Improved cold atom source

Abstract

The present invention provides - a primary atom source (PAS); - a two-dimensional magneto-optical trap called 2D-MOT, a first pair (LB1, LB1') and a second pair (LB2, LB2') of two counter-propagating beams, A magnetic device (MD) configured to generate a magnetic field, said magnetic field comprising: Null values ​​at the center O and on the x-axis at least within the trapping area, A component By along y that has a constant gradient along the z axis within the trapping region, A component By along the y axis that varies along the z axis between two extremes, a positive maximum and a negative minimum, where the absolute value of the extreme located on the opposite side of the primary atom source is strictly greater than the absolute value of the other extreme. Magnetic device (MD) a two-dimensional magneto-optical trap, - a cooling beam (CBm) propagating in the opposite direction to the atomic direction; The present invention relates to a cold atom source (10) including:

Description

[Technical Field]

[0001] The present invention relates to the field of cold atom sources, and more particularly to cold atom sources based on the combination of a two-dimensional magneto-optical trap, called 2D-MOT, and a Zeeman decelerator. [Background technology]

[0002] Cold atom sources have been developed for a variety of applications, including atomic clocks, gravimeters, accelerometers, gyroscopes, among others. For the industrialization of these quantum sensors, there is currently a need to develop miniaturized cold atom sources.

[0003] The first cold atom source 20, called the Zeeman decelerator, was described by Phillips et al. in the publication "Laser Deceleration of an Atomic Beam" (Phys. Rev. Lett. Vol. 48, no. 9, 1982) and is shown in Figure 1. The Zeeman decelerator is based on the deceleration of atoms by a counter-propagating laser beam called the Zeeman beam ZB. The atoms have a two-level atomic structure with a ground state FS and an excited state ExS, and the transition between the two states occurs at a transition wavelength λc or a transition frequency f c The Zeeman laser has a wavelength related to λc. To efficiently slow down the atoms, the photons of the Zeeman beam must be in resonance with the atoms.

[0004] The effective slowing down of atoms is limited by two processes: the Doppler shift of changing atomic velocities away from the resonance of the laser light, and optical pumping limits the number of available photon scattering cycles. The Phillips atom source solves these two problems.

[0005] The cold atom source 20 includes a primary atom source PS that is an oven; atoms with low vapor pressure at 300 K typically require an oven to generate a thermal atomic beam with sufficient flux, such as strontium (Sr), sodium (Na), cadmium (Cd), and ytterbium (Yt), among others. The Phillips source uses Na atoms, with F = 3S (F = 2, M F =2) and ExS=3P (F=3, M F = 3). The typical operating temperature of an oven is several hundred degrees Celsius, which determines the Maxwell-Boltzmann distribution for the velocity of the thermal atomic beam AtB produced by the oven, with a root-mean-square value of several hundred meters per second outside the oven.

[0006] The cold atom source also includes a decelerated laser beam ZB with a fixed frequency and circular polarization, which is generated by a cooled laser CL.

[0007] The Zeeman decelerator uses a spatially varying magnetic field Bz along the axis z of the thermal atomic beam AtB, which is coincident with the decelerating laser beam ZB. The magnetic field Zeeman-tunes the decelerating atoms to always be in resonance with a fixed-frequency cooling laser CL, resulting in selection rules and a Zeeman shift that strongly discriminate against optical pumping. The magnetic field keeps the decelerating atoms in resonance with the fixed frequency of the cooling laser by virtue of the Zeeman shift, resulting in selection rules and a Zeeman shift that strongly suppress optical pumping. The cold atom source 20 includes a 60 cm long solenoid SOL configured to generate a spatially varying magnetic field along z Bz.

[0008] With a constant Zeeman shift γz (expressed in GHz per Gauss), the spatially varying magnetic field that optimally compensates for the varying Doppler shift of an atom experiencing uniform deceleration a is given by: B=B b +B0(1-2az / v0 2 ) 1 / 2 (1)

[0009] Here, B bis a constant bias magnetic field that solves the problems of Doppler shift and pumping, and B0 is the magnetic field at which the Doppler shift and Zeeman shift of atoms exiting the oven at an initial velocity v0 and decreasing to zero velocity coincide.

[0010] Atoms with v < v0 start to decelerate only when they reach a magnetic field that determines a Zeeman shift that exactly compensates for their Doppler shift. As a result, all atoms with an initial velocity up to v0 are grouped into one low-velocity group and adapted to be trapped.

[0011] Given that the magnetic field is aligned with ZB (along z), the cooling light can be polarized so as to correspond only to the target transition, i.e., only to the positive (negative) circular polarization when the magnetic sub-level mF increases (decreases) from FS to ExS. This setup enables the atoms to be efficiently decelerated but has several drawbacks.

