM> = ω<NUM> + ωAOM-ωmod which respectively form pump and probe beams for a saturated absorption spectroscopy arrangement based around a vapour cell <NUM> containing Rb vapour. The probe beam passes through the PBS <NUM> and traverses the vapour cell <NUM> from left-to-right in the drawing. The pump beam is routed via deflection by the PBS <NUM> and suitable mirrors <NUM> and <NUM> as well as passage through a half-wave plate <NUM> and finally deflection by a further PBS <NUM> to traverse the vapour cell <NUM> from right-to-left in the drawing, i.e. in the opposite direction to the probe beam. The probe beam output from the vapour cell <NUM> via the straight-through branch of the PBS <NUM> is focused by a lens <NUM> onto a quadrant photodiode <NUM>. (As an alternative to a quadrant photodiode <NUM> a balanced photodiode or two separate photodiodes could be used. ) The error signal is obtained from the probe beam output of the vapour cell <NUM> via a PBS <NUM> (straight-through path), focusing lens <NUM> and photodiode <NUM>. In the vapour cell, each of the pump and probe beams traversing the vapour cell <NUM> generates a sub-Doppler spectrum, slightly shifted in frequency relative to the other. By subtracting the resultant spectra, an error signal can be generated from the photodiode segment outputs. The error signal is then fed back in a feedback loop via a proportional-integral-derivative (PID) controller to control the laser <NUM> by adding it as a modulation to the laser's drive signal. Since the error signal is generated from two sidebands of the first order diffracted beam, the feedback from the error signal will stabilise the repump laser at an output frequency of ω<NUM> + ωAOM, i.e. shifted by ωAOM from what is required. In order to reverse this shift, a further AOM <NUM> is arranged in the path of the main laser beam, similar to the cooling laser stabilisation system. The first order diffraction beam output from the AOM <NUM> at frequency ω<NUM> is then supplied via mirrors <NUM> and <NUM> to an optical fibre coupler <NUM> which couples the beam into an optical fibre <NUM>, which is used for convenient delivery of the repump laser beam to the trap. An advantage of this repump stabilisation system is that it does not require complicated electronics and so is suited to portable, low-power systems.

The above-described detuning of the cooling and repump lasers from resonance is achieved using AOMs. An alternative would be to use a scheme based on a single laser source and then the laser beam could be used to generate both the cooling and repump beams with an electro-optic modulator (EOM). An EOM is a device which modulates the phase of a beam by driving a low frequency electric field across a crystal that exhibits in response a linear shift of its refractive index.

After stabilisation as described above with reference to <FIG> and <FIG>, the cooling and repump beams are combined into a single beam and delivered to the optical trap in the beam geometry shown in <FIG>.

<FIG> shows the experimental setup for the optical trap <NUM> that was used in the example setup. The cooling and repump beams are delivered to the optical trap setup <NUM> via the respective optical fibres <NUM>, <NUM>. The cooling and repump beams are first combined with a <NUM>-to-<NUM> fibre coupler <NUM>. In the experiments, this was done with a <NUM>:<NUM> power ratio of cooling:repump. The combined beam is then split into three components of equal power by a <NUM>-to-<NUM> fibre splitter <NUM>. The respective output sides of the splitter <NUM> are three sections of optical fibre <NUM>, <NUM>, <NUM>. These combining and splitting functions can be achieved in optical fibre using appropriate combiners and splitters taking care to preserve polarisation as desired, e.g. using non-polarising or polarisation preserving combiners, splitters and fibre. Alternatively, free-space optical components could be used for the combining and splitting. The optical fibres <NUM>, <NUM>, <NUM> terminate in respective optical fibre couplers <NUM>, <NUM>, <NUM> which are arranged to provide the beam geometries for the incident beam paths as described above with reference to <FIG>.

