Atomic Cooling and Trapping Method and Apparatus

Abstract

The present disclosure relates to an atomic cooling and trapping method and apparatus. An optical trap for laser cooling and trapping atoms. Three pairs of laser beams are directed through a common intersection volume within a vacuum chamber, where each pair is formed by two counter-propagating beams. Instead of an orthogonally arranged configuration where each beam pair forms an angle χ of 45° relative to a reference axis, an angle of 5° ≤ χ ≤ 40° is employed here. Additionally, within each beam pair, the counter-propagating beams are not precisely aligned in the same path as in a conventional magneto-optical trap, but are slightly misaligned with respective misalignment angles [α, β, κ] generally in the range of 0.1° to 2°. However, the misalignment angles and the beam widths are selected such that a common intersection volume of all six beams is maintained. This provides an all-optical trap where laser cooling and trapping of atoms occur in the absence of a magnetic field.

Description

[0001] This application is a divisional application of a Chinese patent application with an application date of October 28, 2021, an application number of 2021800738343, and an invention title of "Method and Apparatus for Atomic Cooling and Trapping". Background Art

[0002] The present invention relates to cooling and trapping atoms with lasers.

[0003] In the early studies of laser cooling and trapping in the late 1980s, many research groups found that the trapped atom temperatures were much lower than the limiting scenarios proposed by Doppler cooling at that time. Lett et al. [1] conducted a careful study of temperature determination methods in 1988 to confirm these findings, which were then called "super molasses" compared to the then-accepted Doppler-limited molasses cooling. In the following year, two groups independently submitted theoretical explanations [2, 3] identifying polarization gradient cooling (also known as Sisyphus cooling) as the mechanism behind the additional cooling effect. These theories rely on the internal structure of the atom to scatter additional energy through polarization-dependent modulation of the atomic state. The above effects have been developed and are now well recognized. But during the same period of uncertainty surrounding the super molasses effect, another almost uncharted observation was made. Chu et al. [4] noticed that when the counter-propagating laser beams were slightly misaligned, the number of atoms collected in the molasses increased significantly, by more than an order of magnitude, and remained trapped for several seconds. Some aspects of this effect can be explained by the "race-track mode" [5]. But this observation still seems to have not been extensively explored. A possible theoretical explanation has been presented based on a model caused by the Kapitza pendulum (or inverted pendulum) involving eddy forces [6], but has not been experimentally confirmed. Similar and unexpected atomic cooling and trapping without a magnetic field have also been reported in other literature [7, 8]. The traps reported in these two references have three pairs of counter-propagating beams orthogonally arranged along the three Cartesian axes. The trap of reference [7] requires linearly polarized light, a very good vacuum, and a large-diameter laser beam (≥10 mm) to work successfully. To produce the counter-propagating beam pairs, each incident beam is reflected at a small angle deviating from exact retroreflection, and a misalignment in the range of 0.5° to 1° provides good performance. The assumed trapping mechanism is the dipole force [9]. Like reference [7], the trap of reference [8] also uses large-diameter beams and slightly misaligned counter-propagating beam pairs. The trap of reference [8] works with linearly polarized or circularly polarized light. Its operation requires loading from a standard magneto-optical trap (MOT) before the magnetic field disappears, i.e., it cannot directly form a cooled atomic cloud from the vapor. The authors considered many theoretical processes that could lead to such a trap and particularly suggested that the process could be related to a superlattice dipole trap.

[0004] The reason for cooling and trapping atoms using only an optical field, i.e., without a magnetic field, is unexpected because of the optical equivalent of Earnshaw's theorem

[10] , which states that:

[0005]

[0006] where F S is the scattering force acting on the particle with measurable polarization ability. Substantially, the scattering force alone cannot generate a stable restoring force acting on the dipole in all dimensions because there are no light field sources or light field sinks in free space. This limitation is generally overcome by changing the internal state of the atom by means of a Zeeman shift (as in an MOT) or an AC Stark shift (as in a dipole trap).

[0007] A specially designed all-optical trap is the optical trap developed by Bouyer et al.

[11] , which is called the trap relying on optical pumping (TROOP). TROOP uses uncollimated, i.e., diverging, orthogonally circularly polarized light beams, which are oriented along each Cartesian axis to generate spatially varying and thus position-dependent forces by unbalancing the laser power and optical pumping. Like an MOT or a dipole trap, TROOP is also based on the manipulation of the internal state. Summary of the Invention

[0008] According to a first aspect of the present invention, there is provided an optical trap for trapping and cooling atoms, the optical trap comprising:

[0009] a vacuum chamber, which can be operated to provide a vacuum environment in which atoms of an atomic species can be laser cooled by excitation of an electronic transition of the atomic species called a cooling transition;

[0010] a laser source configured to generate a laser at a detuned frequency below the frequency of the cooling transition;

[0011] an optical arrangement configured to manipulate the laser to generate first, second, and third light beams having respective first, second, and third beam widths and to direct the first, second, and third light beams to propagate through the vacuum chamber along respective first, second, and third incident optical paths deviating from a mutually orthogonal arrangement, in which they all form a 45° axisymmetric angle with respect to a reference axis, but here having respective first, second, and third axisymmetric angles between 25° and 35° with respect to the reference axis; and

[0012] First, second, and third reflectors, which are arranged to reflect first, second, and third light beams to propagate back through the vacuum chamber along their incident light paths in respective first, second, and third reflected light paths that deviate from retroreflection, wherein each reflected light path will coincide with its incident light path based on respective first, second, and third misalignment angles, and the values of the first, second, and third misalignment angles and the beam widths define an intersection volume within the vacuum chamber that is traversed by the first, second, and third light beams when propagating along their incident light paths and their reflected light paths.

[0013] According to a second aspect of the present disclosure, there is provided a method for laser cooling and trapping atoms, the method comprising:

[0014] Providing a vacuum chamber that houses atoms of an atomic species that can be laser cooled by excitation of an electronic transition, referred to as a cooling transition, of the atomic species in a vacuum environment;

[0015] Providing a laser at a detuned frequency below the frequency of the cooling transition;

[0016] Providing first, second, and third laser beams having respective first, second, and third beam widths;

[0017] Directing the first, second, and third light beams to propagate through the vacuum chamber along respective first, second, and third incident light paths, wherein the first, second, and third incident light paths deviate from an orthogonally arranged configuration in which they all form 45° axisymmetric angles with respect to a reference axis, but here have respective first, second, and third axisymmetric angles between 25° and 35° with respect to the reference axis;

[0018] Reflecting the first, second, and third light beams to propagate back through the vacuum chamber along their incident light paths in respective first, second, and third reflected light paths that deviate from retroreflection, wherein each reflected light path will coincide with its incident light path based on respective first, second, and third misalignment angles, and the values of the first, second, and third misalignment angles and the beam widths define an intersection volume within the vacuum chamber that is traversed by the first, second, and third light beams when propagating along their incident light paths and their reflected light paths.

[0019] Using this approach, an all-optical trap can be provided, i.e., an optical trap that does not rely on the presence of a magnetic field. Since a magnetic field is not used for the cooling effect developed in the present invention, of course the corresponding optical trap does not require any magnetic coils or any other form of magnetic field generator, as there is no need to generate a magnetic field within the vacuum chamber. Nor is a Zeeman slower required.

[0020] Implementing the optical trap of the present invention does not necessarily include a magnetic field generator, since laser cooling occurs in the absence of a magnetic field.