[0012] First, to achieve the optimal magnetic field, a large experimental setup (typically at least 50 cm in length, usually more than 1 m depending on the atomic species), a large current, and often a bulky electromagnet configuration that requires water cooling, or alternatively a complex permanent magnet configuration are needed. This setup cannot be miniaturized.

[0013] Second, the atomic trap at the end of the Zeeman decelerator can see the oven, which determines the problem of blackbody radiation and the high collision rate with the background gas, limiting the lifetime of the atoms. To avoid these problems, it is necessary to install a mechanical shutter Ch in the vacuum to mechanically hide the path of the hot atomic beam, or to deflect the exiting atomic beam.

[0014] Third, given the long distance required to decelerate the hot atomic beam, only a small solid angle of the atoms exiting the oven is captured by the atomic trap.

[0015] The new configuration, presented by Tiecke et al. in the publication "High flux two-dimensional magneto-optical-trap source for cold lithium atoms" (Phys. Rev. A, 80, 013409, 2009), relies on a 2D-MOT that is loaded laterally by an atomic beam emitted from an oven along the z-axis.

[0016] The laser beam geometry of Tiecke's 2D-MOT is shown in Figure 2A (perspective view) and Figure 2B (yz-plane - 2D-MOT plane), while Figures 2C and 2D show the magnet configuration in the yz-plane (magnet plane). Note that in Figures 2A to 2D, axis z (propagation of the atomic beam) corresponds to Tiecke's axis y, and axis x (towards the second chamber) corresponds to Tiecke's axis z.

[0017] The 2D-MOT cools and traps atoms along the yz plane, leaving x free for the transfer of atoms to another chamber (actuated by a push beam) where another MOT is located, called the 3D-MOT (retrapping). The 2D-MOT is the first stage of the cooling process, while the second stage occurs in the second chamber with the 3D-MOT.

[0018] The 2D-MOT system includes four counter-propagating laser beams: a first pair (LB1, LB1') and a second pair (LB2, LB2'), where the two pairs (LB1, LB1') and (LB2, LB2') are perpendicular to each other. The beams are positioned at ±π / 4 angles with respect to the z-axis in the yz-plane (2D-MOT plane) and are red-detuned to the cooling transition. The two pairs have opposite circular polarizations, and the polarizations of the two beams in each pair are also opposite. The area ZTr at the intersection of the beams defines the size of the trap with its center O. In Tiecke, the atoms are lithium, and the cooling transition is near 671 nm. The four beams for the 2D-MOT system (and the six beams for the 3D-MOT system) are provided by a dedicated laser system.

[0019] 2D-MOT is i) a zero magnetic field along the x-axis at the center O within the trapping region ZTr; and ii) The component By along y, which has an approximately constant gradient ∇B=δBy / δz (monotonically varying) around the point O in the trapping region ZTr, where the constant value can be negative or positive with adaptation of the polarization of all 2D-MOT beams. The magnets also include two sets of laminated permanent magnets S1t and S2t configured to generate a two-dimensional magnetic field by

[0020] These two sets are arranged symmetrically along y with respect to the z axis as shown in FIG. 2C and have equal but opposite magnetizations +M / −M along z.

[0021] Since the B field is null along the x axis and along the z axis is aligned on y and has a constant gradient, Maxwell's second equation (i.e., Gauss's law of magnetism) imposes that along the y axis the B field is aligned on z and has a gradient opposite to the gradient along the z axis.

[0022] This B-field, which is a magnetic field that is null along one axis (the x-axis) and varies linearly and with opposite gradients along the other two axes, is commonly referred to as a linear quadrupole magnetic field.

[0023] Applying an optimized magnetic field as described above is a prerequisite for efficient trapping of atoms in a 2D-MOT. The optimal value of the constant gradient G depends on the atomic species and is analytically determined to obtain overdamped motion of atoms trapped in the 2D-MOT (see, for example, Raab et al., Phys. Rev. Lett., vol. 59, no. 23, p. 2631, 1987).

[0024] In the 3D-MOT configuration, the B field is null at only one point and the gradient G is along one axis. 3D and along the other two axes the gradient -G 3D Note that we have a / 2.

[0025] Atoms with velocities low enough to be trapped by the 2D-MOT that fall within the overlap region of the 2D-MOT laser beams experience a combination of friction and central forces that cool the atoms and trap them along the x-axis. Unlike 3D MOTs, which have forces acting along three major axes, in 2D MOTs, forces act along two axes (y and z), while the atoms are free along a third axis (x).

[0026] This configuration has the advantage of being very compact, strongly reducing the distance between the oven and the atom trapping region, and therefore increasing the trapping solid angle compared to the Phillips configuration. The magnetic field is generated by permanent magnets, which are more compact than the Phillips solenoid, consume less power, and do not require water cooling.

[0027] The 2D MOT produces a jet of cooled atoms that is transferred to another vacuum chamber, where the atoms are recollected (typically in a 3D MOT) and used in an experiment. The location where the atoms are recollected is along the x-axis, where the B field generated by the 2D MOT's permanent magnets is zero. Therefore, the magnet configuration of the 2D MOT does not interfere with the final experiment.