In the example set-up, the three beams output from the respective optical fibre couplers <NUM>, <NUM>, <NUM> have an approximate Gaussian power distribution in cross-section and are each collimated with a collimator lens (not separately shown) to a diameter of <NUM>, where the diameter is taken as the <NUM>/e<NUM> value. The light polarisation state in the three beams output from the optical fibres <NUM>, <NUM>, <NUM> is set to circular using respective PBSs <NUM>, <NUM>, <NUM> and quarter waveplates <NUM>, <NUM>, <NUM>. The three beams then traverse a vacuum chamber <NUM> which has windows that are transparent to the wavelengths of the beams or is entirely made of transparent material, e.g. a suitable glass. After traversing the vacuum chamber <NUM> each beam is reflected by a quarter waveplate and dielectric mirror combination <NUM>/<NUM>, <NUM>/<NUM>, <NUM>/<NUM> where the reflection is close to retro-reflection, i.e. reflection back along the same path, but slightly misaligned, as described above with reference to <FIG>. After reflection, the beams then traverse the vacuum chamber <NUM> for a second time.

As discussed with reference to <FIG>, because of the finite beam widths (i.e. cross-sections) of the incident and reflected beam components, a volume of intersection of the beams, V, shown schematically with a dotted ellipse in <FIG>, is formed within the vacuum chamber <NUM>. The vacuum chamber <NUM> is formed in the example set-up by an anti-reflection coated glass vacuum cell with dimensions of <NUM> x <NUM> x <NUM>. The rubidium atoms in the vacuum chamber are cooled and concentrated in a cloud within the beam intersection volume V.

The vacuum chamber <NUM> is operable to provide a vacuum atmosphere through the action of a suitable vacuum pump <NUM>, e.g. an ion pump, arranged in fluid communication with the vacuum chamber <NUM> via appropriate vacuum conduits <NUM>. A vacuum valve <NUM> for the vacuum space is also provided. In the example experiments, the vacuum cell was generally maintained at a vacuum of <NUM> x <NUM>-<NUM> mbar. The vacuum space also includes a source of atoms to be cooled, in the example setup an atom source <NUM> provides the rubidium atoms. The rubidium atoms are release by heating the source material, e.g. with an electrical heater element <NUM> that is operable to supply a DC current to heat the source material. In the example experiments, the rubidium vapour is provided by an alkali metal dispenser which increases the background vapour pressure to <NUM> x <NUM>-<NUM> mbar during operation of the trap. Other forms of heating, e.g. with laser light, may also be used.

In order to characterise the behaviour of the optical trap, the number of trapped atoms, N, and their temperature, T, are measured as a function of various parameters including total beam power, P, and the level of red detuning, δ, of the cooling laser from the <NUM>Rb cooling transition. In the following, the stated values of the total beam power represent the sum of the powers of all three incident beams, which includes the powers of both cooling and repump components. As already mentioned above, the power ratio between the cooling and repump components is <NUM>:<NUM> and the three incident beams have equal power.

<FIG> is a graph showing, for four different values of total beam power (<NUM> mW, <NUM> mW, <NUM> mW and <NUM> mW), the mean number of trapped atoms, N, as a function of detuning, δ, to lower frequencies (i.e. so-called red detuning) referenced to the <NUM>Rb cooling transition, the detuning, δ, being represented in units of Γ, where Γ = 2π x <NUM>, which is the natural decay rate of <NUM>Rb. The atom number was measured via the fluorescence from the atom cloud which was collected by a photodiode (not shown) using a simple non-magnifying optical system which is assumed to have minimum loss in light collection. The trap was loaded with rubidium atoms by heating a suitable rubidium source optically or electrically for ten seconds. Each data point in the graph is the mean of three measurements and the error bar shows the range of the three measurements. The maximum atom number, N, in the cloud of approximately <NUM> x <NUM><NUM> is observed for a total beam power of <NUM> mW with a detuning to lower frequencies of δ = -<NUM>. More generally, it is seen that the maximum atom number in the cloud reduces with increasing intensity in a nonlinear manner. The experimental results show that the maximum number of atoms is obtained at relatively low power and with small levels of detuning compared to the behaviour of MOTs [<NUM>, <NUM>]. Comparing the number of trapped atoms, N, with what would be expected from MOT scaling laws [<NUM>] and with comparable beam diameters, d, and beam powers, the experimental results show that the optical trap is capable of trapping almost an order of magnitude more atoms than a comparable MOT. The optical trap performance is closer to a N proportional to d<NUM> scaling prediction, compared to the N proportional to d<NUM> scaling found in MOTs with d > <NUM>. It is a significant practical advantage for the optical trap according to embodiments of the invention that large numbers of atoms can be trapped at low beam powers, since this makes the technique inherently suited to low power applications, e.g. battery-operated and/or small devices, such as may be needed in quantum computing or other quantum technologies.