[0021] In some embodiments, the misalignment angles meet one or more of the following conditions:

[0022] Each of the misalignment angles is greater than 0.1°;

[0023] Each of the misalignment angles is less than 2°;

[0024] At least one of the misalignment angles is greater than 0.5°; and

[0025] At least two of the misalignment angles are greater than 0.5°.

[0026] In some embodiments, the first, second, and third pair of axis angles are equal to each other. In other embodiments, at least two of the first, second, and third pair of axis angles are different from each other.

[0027] The first, second, and third reflectors may be configured such that the reference axis and each pair of incident and reflected optical paths are at least substantially in the same plane, thereby defining such first, second, and third planes. The first, second, and third planes may be substantially equally angularly spaced when viewed along the reference axis.

[0028] In some embodiments, the polarization components are arranged to provide first, second, and third beams having respective specified polarization states upon entering the vacuum chamber. The first, second, and third reflectors may be configured to ensure that the specified polarization states of the first, second, and third beams are maintained upon reflection, such as circular polarization or linear polarization.

[0029] For certain atomic species, there are further electronic transitions called repump transitions, which are required to be excited for efficient cooling to occur. In such a case, the laser source or another laser source is designed to produce another laser at another frequency tuned according to the frequency of the repump transition. The optical arrangement may then further include a beam combiner operable to combine the laser and the other laser such that the first, second, and third beams each contain both the laser and the other laser.

[0030] Preferably, the first, second, and third beams are at least substantially collimated as they pass through the vacuum chamber. The characteristic of being at least substantially collimated may be the beam divergence, where the beam divergence Θ = 0 corresponds to a collimated beam, and the at least substantially collimation relevant to the present invention may be that the beam divergence Θ is less than or equal to 1°, 2°, 3°, 4°, 5°, 6°, 7°, 8°, 9°, or 10°.

[0031] In a principal embodiment, the first, second, and third pair of axis angles form an angle between 25° and 35° with respect to the reference axis, while other embodiments have pair of axis angles outside this range. For example, with respect to the reference axis, the lower limit may be as low as 20°, 21°, 22°, 23°, or 24°, and the upper limit may be as high as 36°, 37°, 38°, 39°, or 40°.

[0032] According to another aspect of the present disclosure, there is provided an optical trap for capturing and cooling atoms, the optical trap comprising:

[0033] a vacuum chamber operable to provide a vacuum environment within which atoms of an atomic species can be laser cooled by excitation of an electronic transition of the atomic species referred to as a cooling transition;

[0034] a laser source configured to generate first to sixth laser beams having respective first to sixth beam widths, all of the beams having a frequency detuned to a frequency lower than the frequency of the cooling transition;

[0035] an optical arrangement configured to:

[0036] direct the first, second, and third beams to propagate through the vacuum chamber along respective first, second, and third incident optical paths that deviate from a mutually orthogonal arrangement, wherein in the orthogonal arrangement each incident optical path forms a 45° off-axis angle with respect to a reference axis, but here each has respective first, second, and third off-axis angles between 5° and 40° with respect to the reference axis; and

[0037] direct the fourth, fifth, and sixth beams to propagate through the vacuum chamber generally along the optical paths of the first, second, and third beams but in opposite propagation directions to form three pairs of counter-propagating beams, each pair of counter-propagating beams being offset from respective paths in which their optical paths would coincide based on respective first, second, and third misalignment angles, the values of the first, second, and third misalignment angles and the first to sixth beam widths defining an intersection volume within the vacuum chamber traversed by all of the first to sixth beams.

[0038] A number of alternatives are provided for generating and properly directing the cooling beams. For example, the cooling laser source can consist of a single laser whose output beam is split to produce the first to third beams. Alternatively, the cooling laser source can consist of three lasers, each producing one of the first to third beams. First, second, and third reflectors can be provided, which are arranged to reflect the first, second, and third beams after they have propagated through the vacuum chamber so that they are returned, respectively, as the fourth, fifth, and sixth beams to propagate through the vacuum chamber. The laser source can also consist of six lasers, each producing one of the first to sixth beams, in which case no reflectors are required.

[0039] In some embodiments, for each pair of counter-propagating beams, the two beam widths and the misalignment angle between the two beams are jointly designed such that at least half of the beam area of the beam having the smaller beam area intersects the beam area of the beam having the larger beam area within the intersection volume. The beam width is defined as 1 / e 2a value and will be the beam diameter if the beam has a circular cross-section or two values for the major and minor axes if the beam has an elliptical cross-section.

[0040] In some embodiments, the misalignment angles meet one or more of the following conditions:

[0041] each of the misalignment angles is greater than 0.1°;

[0042] each of the misalignment angles is less than 2°;

[0043] at least one of the misalignment angles is greater than 0.5°; and

[0044] at least two of the misalignment angles are greater than 0.5°.

[0045] The polarization components may be arranged to provide first to sixth beams having respective prescribed polarization states upon entering the vacuum chamber.

[0046] In some embodiments, the atomic species has a further electronic transition called a repump transition, which is required for excitation to occur for efficient cooling. The above laser source or another laser source is then designed to produce another laser at another frequency tuned according to the frequency of the repump transition. Then, a beam combiner may be provided, which can be operated to combine the laser and the other laser such that the first to sixth beams each contain both the laser and the other laser.

[0047] The first to sixth beams may be at least substantially collimated as they pass through the vacuum chamber. The characteristic of substantially collimated may be the beam divergence, where the beam divergence Θ = 0 corresponds to a collimated beam, and the substantially collimated relevant to the present invention may be that the beam divergence Θ is less than or equal to 1°, 2°, 3°, 4°, 5°, 6°, 7°, 8°, 9° or 10°.

[0048] The optical trap designed according to the above is different from the prior art in that it does not require a magnetic field generator.

[0049] The first, second and third pairs of axis angles may be between 20° and 40°, more particularly between 25° and 35°.

[0050] According to another aspect of the present invention, there is provided a method of laser cooling and trapping atoms, which includes:

[0051] providing a vacuum chamber that houses atoms of an atomic species that can be laser cooled by excitation of an electronic transition called a cooling transition within the vacuum environment by the atomic species;

[0052] providing a laser at a detuned frequency below the frequency of the cooling transition;

[0053] Provide first, second, and third laser beams having respective first, second, and third beam widths;

[0054] Provide first through sixth laser beams having respective first through sixth beam widths and frequencies detuned to frequencies below the cooling transition;

[0055] Direct the first, second, and third beams to propagate through a vacuum chamber along respective first, second, and third incident optical paths that deviate from a mutually orthogonal arrangement, in which they would each form a 45° angle to the axis with respect to a reference axis, but instead have respective first, second, and third angles to the axis between 5° and 40° with respect to the reference axis; and

[0056] Direct the fourth, fifth, and sixth beams, respectively, to propagate through the vacuum chamber generally along the optical paths of the first, second, and third beams but in opposite propagation directions to form three pairs of counter-propagating beams, each pair of counter-propagating beams being offset from a respective path in which their optical paths would coincide based on respective first, second, and third misalignment angles, the values of the first, second, and third misalignment angles and the first through sixth beam widths defining an intersection volume within the vacuum chamber traversed by all of the first through sixth beams.

[0057] In summary, provide an optical trap for laser cooling and trapping atoms having three pairs of laser beams directed through a common intersection volume within a vacuum chamber, where each pair is formed by two counter-propagating beams. Different from each beam pair forming a 45° angle χ with respect to a reference axis in a mutually orthogonal arrangement, an angle of 5° ≤ χ ≤ 40° is substituted. Additionally, in each pair of beams, the counter-propagating beams are not precisely aligned in a common path as in a conventional magneto-optical trap but are slightly misaligned by respective misalignment angles [α, β, κ] generally in the range of 0.1° to 2°. However, the misalignment angles and beam widths are chosen such that a common intersection volume for all six beams is maintained. This provides an all-optical trap in which atomic laser cooling and trapping occur in the absence of a magnetic field. Description of the Drawings

[0058] The present invention will now be further described by way of example only with reference to the drawings.

[0059] Figure 1 is a perspective schematic view showing the geometry of the laser beams used to implement the optical trap of the present invention.

[0060] Figure 2 Shows an optical setup for providing a stabilized cooling laser beam.

[0061] Figure 3 Shows an optical setup for providing a stabilized repump laser beam.

[0062] Figure 4Shows an optical trap setup.

[0063] Figure 5 Is a graph showing the experimental results of the optical trap from Figures 1-4 The graph plots the variation of the number of trapped atoms N as a function of the red detuning frequency δ for different values of the total beam power, namely 0.9 mW, 1.6 mW, 4.5 mW, and 6.3 mW.

[0064] Figure 6A and 6B Are graphs representing the experimental results of the optical trap from Figures 1-4 These graphs show the average temperature T of the atoms stretching along the long axis ( Figure 6A ) and the short axis ( Figure 6B ) of the atomic cloud as a function of the red detuning frequency δ of the cooling laser for three different values of the total beam power, namely 1.6 mW, 4.2 mW, and 6.3 mW.

[0065] Figure 7 Is a graph representing the simulation results, which corresponds to Figure 5 The experimental results.

[0066] Figure 8A 、 8B And 8C show cross-sections in the x - y plane of the atomic distribution as the cooling and trapping process progresses. Each point represents a single atom. The three cross-sections show the atomic positions at t = 0 ms, t = 5 ms, and t = 10 ms during the cooling and trapping process, where t = 0 is the start time.

[0067] Figure 9 Is a schematic diagram of the interference between two counter-propagating beams forming a small opposing angle θ with each other according to an embodiment of the present invention. At this time, the atoms migrate at an angle φ with respect to the perpendicular to the bisecting angle of the propagation directions of the two counter-propagating beams.

[0068] Figure 10 Is a schematic diagram of a first alternative embodiment.

[0069] Figure 11 Is a schematic diagram of a second alternative embodiment.

[0070] Figure 12 Is a schematic diagram of a third alternative embodiment. Detailed Description

[0071] Hereinafter, for cooling 85The present invention will be described by taking Rb atoms as an example. The present invention can be applied to any atomic species that can be optically cooled. In principle, any atom in the first or second group of the periodic table can be optically cooled. In the practice so far, the atomic species for which optical cooling has been verified include: Rb, Cs, Li, Sr, Ca, K, and Fr. In the case of Sr, it should also be noted that no repumping is required, so the corresponding devices described in conjunction with repumping will be omitted hereinafter.

[0072] Figure 1 is a perspective schematic view showing the geometry of the laser beams used in the optical trap according to an embodiment of the present invention. These two circles represent two vertical offset planes perpendicular to the z-axis. Each different optical path is schematically indicated by a respective straight line corresponding to its principal optical axis, and the arrows at this time indicate the direction of beam propagation. For ease of representation, the finite beam cross-section of the beam is not shown.

[0073] Three laser beams travel in a circular polarization along their respective incident optical paths (lines with downward arrows) to jointly form a tripod-like arrangement. The incident optical paths are radially equidistant with respect to the z-axis, so that they form an angle of γ = 120° with each other when viewed along the z-axis. The equal radial spacing may not be exact. For example, a deviation from the 120° radial spacing may be feasible, such as a deviation up to ±1°, ±2°, ±3°, ±4°, ±5°, ±6°, ±7°, ±8°, ±9°, ±10°. The three incident optical paths are oriented at an inclination angle χ with respect to the z-axis. A common inclination angle of χ = 30° is shown, but unequal inclination angles can be used in other embodiments. Thus, each incident optical path lies in a plane containing the z-axis and forms an inclination angle χ with respect to the z-axis. Each of these three planes is oriented at a 120° facing angle with respect to the other two planes to provide an equal angular spacing of the three beams. In the following description, it is assumed that the laser beams are collimated. In practice, collimated beams or at least only weakly diverging or weakly converging beams are required. Each beam is reflected back from its incident optical path to a reflected optical path, and the reflection occurs in the plane of the lower circle. Each reflection is performed to maintain the polarization state of the beam, such as circular or linear. The maintenance of circular polarization can be obtained by a combination of a quarter-wave plate and a dielectric mirror. The three reflected optical paths (lines with upward arrows) deviate from the retroreflection at their respective angles [α, β, κ], where retroreflection means that the reflected optical path coincides with its incident optical path. In each case, the misalignment is tilted towards the z-axis, that is, each reflected optical path lies in the common plane described above with its incident beam, but the inclination angle with respect to the z-axis is reduced. The angles [α, β, κ] can generally be different from each other, but they can be exactly the same, or two of them can be the same.

[0074] As a further geometric observation, note that all six optical paths intersect the z-axis at their respective points. Figure 1The incident optical paths with a common intersection point are shown. Since the misalignment angles are usually not equal, the three reflected optical paths will typically intersect the z-axis at different points, each slightly above the common intersection point of the incident optical paths. The misalignment angles [α, β, κ] and the finite beam width result in the formation of an intersection volume, which is the volume that the beam passes through along both its incident and reflected optical paths. The six beam components interfere with each other in the beam intersection volume. This interference is the cause of the formation of the cooled atomic cloud in the intersection volume.

[0075] For the efficient operation of the optical trap according to an embodiment of the present invention, it is considered necessary that all the beams are at least approximately collimated and the beam diameter, inclination angle, and misalignment angles are jointly selected such that all six beam components intersect in a common region (the beam intersection volume).

[0076] In experiments performed so far with a common inclination angle of 30°, for efficient cooling and trapping to directly form a cloud within the beam crossing volume, in combination with a beam diameter of about 5 mm, the typical magnitudes of the misalignment angles are from 0.1° to 2°, where the beam diameter is taken as the 1 / e 2 value. It should be noted that the available range of misalignment angles depends on the beam diameter, where the larger the beam diameter, the larger the misalignment angle. For good performance, it also seems necessary that at least two of the misalignment angles are different from each other.

[0077] In particular, very good performance is obtained with the following combination of misalignment angles: The first pair of optical paths has misalignment angles such that the incident and reflected beams are separated by approximately half of the beam width in the beam crossing volume. The misalignment angles of the second pair of optical paths are set to very small values, possibly 5 to 20 times lower than those of the first beam pair. The misalignment angles of the third pair of optical paths are set to be approximately the same as or slightly larger than those of the first pair of optical paths, possibly 1 to 2 times.

[0078] An important experimental observation is that the formation of the cooled atomic cloud from the vapor is not at all affected by these geometric parameters or detuning levels. On the contrary, it is easy to find combinations of parameters that result in the formation of a cloud from the vapor, and once the cloud is formed, it is possible to easily optimize the combination of parameters because when one of the said parameters is adjusted, the cooling performance gradually and monotonically improves or deteriorates. Therefore, in the experiment, simply adjust one parameter at a time in a stepwise or continuous manner, for example, adjust each misalignment angle or the cooling detuning level in turn, to improve the cloud formation, for example, in terms of its temperature, shape, or density, so as to find the optimal combination of parameters for forming a dense, low-temperature, and approximately spherical cloud.

[0079] According to simple trigonometry, when the misalignment angle θ is as follows, the misalignment angle values that result in the incident and reflected optical paths being separated by up to half of the beam width at the intersection point are satisfied:

[0080]

[0081] Where r is the beam radius, i.e., half of the beam diameter, and l is the distance from the reflection plane to the intersection point.