<FIG> and <FIG> are graphs showing experimental results from the optical trap. For three different values of laser beam power (<NUM> mW, <NUM> mW and <NUM> mW), the graphs show the mean temperature, T, of the atoms as a function of red detuning frequency, δ, in units of Γ, i.e. the same x-axis as <FIG>. <FIG> shows results expanding along the long axis of the atom cloud, i.e. generally along the incident/reflected beam direction, and <FIG> expanding along a short axis of the atom cloud, i.e. in a direction transverse thereto. The temperature of the atom cloud was measured using the time-of-flight method. The cooling and repump beams were extinguished for up to <NUM> to allow the atom cloud to expand. The cloud was then illuminated and imaged using a fast camera. The width of the atom cloud after each time-of-flight measurement was determined by a two-dimensional Gaussian fit to the profile of the captured image. Due to the elongate shape of the cloud, the temperature was measured along both the long and short axes of the cloud. The mean value of three time-of-flight measurements forms a single data point in the results presented in <FIG> and <FIG>. These results show that the temperature of the atom cloud is only weakly dependent on detuning, varying by ~<NUM>% for the detuning ranges covered, but is strongly dependent on beam power. Moreover, comparing <FIG> with <FIG>, it is seen that atoms moving in a direction aligned with the short axis of the cloud are generally hotter than those moving in alignment with the long axis, i.e. cooling along the beam direction is more effective than cooling transverse thereto. The lowest measured temperatures were <NUM>µK for atoms expanding along the long axis of the cloud and <NUM>µK for the short axis. For both axes, the lowest temperatures were achieved at the lowest red detuning values (δ=-<NUM>. 8Γ) and with the lowest beam powers (<NUM> mW). These results further show that the optical trap appears to be most efficient at low red detuning from the cooling transition and at small laser powers, unlike the trends found in MOTs. More generally, it is seen that the mean temperatures are strongly dependent on beam power but only weakly on the amount of detuning, although a weak trend towards lower temperatures with smaller levels of detuning is evident.

The physical mechanisms behind the experimental results of <FIG> and <FIG> and <FIG> are now discussed. The directional effect seen in <FIG> and <FIG> is likely due to the stronger Doppler shifts along the beam wavevectors resulting in greater molasses cooling. Simple analytical modelling of the cooling and trapping forces resulting from scattering alone cannot produce a stable trap in three dimensions, so we can discount mechanisms such a spatially varying intensity imbalances as found in [<NUM>]. We suspect the spatially restoring force to be the dipole force, due to the shift of the peaks in <FIG> which may be due to AC-Stark shifts. The flattening out of the distribution is likely caused by saturation of the state. Typically, dipole traps are tuned far off-resonance to reduce the effect of heating through single photon scattering. To counter the reduced force, the intensity of the trapping beams must be well above saturation. Typically, dipole traps use a laser detuned by several nanometres from resonance and with several Watts of optical power focused to a diffraction-limited spot. As shown by Letokhov and Minogin [<NUM>], as one tunes the laser close to resonance, cooling and trapping in an optical lattice is possible, albeit with a trap depth equal to the heating induced by scattered photons. The near-resonant dipole trap suggested by Letokhov and Minogin has chiefly been neglected as it was deemed to be too 'leaky' as the trap depth would be on the order the Doppler cooling limit. However, this trap was proposed nearly a decade before polarization gradient cooling was discovered. If the atoms are efficiently cooled to sub-Doppler temperatures as they enter the dipole trap (as one typically does in a MOT), then they should remain trapped. If this is also the process that is operating within the optical trap according to embodiments of the invention, then the question arises as to why such efficient cooling of atoms directly from the background vapour occurs, and in sufficient quantities, is observed in the experimental results. The suggestion of a superlattice in [<NUM>] could be the answer, if the lattice pitch is large enough to cool atoms with velocities of several tens of metres/sec. To understand this better, we have explored the scale of each effect via simulations and simplified analytical models as discussed in the following.