[0082] Experiments to date have shown that the performance of the optical trap is similar to that of a conventional MOT in terms of the number of atoms (~1 °8 ), cloud density (10 11 atoms / cm 3 ) and cloud temperature (<50 μK). The atomic cloud formed at the beam intersection volume is typically millimeter-sized and has a slightly elongated (roughly elliptical) shape, with the major axis of the ellipse oriented along one of the said optical paths. The shape and volume of the cloud can be experimentally varied by gradually adjusting the magnitude of one or more of the misalignment angles [α, β, κ]. This effect can be utilized to find the optimal combination of misalignment angles by gradually reducing the size and aspect ratio of the cloud in order to form a small, dense cloud with a near-spherical shape, as is typically required.

[0083] Figures 2-4 Schematic diagrams show the parts of a system used to experimentally demonstrate optical trap operation using 85 Rb atomic vapor.

[0084] Figure 2 And Figure 3 show the optical setups for providing the stabilization cooling and repump laser beams, respectively. It should be noted that both of these stabilization schemes are known and other suitable stabilization schemes are also known to the person skilled in the art. Figure 4 Shows the system setup around the optical trap vacuum chamber.

[0085] Referring to Figure 2 , the cooling setup 100 is based on the laser source 102, which is a distributed feedback diode (DFB) laser. The center wavelength of the DFB is 780 nm, the linewidth is approximately 0.6 MHz, and the output power ranges from 20 to 80 mW. The cooling laser is stabilized to 85 the Rb transition:

[0086] 5 2 S 1 / 2 F = 3 → 5 2 P 3 / 2 F' = 4

[0087] For this purpose, modulation transfer spectroscopy

[13] is used. The beam from the cooling laser 102 initially passes through the optical isolator 104 and the half-wave plate 106. A polarization beam splitter (PBS) 108 is arranged in the beam to split it into two branches. One branch with a small fraction of the beam power is used as the input to the control laser stabilization system (vertical branch), while the remaining optical power, called the main beam, ultimately provides the incident beam to the trap (direct-through branch). The stabilization branch is provided to another PBS 120 via the mirror 118, which again splits the beam in two. The direct-through branch from the PBS 120 goes directly to the vapor cell 122 and forms the probe beam of the pump-probe scheme, which has the frequency of the laser 102. Thus, the probe beam passes through the vapor cell 122 from right to left in the figure. The branch deflected from the PBS 120 is used to generate the pump beam. The pump beam branch is guided to the acousto-optic modulator (AOM) 142 via other mirrors 138 and 140. The AOM 142 diffracts the input beam to output a zero-order diffracted beam and two first-order diffracted beams. These three beams are reflected back from the mirror 148 and recombined into a single beam when they return via the AOM 142. A quarter-wave plate 146 is arranged between the AOM 142 and the mirror 148 to provide the required circular polarization. The combined reflected beam passes through the mirrors 140 and 138, passes directly through the PBS 120, is further directed via the mirrors 126 and 130 and another PBS 124, and passes through the half-wave plate 128 and passes through the vapor cell 122 from left to right in the figure, i.e., in the opposite direction to the probe beam, as the pump beam. Thus, these components together form a saturated absorption spectroscopy arrangement to generate an error signal from the four-wave mixing in the rubidium atoms contained in the vapor cell. In the vapor cell, both the pump beam and the probe beam passing through the vapor cell 122 generate sub-Doppler spectra, which are slightly offset from each other in frequency. By subtracting the resulting spectra, an error signal is generated from the output of the photodiode. The first-order diffracted beam for laser stabilization consists of a main carrier with a frequency of ω C = ω0 + ω AOM and sidebands with a frequency of ω S = ω C ± ω mod . The main carrier beam is further modulated due to passing through the AOM 142 twice, and it now has a frequency of ω = ω0 + 2ω AOM , and the sideband offset is now ± ω mod . In the experimental setup, the frequency shift of the pump beam is ω shift = 160 MHz, and the additional modulation is ω mod = 2π × 0.3 MHz. Considering that the atoms move with a velocity v in the vapor cell, they interact with the probe beam at a frequency of ω probe = ω0 - kv. In the case of the pump beam, the atoms interact with it at a frequency of ω pump= ω0 + 2ω AOM The frequency interaction of +kv, where ±k are the wave vectors of the pump beam and the probe beam. A spectrum is generated only when the atom resonates with both beams simultaneously. Therefore, the only atoms that interact are those that migrate towards the probe beam at a velocity v = ω AOM / k. Since the error signal is generated by the two sidebands of the first-order diffracted beam, the feedback from the error signal will stabilize the laser 102 at the output frequency of ω0 + ω AOM , that is, offset from the desired frequency by ω AOM . To reverse this offset, another AOM 110 is arranged in the main laser beam path. Then, the first-order diffracted beam output from the AOM 110 at the frequency ω0 is provided to the fiber coupler 116 through the mirrors 112, 114 to couple the light into the fiber 117, which is used to conveniently transmit the cooling laser beam to the trap. The laser detuning δ (the so-called red detuning) below the resonance frequency, in this case originating from 85 the Rb cooling transition, can be conveniently expressed in units of Γ, where Γ = 2π × 6 MHz is 85 the natural decay rate of Rb. For the example system, the detuning δ = -1.5Γ. The error signal is extracted from the left-hand side output of the vapor cell 122 through the PBS24 (direct path), the focusing lens 132, and the photodiode 134. The electrical signal output from the photodiode 134 is then amplified and demodulated with a suitable demodulation electronics 136 to generate the error signal. Then, the error signal is fed back in a feedback loop through a proportional-integral-differential (PID) controller to control the laser 102 by adding the error signal as a modulation to the drive signal of the laser.

[0088] Reference Figure 3 , the repump laser setup 200 is based on the laser source 202, which is matched with the cooling laser source 102 to form a pair, that is, in this case, another DFB with the same specifications. The repump laser is stabilized to the following 85 Rb transition:

[0089] 5 2 S 1 / 2 F = 2 → 5P 3 / 2 F' = 3

[0090] For this purpose, carrier modulation spectroscopy

[14] is used. A method similar to that for the cooling laser is used to stabilize the repump laser 202, but no dedicated demodulation electronics for demodulating the signal are required

[14] . The repump laser beam passes through the optical isolator 204 and the half-wave plate 206. Then the repump laser beam is split into two by the PBS 208. One beam (which has a small fraction of the beam power) is used as the input (vertical branch) for controlling the laser stabilization system, while the remaining optical power (referred to as the main beam) ultimately provides the incident beam for the trap (direct-through branch). The branch for laser stabilization is provided to the AOM 242 via the mirror 218. The AOM 242 has an additional modulation superimposed on its inherent frequency, as described above in the cooling laser stabilization setup. The modulation added to the AOM 242 is in the form of a square wave with a frequency ω mod = 17 MHz. This causes the first-order diffracted beam from the AOM to be decomposed into two components with frequencies ω1 = ω0 + ω AOM + ω mod and ω2 = ω0 + ω AOM - ω mod . These two components respectively form the pump beam and the probe beam for the saturation absorption spectroscopy arrangement based on the vapor cell 222 containing Rb vapor. The probe beam passes through the PBS 220 and passes through the vapor cell 222 from left to right in the figure. The pump beam is directed as follows: deflected by the PBS 220 and suitable mirrors 226 and 230 and passing through the half-wave plate 228, and finally deflected by another PBS 224 to pass through the vapor cell 222 from right to left in the figure, i.e., in the opposite direction to the probe beam. The probe beam output from the vapor cell 222 via the direct-through branch of the PBS 224 is focused by the lens 232 onto a quadrant photodiode 234 (as an alternative to the quadrant photodiode 234, a balanced photodiode or two separate photodiodes can be used). The error signal is obtained from the probe beam output of the vapor cell 222 through the PBS 224 (direct-through path), the focusing lens 232, and the photodiode 234. In the vapor cell, both the pump beam and the probe beam passing through the vapor cell 222 generate sub-Doppler spectra that are slightly offset from each other in frequency. By subtracting the resulting spectra, an error signal can be generated from the output of the photodiode segments. Then, the error signal is fed back in a feedback loop through a proportional-integral-derivative (PID) controller to control the laser 202 by adding it as a modulation to the drive signal of the laser. Since the error signal is generated by the two sidebands of the first-order diffracted beam, the feedback from the error signal will stabilize the repump laser at the output frequency ω0 + ω AOM , i.e., offset from the desired frequency by ω AOM。To reverse this offset, another AOM 210 is arranged in the path of the main laser beam, similar to the cooling laser stabilization system. Then, the first-order diffracted beam output from the AOM 210 at frequency ω0 is provided to the fiber coupler 216 through the mirrors 212 and 214. The fiber coupler couples the beam into the fiber 217, which is used to conveniently transmit the repump laser beam to the trap. One advantage of this repump stabilization system is that it does not require complex electronics and is thus suitable for portable low-power systems.

[0091] The above-mentioned resonant detuning of the cooling and repump lasers is obtained using an AOM. An alternative would be to use a scheme based on a single laser source, so that the laser beam can be used to generate the cooling and repump beams with an electro-optic modulator (EOM). An EOM is a device that modulates the phase of a beam by driving a low-frequency electric field through a crystal, and its effect responds to a linear shift in its refractive index.

[0092] After the stabilization as referred to above Figure 2 and Figure 3 described, the cooling beam and the repump beam are combined into a single beam and delivered to the optical trap in the beam geometry Figure 1 shown.

[0093] Figure 4 An experimental setup of the optical trap 300 used in the example setup is shown. The cooling beam and the repump beam are transmitted to the optical trap setup 300 via the respective fibers 117 and 217. The cooling beam and the repump beam are first combined by means of a 2-in-1 fiber coupler 301. In the experiment, this is done at a cooling:repump power ratio of 3:1. Then, the combined beam is split into three equal-power components by a 1-into-3 fiber splitter 302. The respective output sides of the splitter 302 are three parts of the fibers 304, 306, and 308. These beam combining and splitting functions can be obtained in the fiber using appropriate combiners and splitters, while taking care to maintain polarization as required, for example, using non-polarizing or polarization-maintaining combiners, splitters, and fibers. Alternatively, free-space optical components can be used for beam combining and splitting. The fibers 304, 306, and 308 terminate in the respective fiber couplers 310, 312, and 314, which are arranged to provide the beam geometry to the incident optical path, as referred to above Figure 1 described.

[0094] In the example setup, the three beams output from the respective fiber couplers 310, 312, and 314 have an approximately Gaussian power distribution in the cross-section and are all collimated to a diameter of 5.4 mm by means of collimating lenses (not shown individually), where the diameter is taken as 1 / e 2Values. The polarization state of light in the three beams output by the optical fibers 310, 312, 314 is set to circular using respective PBSs 316, 318, 320 and quarter-wave plates 322, 324, 326. Then these three beams pass through the vacuum chamber 350, which has a plurality of windows transparent to the beam wavelength or is made entirely of a transparent material such as a suitable glass. After passing through the vacuum chamber 350, each beam is reflected by a combination of a quarter-wave plate and a dielectric mirror 328 / 334, 330 / 336, 332 / 338, where the reflection is close to retroreflection, i.e., reflected back along the same path but slightly misaligned, as referred to above with reference to Figure 1 described. After reflection, the beams then pass through the vacuum chamber 350 a second time.

[0095] As discussed with reference to Figure 1 , due to the finite beam width (i.e., cross-section) of the incident and reflected beam components, an intersection volume V of the beams is formed within the vacuum chamber 350, as shown by the dashed ellipse in Figure 4 . In an example setup, the vacuum chamber 350 is formed by an anti-reflection coated glass vacuum cell sized 3 cm × 3 cm × 10 cm. The rubidium atoms in the vacuum chamber are cooled and concentrated in a cloud within the beam intersection volume V.

[0096] The vacuum chamber 350 can be operated to provide a vacuum environment by the action of a suitable vacuum pump 340 such as an ion pump, which is arranged to be in fluid communication with the vacuum chamber 350 via a suitable vacuum conduit 348. A vacuum valve 346 is also provided for the vacuum space. In an example experiment, the vacuum cell is typically maintained at a vacuum of 4 × 10 -10 mbar. The vacuum space also includes an atomic source to be cooled, and in an example setup, the atomic source 342 provides rubidium atoms. The rubidium atoms are released by heating the source material, for example, with an electrical heating device 344, which can be operated to provide a DC current to heat the source material. In an example experiment, rubidium vapor is provided by an alkali metal dispenser, which increases the background vapor pressure to 5 × 10 -9 mbar during trap operation. Other forms of heating can also be used, such as heating by means of a laser.

[0097] To characterize the optical trap properties, the number of trapped atoms N and its temperature T are measured as functions of various parameters, including the total beam power P and the red detuning level δ of the cooling laser originating from the 85 Rb cooling transition. Hereinafter, the stated value of the total beam power represents the sum of the powers of all three incident beams, which includes the powers of both the cooling component and the repump component. As described above, the power ratio between the cooling component and the repump component is 3:1, and the three incident beams have equal power.

[0098] Figure 5The graph shows the average number N of trapped atoms for four different total beam power values (0.9 mW, 1.6 mW, 4.5 mW, and 6.3 mW), which varies with the detuning δ to lower frequencies (so-called red detuning) referenced to the 85 Rb cooling transition, with the detuning δ expressed in units of Γ, where Γ = 2π × 6 MHz, which is 85 the natural decay rate of Rb. The number of atoms is measured by fluorescence from the atomic cloud, and the fluorescence is collected by a photodiode (not shown) using a simple non-amplified optical system, which is considered to have minimal light collection losses. The trap is loaded with rubidium atoms by heating a suitable rubidium source optically or electrically for 10 seconds. Each data point in the graph is the average of three measurements, and the error bars show the range of the three measurements. For a total beam power of 0.9 mW and a detuning to lower frequency δ = -1.2Γ, a maximum number N of atoms of approximately 1×10 8 is observed in the cloud. More generally, it can be seen that the maximum number of atoms in the cloud decreases non-linearly with increasing intensity. The experimental results show that, compared to the characteristics of the MOT [15, 16], the maximum number of atoms is obtained at relatively low power and low detuning levels. Comparing the number of trapped atoms N with what is expected from the MOT scaling law

[17] for a similar beam diameter d and beam power, the experimental results show that the optical trap can trap almost an order of magnitude more atoms than a similar MOT. Compared to N scaled proportional to d 3.6 found in a MOT with d > 2 mm, the performance of the optical trap is closer to N predicted proportional to d 6 scaling. For the optical trap according to an embodiment of the present invention, the ability to trap a large number of atoms at low beam power is a significant practical advantage, as it makes the technology itself suitable for low-power applications, such as battery-operated and / or small devices such as those that may be required in quantum computing or other quantum technologies.