The variation of the final (trapped) number of atoms with the laser power and detuning is investigated by conducting a number of simulations with different initial randomised atom configurations, before averaging to obtain a final atom number. The simulations take account of interactions between the atoms and the laser beams and AC Stark detuning.

<FIG> is a graph showing these simulation results in the form of a plot of atom number, N, versus red detuning, δ in units of Γ, for four different laser powers (<NUM> mW, <NUM> mW, <NUM> mW and <NUM> mW), i.e. the same four values as for the experimental results shown in <FIG>. Each dataset consists of twenty points formed from the average of six repetitions at each position. The maximum time was t = <NUM> for a timestep of one microsecond, dt = <NUM> x <NUM>-<NUM> s. As seen in <FIG> the simulation results follow the same general trends as the experimental results in that lower beam powers and lower detuning values yield higher final atom numbers.

<FIG> show a further aspect of the simulations in the form of 2D sections in the xy-plane of the atom distributions over time as the cooling and trapping is proceeding. The illustrated area corresponds to a cross-section of the volume of beam intersection where the cloud is expected to form, i.e. is much smaller than the vacuum cell cross-section. The simulation results are for the example of a <NUM> mW beam power and a detuning value, δ = -<NUM>. <FIG> show the atom distributions at times t = <NUM>, t = <NUM> and t = <NUM> respectively, where t = <NUM> is the time when the beams are introduced into the trapping chamber. The atom distribution after cooling and trapping, i.e. at t = <NUM>, as well as partway through the process at t = <NUM>, are consistent with the general behaviour seen in the experimental results in that the atoms concentrate off-centre and in a non-spherical cloud.

The optical fields generated in the optical trap provide both a velocity-dependent and a position-dependent restoring force such that a dense cloud of sub-Doppler temperature atoms are formed near the trap centre. The experimental results and simulations indicate that the misalignment of the incident and retro-reflected beams is key to the efficient operation of the magnetic-field-free optical trap according to embodiments of the invention. It is now discussed why this may be the case.

<FIG> is a schematic drawing of the interference between a pair of counter-propagating beams that subtend a small angle θ to each other as in the optical trap according to embodiments of the invention, i.e. θ is a proxy for any of α, β, κ. When two counter-propagating beams are slightly misaligned in this way, a set of interference fringes are formed with the fringes extending roughly perpendicularly to the beam's wavevector, as schematically illustrated. Assuming the two counter-propagating beams are in vacuum, the fringe spacing (or "pitch") p is given by: <MAT>.

While an atom passing perpendicularly through the fringe pattern, i.e. with a trajectory φ = <NUM>°, will not experience any cooling force, because any net momentum transferred to the atom does not oppose the atom's velocity, an atom passing through the fringe pattern at any other angle, i.e. with φ ≠ <NUM>°, will experience a scattering force. Increasing the trajectory angle φ will also increase the apparent fringe spacing. Assuming a beam misalignment angle of θ = <NUM>° and an atom travelling along a trajectory of φ = <NUM>°, the effective fringe spacing would increase by a factor of <NUM> compared with a trajectory with φ = <NUM>°. If polarization gradients are still in effect for this perpendicular standing wave, then one may expect similar increases in the capture velocity. An atom travelling through the fringes formed by the misalignment of the counter-propagating beams will thus experience polarization gradient cooling, resulting in a greater capture velocity. This could explain why such efficient cooling of large numbers of atoms is observed in the experimental results.

It is further noted that according to our understanding of the physics, formation of a cooled atom cloud will require misalignment of all three counter-propagating beam component pairs.

The experimental results showed that optical trap according to embodiments of the invention could operate under a wide parameter space, such as with variation of parameters including: beam polarization, beam power, level of red detuning, inclination angles and misalignment angles.

For the parameter space experimentally probed to date, we have found that consistently reliable formation of a dense cloud of cooled atoms is achieved over the following ranges of misalignment angles: <MAT> (but α <> <NUM>°; see discussion below) <MAT> <MAT>.