[0099] Figure 6A and 6B are graphs showing the experimental results of the optical trap. For three different laser beam power values (1.6 mW, 4.2 mW, and 6.3 mW), the average temperature T of the atoms is shown in the graph varying with the red detuning frequency δ in units of Γ (i.e., on the same x-axis as Figure 5 ). Figure 6A Shows the results along the long axis of the atomic cloud, i.e., typically along the incident / reflected beam direction, Figure 6BShows the results extended along the short axis of the atomic cloud, i.e., its transverse direction. The temperature of the atomic cloud is measured using the time-of-flight method. The cooling beam and the repump beam are extinguished for up to 12 milliseconds to allow the atomic cloud to expand. Then the cloud is illuminated and imaged with a fast camera. The width of the atomic cloud after each time-of-flight measurement is determined by a two-dimensional Gaussian fit to the acquired image profile. Due to the elongated shape of the cloud, the temperature is measured along both the long axis and the short axis of the cloud. The average value of three time-of-flight measurements forms Figure 6A and 6B a single data point in the results shown. These results indicate that the atomic cloud temperature is only weakly correlated with the detuning, varying by about 10% over the covered detuning range, but is significantly correlated with the beam power. Additionally, comparing Figure 6A with Figure 6B it can be seen that the atoms moving in the direction consistent with the short axis of the cloud are generally hotter than those moving in the direction consistent with the long axis, i.e., the cooling along the beam direction is more effective than its transverse cooling. For the atoms expanding along the long axis of the cloud, the lowest measured temperature is 40 μK, while for those expanding along its short axis it is 120 μK. For both axes, the lowest temperature is obtained at the lowest red detuning value (δ = -0.8Γ) and the lowest beam power (1.6 mW). These results further indicate that, different from the trend found in MOT, the optical trap seems to be most effective at low red detuning and small laser power originating from the cooling transition. More generally, it can be seen that the average temperature strongly depends on the beam power but only weakly depends on the detuning amount, although there is clearly a weak trend for the temperature to tend to decrease as the detuning level decreases.

[0100] Now discuss Figure 5 and Figure 6A and 6B the physical mechanisms behind the experimental results of Figure 6A and 6B The directional effect shown in Figure 5Peak shifts in [the figure] may be due to the AC Stark shift. Flattening of the distribution may be caused by state saturation. Usually, the dipole trap is tuned to be far detuned to mitigate heating effects through single-photon scattering. To counteract the reduced force, the trapping beam intensity must be much higher than saturation. Usually, the laser used in the dipole trap is resonantly detuned by several nanometers and focused to a diffraction-limited spot with an optical power of several watts. As shown by Letokhov and Minogin

[18] , when one tunes the laser close to resonance, cooling and trapping in an optical lattice can be achieved, although the trapping depth equals the heating caused by scattered photons. The near-resonant dipole trap proposed by Letokhov and Minogin is usually ignored because it is considered too "leaky" as the trap depth would be on the order of the Doppler cooling limit. But this trap was proposed nearly a decade before the discovery of polarization gradient cooling. If the atoms are effectively cooled to sub-Doppler temperatures when entering the dipole trap (as is often done in a MOT), then they should remain trapped. If this is also the operating process within the optical trap according to an embodiment of the present invention, then the question that arises is why such efficient cooling and a sufficient number of atoms directly from the background vapor are observed in the experimental results. If the lattice spacing is large enough to cool the atoms at a speed of dozens of meters per second, then the superlattice proposed in [8] might be the answer. To better understand this, we explored the scale of each effect through simulations and a simplified analytical model as described below.

[0101] Before averaging to obtain the final atom number, the variation of the final (trapped) atom number with laser power and detuning was studied by performing multiple simulations with different initial random atom configurations. This simulation considered the interaction between the atoms and the laser beam as well as the AC Stark detuning.

[0102] Figure 7 The graph of [the figure] shows these simulation results in the form of a plot of the atom number N versus the red detuning δ in units of Γ for four different laser powers (0.9 mW, 1.6 mW, 4.5 mW, and 6.3 mW), i.e., for four values identical to the experimental results shown in Figure 5 Each data set consists of 20 points, which are formed by averaging six repetitions at each position. The maximum time is t = 10 ms, and the time step is 1 microsecond, i.e., dt = 1×10 -6 seconds. As shown in Figure 7 the simulation results follow the same general trend as the experimental results, that is, lower beam power and lower detuning values result in higher final atom numbers.

[0103] Figure 8A , 8B8C shows another aspect of the simulation in the form of 2D cross-sections in the atomic distribution x-y plane that vary over time during the cooling and trapping processes. The region shown corresponds to the cross-section of the intersection volume of the beams where the cloud is expected to form, i.e., much smaller than the cross-section of the vacuum chamber. The simulation results are shown for a beam power of 0.9 mW and a detuning value δ = -1.25Γ. Figure 8A , 8B 8C show the atomic distributions at t = 0 ms, t = 5 ms, and t = 10 ms, respectively, where t = 0 is the time when the beam is introduced into the trapping chamber. The atomic distribution after cooling and trapping, i.e., at t = 10 ms, and the atomic distribution midway through the process at t = 5 ms are consistent with the general behavior seen in the experimental results, where the atoms are eccentrically concentrated in a non-spherical cloud.

[0104] The optical field generated in the optical trap provides a velocity-dependent restoring force and a position-dependent restoring force, thereby forming a sub-Doppler temperature atomic dense cloud near the trap center. Both the experimental results and the simulation show that the misalignment of the incident beam and the retro-reflected beam is crucial for the effective operation of the magnetic-field-free optical trap according to the embodiments of the present invention. Now, why this is the case is discussed.

[0105] Figure 9 is a schematic diagram of the interference between a pair of counter-propagating beams that are at a small angular θ with respect to each other in the optical trap according to an embodiment of the present invention, i.e., θ represents any one of α, β, κ. When the two counter-propagating beams are slightly misaligned in this way, a set of interference fringes is formed, where the fringes extend approximately perpendicular to the beam wave vectors, as schematically shown. Assuming that the two counter-propagating beams are in a vacuum, the fringe spacing (or "pitch") p is given by:

[0106] p = λcosφ / 2sinθ

[0107] where λ is the wavelength of the light, θ is the angle between the beams, and φ is the angle perpendicular to the interference fringes.

[0108] Although atoms passing vertically through the fringe pattern, i.e., atoms with a trajectory φ = 0°, do not encounter any cooling force because any net momentum transferred to the atoms is not opposite to the atomic velocity, atoms passing through the fringe pattern at any other angle (i.e., φ ≠ 0°) will encounter a scattering force. Increasing the trajectory angle φ also increases the apparent fringe spacing. Assuming a beam misalignment angle of θ = 1° and the atoms moving along a trajectory of φ = 45°, the effective fringe spacing will be increased by 20 times compared to a trajectory of φ = 0°. If the polarization gradient is still effective for this vertical standing wave, a similar increase in the trapping velocity can be expected. Therefore, atoms moving through the fringes formed by the misalignment of the counter-propagating beams will experience polarization gradient cooling, resulting in a greater trapping velocity. This can explain why such efficient cooling of a large number of atoms is observed in the experimental results.

[0109] It is further pointed out that, according to our understanding of physics, the formation of a cooled atomic cloud would require the misalignment of all three pairs of counter-propagating beam components.

[0110] Experimental results show that the optical trap according to an embodiment of the present invention can operate in a wide parameter space, for example, operate with the change of parameters, and the parameters include: beam polarization, beam power, red detuning level, tilt angle, and misalignment angle.

[0111] For the parameter space explored by experiments so far, we have found that the continuous and reliable formation of a cooled atomic dense cloud can be achieved within the following misalignment angle ranges:

[0112] α≈0° (but α<>0°; see the discussion below)

[0113] 1°≤β≤2°

[0114] 0°<κ≤0.5°

[0115] Although from the perspective of the experimenter, the mirror is adjusted for retroreflection, i.e., α is set to 0°, this must be adjusted based on the above understanding of physics. Therefore, although good performance can be observed when α is nominally set to 0°, in reality, it is considered that there must be a slight misalignment (or possibly a deviation from perfect beam collimation).

[0116] When changing parameters such as polarization or beam power, the following reliable processes for generating a dense atomic cloud along the axis were found:

[0117] · Set the first beam such that the reflected beam is nominally the retroreflection of the incident beam (α≈0°),

[0118] · Set the second beam to be misaligned such that the incident and reflected beam spots are separated by approximately half a beam width at the intersection point, and

[0119] · Set the third beam to be misaligned by the same or slightly larger amount as the second beam, for example, between half a beam width and one beam width at the intersection point.

[0120] This method of aligning the axis has been proven to be very reliable for directly forming a cloud from vapor.

[0121] For practical convenience, in order to limit the parameter space, the systematic experiments conducted so far have mainly been limited to a finite parameter space, in which the number of beams (three), beam geometry (tilt angle 30°), and polarization (circular) are fixed, and only the beam power, beam misalignment angle, red detuning level of the cooling beam, and red detuning level of the repump beam are systematically changed.

[0122] That being said, the experiment was extended to more broadly explore the parameter space in the following areas:

[0123] The influence of the variation of the inclination angle was studied. What was noted as a preliminary conclusion is that an inclination angle of 45° corresponds to the conventional optical cooling geometry, in which three pairs of counter-propagating beams extend along mutually orthogonal axes, i.e., a Cartesian setup. Additionally, with reference to Figure 1 it can be seen that an inclination angle of χ = 30° is exactly equal to an inclination angle of χ = 60°, because they deviate from the orthogonal by ±15°. So by changing χ = 30° to 60°, all that happens is that the tripod rotates by 90° (additionally, when χ > 45°, the signs of the misalignment angles α, β, κ will be reversed compared to the values given elsewhere in this document). Therefore, we refer to the inclination angle in terms of the angular deviation Δχ from the orthogonal beam, i.e., χ = 45°. In the case of an angular deviation Δχ = 25° (i.e., an inclination angle χ as shown Figure 1 as 20°), the formation of clouds was observed, but the quality was poor in terms of cooling, density, and the number of atoms. Therefore, an angular difference of Δχ = 25° seems to be close to the effective boundary. In the case of an angular difference range of 10° ≤ Δχ ≤ 20° (i.e., the inclination angle range of 25° ≤ χ ≤ 35° as shown Figure 1 ), continuously good performance was observed.

[0124] Additionally, it has been seen that this effect also occurs with the linear polarization (and circular polarization) of the accompanying beams.

[0125] Additionally, in principle, the inclination angles of each incident beam path may be different from each other, although this parameter variation has not been systematically explored in the experiment.

[0126] Due to the stability of the effect and the large parameter space created (in which effective cooling and trapping have been observed), the experiments conducted so far may not have found the optimal conditions in terms of the number of atoms (highest), atomic density (highest), and atomic temperature (lowest), or may not have explored the boundary conditions that will work efficiently. Other combinations of the above parameters such as the inclination angle and misalignment angle can also produce good or better results. It should also be noted that other embodiments can use more than three beams, such as four beams, five beams, or six beams.

[0127] Those skilled in the art will appreciate that many improvements and modifications can be made to the foregoing embodiments without departing from the scope of this document.

[0128] For those embodiments that require repumping, the repumping light does not have to be introduced to co-propagate with each or every cooling beam as described above. The repumping light can be added to co-propagate with only one of the cooling beams or some other subset of the cooling beams. The repumping light can also be directed along one or more optical paths independent of the optical paths of the cooling beams to the intersection volume, i.e., it does not need to co-propagate with the cooling beams.

[0129] In addition, as explained above, in the main embodiment, the first, second, and third pairs of axis angles form angles between 25° and 35° with the reference axis, and the pairs of axis angles in other embodiments are outside this range. For example, the lower limit can be as low as one of 5°, 6°, 7°, 8°, 9°, 10°, 11°, 12°, 13°, 14°, 15°, 16°, 17°, 18°, and 19°, or as low as one of 20°, 21°, 22°, 23°, and 24° as described above, and as described above, the upper limit can be as high as 36°, 37°, 38°, 39°, or 40° relative to the reference axis.

[0130] Some specific preferred ranges of the misalignment angle of the cooling laser beam are described in the above description. However, in this case, the effective range of the misalignment angle will vary with the beam width, the optical path length of the corresponding beam, and the beam power. For any given beam power, sufficient intersection of each pair of counter-propagating beams must be maintained within the intersection volume. Therefore, an alternative definition of the preferred range of the misalignment angle can be expressed by the following formula: For each pair of counter-propagating beams, the two beam widths and the misalignment angle between the two beams are jointly designed to ensure that at least half of the beam area of the beam with the smaller beam area in the intersection volume intersects with the beam area of the beam with the larger beam area. In the special case where the two beams have the same beam area, this definition simplifies to: For each pair of counter-propagating beams, the two beam widths and the misalignment angle between the two beams are jointly designed to ensure that at least half of the beam area intersects within the intersection volume.

[0131] In the above embodiment, the output beam of a single laser is divided into three components to generate the first, second, and third cooling beams. In addition, the first, second, and third beams are redirected back through the vacuum chamber by their respective first, second, and third reflectors. However, multiple variations of this scheme are possible. For example, the laser source can consist of three lasers, each generating one of the first to third beams. In another variation, the reflectors can be omitted and the laser source can consist of six lasers, each generating one of the first to sixth beams.

[0132] Figures 10-12 is a schematic diagram of an alternative embodiment. The vacuum chamber and related components are not shown, but will be present as Figure 4 shown. Not all optical components (such as optical fibers, fiber couplers, etc.) are marked, but these will be understood from Figure 4 this.

[0133] Figure 10Schematic diagram of a first alternative embodiment. In this embodiment, six cooling lasers 102_1 to 102_6 are provided to generate first to sixth cooling beams. Additionally, a single optional repump laser 202 is shown, whose output beam is combined with one of the cooling beams, namely the output from cooling laser 102_4, for example using the fiber coupler shown. It is not necessary to combine the repump beam into one or more of the cooling beams, but it can be an option.

[0134] Figure 11 Schematic diagram of a second alternative embodiment. Three cooling lasers 102_1, 102_2, 102_3 are provided. Counter-propagating beam pairs are generated in the same manner as in the Figure 4 embodiment by respective mirrors 334, 336, 338. Repump light is provided in the same manner as in Figure 10 by combining the output of the repump laser 202 with the output of one of the cooling lasers (here cooling laser 102_1).

[0135] Figure 12 Schematic diagram of a third alternative embodiment. In this embodiment, the cooling beam arrangement is the same as in Figure 11 , but the repump beam is provided transversely through free space in the vacuum chamber, denoted by reference numeral 203, which is geometrically independent of any cooling beam and can be at any angle. All that is required is that the intersection volume V of the repump beam and the cooling beam intersects.

[0136] Many other variants for generating and properly guiding the cooling beams and the optional repump light will be readily apparent to those skilled in the art.