While from an experimenter's point-of-view, the reflecting mirror is adjusted for retro-reflection, i.e. α is set to <NUM>°, this must be tempered with the above understanding of the physics, so while good performance is observed when α is nominally set to <NUM>°, it is assumed that there must nevertheless be a slight misalignment in reality (or perhaps a deviation from perfect collimation of the beam).

When altering parameters such as polarization or beam power, it was found that the following alignment procedure reliably generated a dense atom cloud:.

This alignment method proved to be very reliable for forming a cloud direct from vapour.

For practical convenience, in order to limit the parameter space, the systematic experiments performed to date were restricted mostly to a limited parameter space in which the number of beams (three), the beam geometry (inclination angle <NUM>°) and polarizations (circular) were fixed and only the beam power, beam misalignment angles, red detuning level of the cooling beam and red detuning level of the repump beam were systematically varied.

Having said that, the experiments were extended to probe the parameter space more widely in the following areas:
The effect of variation of inclination angle was studied. As an initial comment it is noted that an inclination angle of <NUM>° corresponds to a conventional optical cooling geometry with three pairs of counter-propagating beams extending along mutually orthogonal axes, i.e. a Cartesian setup. Moreover, referring to <FIG>, it can be appreciated that the inclination angle of χ = <NUM>° is exactly equivalent to an inclination angle of χ = <NUM>°, since they deviate by ±<NUM>° from orthogonal, so by changing from χ = <NUM>° to <NUM>° all that has happened is a <NUM>° rotation of the tripod. (In addition, with χ > <NUM>°, the sign of the misalignment angles α, β, K would be reversed compared to the values given elsewhere in this document. ) We therefore refer to inclination angle in terms of angular deviation ΔX from orthogonal beams, i.e. from χ = <NUM>°. With an angular deviation of Δχ = <NUM>° (i.e. inclination angle, χ, as shown in <FIG> of <NUM>°) formation of a cloud was observed, but with very poor quality in terms of cooling, density and atom number. An angular deviation of ΔX = <NUM>° therefore would appear to be close to the boundary of what will function. Consistently good performance was observed with angular deviations in the range <NUM>° ≤ Δχ ≤ <NUM>° (i.e. an inclination angle range as shown in <FIG> of <NUM>° ≤ χ ≤ <NUM>°).

Moreover, it has been seen that the effect also occurs with linear polarization (as well as with circular polarization) of the beams.

Moreover, in principle, the inclination angle for each of the incident beam paths could be different from one another, although experiments have not systematically probed this parameter variation.

Because of the stability of the effect and the resultant large parameter space over which efficient cooling and trapping has been observed, the experiments performed to date may not yet have found the most optimal conditions in terms of atom number (highest), atom density (highest) and atom temperature (lowest) or probed the boundaries of what will work efficiently. Other combinations of the above parameters, e.g. inclination angle and misalignment angle, may also produce good or better results. It is also noted that further embodiments may use more than three beams, e.g. four beams, five beams or six beams.

Claim 1:
An optical trap for trapping and cooling atoms, the optical trap comprising:
a vacuum chamber (<NUM>) operable to provide a vacuum atmosphere in which atoms of an atomic species can be laser cooled via excitation of an electronic transition of the atomic species, referred to as the cooling transition;
a laser source (<NUM>) configured to generate laser light at a frequency detuned below the frequency of the cooling transition;
an optical arrangement (<NUM>) configured to manipulate the laser light to generate first, second and third beams with respective first, second and third beam widths, and to direct the first, second and third beams to propagate across the vacuum chamber along respective first, second and third incident beam paths that deviate from a mutually orthogonal arrangement in which they would each form an alignment angle of <NUM>° to a reference axis, having instead respective first, second and third alignment angles of between <NUM>° and <NUM>° to the reference axis; and
first, second and third reflectors arranged to reflect the first, second and third beams to propagate back across the vacuum chamber along their incident beam paths in respective first, second and third reflected beam paths that deviate from a retro-reflection, in which each reflected beam path would be coincident with its incident beam path, by respective first, second and third misalignment angles, the first, second and third misalignment angles (α, β, K) and beam widths having values that define a volume of intersection (V) within the vacuum chamber traversed by the first, second and third beams both when propagating along their incident beam paths and their reflected beam paths.