[0137] Reference Signs

[0138] 100 Cooling laser arrangement

[0139] 102 Cooling laser, such as DFB at 780 nm

[0140] 104 Optical isolator

[0141] 106 Half-wave plate

[0142] 108 Polarizing beam splitter (PBS)

[0143] 110 Acousto-optic modulator (AOM)

[0144] 112 Mirror

[0145] 114 Mirror

[0146] 116 Fiber coupler

[0147] 117 Optical fiber

[0148] 118 Reflector

[0149] 120 PBS

[0150] 122 Vapor cell for cooling laser stabilization

[0151] 124 PBS

[0152] 126 Reflector

[0153] 128 Half-wave plate

[0154] 130 Reflector

[0155] 132 Lens

[0156] 134 Photodiode (PD)

[0157] 136 Demodulation electronics

[0158] 138 Reflector

[0159] 140 Reflector

[0160] 142 AOM

[0161] 144 Collimating lens

[0162] 146 Quarter-wave plate

[0163] 148 Dielectric mirror

[0164] 200 Repump laser setup

[0165] 202 Repump laser, such as DFB at 780 nm

[0166] 203 Repump laser beam

[0167] 204 Optical isolator

[0168] 206 Half-wave plate

[0169] 208 PBS

[0170] 210 AOM

[0171] 212 Reflector

[0172] 214 Reflector

[0173] 216 Fiber optic coupler

[0174] 217 Optical fiber

[0175] 218 Reflector

[0176] 220 PBS

[0177] 222 Vapor cell for repumping laser stabilization

[0178] 224 PBS

[0179] 226 Mirror

[0180] 228 Half-wave plate

[0181] 230 Mirror

[0182] 232 Lens

[0183] 234 Quadrant photodiode

[0184] 238 Mirror

[0185] 240 Mirror

[0186] 242 AOM

[0187] 300 Optical trap setup

[0188] 301 2-in-1 fiber coupler

[0189] 302 1x3 fiber splitter

[0190] 304 Optical fiber

[0191] 306 Optical fiber

[0192] 308 Optical fiber

[0193] 310 Fiber coupler

[0194] 312 Fiber coupler

[0195] 314 Fiber coupler

[0196] 316 PBS

[0197] 318 PBS

[0198] 320 PBS

[0199] 322 Quarter-wave plate

[0200] 324 Quarter-wave plate

[0201] 326 Quarter-wave plate

[0202] 328 Quarter-wave plate

[0203] 330 Quarter-wave plate

[0204] 332 Quarter-wave plate

[0205] 334 Rearview mirror

[0206] 336 Rearview mirror

[0207] 338 Rearview mirror

[0208] 340 Ion pump

[0209] 342 Atomic (e.g., rubidium) source

[0210] 344 Atomic source heater

[0211] 346 Vacuum valve

[0212] 348 Vacuum pipe

[0213] 350 Vacuum chamber

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[17] G. W. Hoth, E. A. Donley and J. Kitching, Atom number in magneto-optical traps with millimeter scale laser beams, Optics letters 38, 661 (2013).

[0232]

[18] V. Letokhov and V. Minogin, Cooling, trapping, and storage of atoms by resonant laser fields, JOSA 69, 413 (1979).

Claims

1. An optical trap for capturing and cooling atoms, the optical trap comprising: - A vacuum chamber operable to provide a vacuum environment in which atoms of an atomic species can be laser cooled by excitation of an electronic transition of the atomic species called a cooling transition; - A laser source configured to produce laser light at a frequency detuned below the frequency of the cooling transition; - An optical arrangement configured to manipulate the laser light to produce first, second, and third beams having respective first, second, and third beam widths, and to direct the first, second, and third beams to propagate through the vacuum chamber along respective first, second, and third incident optical paths deviating from a mutually orthogonal arrangement, wherein they have respective first, second, and third pairs of axis angles between 25° and 35° with respect to a reference axis, wherein the mutually orthogonal arrangement means that each of the incident optical paths will form a 45° pair of axis angles with respect to the reference axis, and wherein the first, second, and third beams are at least substantially collimated as they pass through the vacuum chamber; and - First, second, and third reflectors arranged to reflect the first, second, and third beams to propagate back through the vacuum chamber along their incident optical paths in respective first, second, and third reflected optical paths deviating from retroreflection, wherein each reflected optical path will coincide with its incident optical path based on respective first, second, and third misalignment angles, wherein each of the misalignment angles is greater than 0.1°, and the values of the first, second, and third misalignment angles and the beam widths define an intersection volume within the vacuum chamber through which the first, second, and third beams both pass as they propagate along their incident and reflected optical paths.

2. The optical trap according to claim 1, wherein, The misalignment angles comply with one or more of the following additional conditions: Each of the misalignment angles is less than 2°; At least one of the misalignment angles is greater than 0.5°; and At least two of the misalignment angles are greater than 0.5°.

3. The optical trap according to any one of the preceding claims, wherein, The first, second, and third reflectors are arranged such that the reference axis and each pair of incident and reflected optical paths are at least substantially in a common plane, thereby defining such first, second, and third planes.

4. The optical trap according to claim 3, wherein, The first, second, and third planes are substantially equally angularly spaced when viewed along the reference axis.

5. The optical trap according to claim 1 or 2, further comprising polarization components arranged to provide first, second, and third beams having respective specified polarization states when the first, second, and third beams enter the vacuum chamber.

6. The optical trap according to claim 5, wherein The first, second, and third reflectors are configured to ensure that the specified polarization states of the first, second, and third beams are maintained upon reflection.

7. The optical trap according to claim 1 or 2, wherein, The atomic species has a further electronic transition called a repump transition that is required to be excited for efficient cooling, and wherein the laser source or another laser source is configured to produce another laser at another frequency detuned below the frequency of the repump transition.

8. The optical trap according to claim 7, wherein the optical arrangement further comprises a beam combiner operable to combine the laser and the another laser such that the first, second, and third beams each contain both the laser and the another laser.

9. The optical trap according to claim 1 or 2, wherein The optical trap does not include a magnetic field generator.

10. A method for laser cooling and trapping atoms, the method comprising: - providing a vacuum chamber that houses atoms of an atomic species, the atoms of the atomic species being capable of being laser cooled in a vacuum environment by excitation of an electronic transition of the atomic species referred to as a cooling transition; - providing a laser at a frequency detuned below the frequency of the cooling transition; - providing first, second, and third laser beams having respective first, second, and third beam widths; - directing the first, second, and third beams to propagate through the vacuum chamber along respective first, second, and third incident optical paths that deviate from a mutually orthogonal arrangement, wherein they have respective first, second, and third pairs of axis angles between 25° and 35° relative to a reference axis, wherein the mutually orthogonal arrangement means that each of the incident optical paths will form a 45° pair of axis angles relative to the reference axis, and wherein the first, second, and third beams are at least substantially collimated as they pass through the vacuum chamber; - reflecting the first, second, and third beams to propagate back through the vacuum chamber along their respective first, second, and third reflection optical paths that deviate from retroreflection, wherein each reflection optical path will coincide with its incident optical path based on respective first, second, and third misalignment angles, wherein each of the misalignment angles is greater than 0.1°, and the values of the first, second, and third misalignment angles and the beam widths define an intersection volume within the vacuum chamber through which the first, second, and third beams both pass as they propagate along their incident and reflection optical paths, and wherein laser cooling occurs in the absence of a magnetic field; 11. The method according to claim 10, wherein, The atomic species has a further electronic transition, referred to as a repump transition, that is required to be excited to effect efficient cooling, and wherein the method further comprises: providing another laser at another frequency detuned below the frequency of the repump transition, wherein the first, second, and third beams include the another laser.

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