[0028] The drawback is that the flux of cold atoms captured by the 2D-MOT in the configuration reported by Tiecke is low compared to a standard Zeeman decelerator.

[0029] In two publications, Lamporesi et al. (Review of scientific Instruments 84, 063102, 2013) and Nosske et al. (Physical.Review A, 96, 053415, 2017) each improved the atomic flux reported by Tiecke. Lamporesi realized a sodium source, and Nosske a strontium source. In both setups, they implemented a compact, unoptimized Zeeman decelerator by exploiting the tail of the 2D MOT magnetic field. The Zeeman decelerator uses a cooled laser beam CB that enters the setup along the z-axis in the opposite direction to the thermal beam AtB. The Zeeman decelerator is unoptimized for the following reasons: i) The magnetic field along the propagation direction of the atomic beam is perpendicular to the beam in the Zeeman decelerator, rather than parallel to it, and its z-dependence does not satisfy Eq. ii) Given the detuning and setup configuration adopted for the CB, only half of the optical power of the Zeeman beam is used to cool the atomic beam. The polarization of the CB is set to be linear along x, which determines equal contributions of positive and negative circular polarizations in the reference frame of the atoms when the magnetic field is oriented along y. Adopting a linear polarization along y for the CB results in π polarization for the atoms, which makes the Zeeman shift constant along the z axis and therefore cannot compensate for the changing Doppler shift of the decelerating atoms.

[0030] The geometric configuration of the 2D MOT of the atom source is shown in Figures 2A to 2D, but with a different magnet arrangement (a stack of four magnets instead of two). The complete setup of Nosske's cold atom source 30 is shown in Figure 3.

[0031] The thermal atomic beam AtB is generated by a strontium oven OV, which operates at a temperature range of 450° to 580°C for strontium. The different beams are contained in a high-vacuum tube, and the trapped atoms are located in the center of a multi-way cross vacuum chamber. The intersection between the four 2D-MOT beams defines the trap size, defined by the area ZTr. The transfer of the trapped atoms from the trap chamber to the ultra-high vacuum chamber of the 3D-MOT is achieved by a differential pumping tube DPT along x and by a push beam PB. The beam AtBC is the cooled atomic beam pushed into the 3D-MOT chamber.

[0032] In these two publications, the required 2D axisymmetric linear (along z) (since the zero field is a single line, along the axis x) quadrupole magnetic field is provided by four sets S1 to S4, each set having nine permanent single-piece magnets.

[0033] Starting from Tiecke, an equivalent configuration to obtain the same magnetic field is to rotate the two sets and their magnetization directions along the z-axis, as shown in FIG.

[0034] However, this configuration is not possible because the magnets would block the atomic beam. Therefore, we "split" each of the two sets of Tiecke in two, and translated each half to + / -x0, as shown in Figure 5 (the left side is in the xz plane, the right side is in the yz plane). The magnetization axes of S1 and S2 are opposite to those of S3 and S4. These sets are symmetrically arranged around the chamber at the corners of a rectangle R in the xz plane, centered on the x and z axes, with a distance of x0 = + / -75 mm and z0 = + / -88 mm in the x and z directions.

[0035] With this configuration, the permanent magnets generate a linear quadrupole magnetic field for 2D-MOT with a gradient of about 50 G / cm near the origin O where the field equals zero.

[0036] The magnetic field By(z) generated in the z direction by the magnet configuration is shown in FIG.

[0037] In addition to being used in 2D-MOT, this magnetic field is also used in auxiliary Zeeman decelerators. Given that the magnetic field is orthogonal to the AtB and ZC directions, both Lamporesi et al. (end of §II.C of the publication) and Nosske et al. (end of §II.A of the publication) observed that up to half of the optical power of the Zeeman decelerator beam can be set for each of the two polarizations in the atomic reference frame and thus can be used to decelerate atoms. This configuration is achieved by choosing a linear polarization for the Zeeman decelerator beam along an axis perpendicular to the magnetic field, i.e., x in the case of Nosske and y in the case of Lamporesi. By choosing a linear polarization along the magnetic field axis, i.e., y in the case of Nosske and x in the case of Lamporesi, only π transitions are induced in the atoms, and Zeeman deceleration is not possible because the ground and excited states of the corresponding transitions are shifted in the same way by the magnetic field.

[0038] The cooled beam of the Zeeman decelerator and the 2D-MOT beam have a frequency offset equal to several natural linewidths Γ (the linewidth of two hyperfine levels of the atomic structure specific to each atomic species).

[0039] In the Nosske setup of Figure 6, the trap center is located 125 mm from the exit of the oven (strontium source). The size of the ZTr region Try along the y-axis is + / - 15 mm.

[0040] The cooling transition of strontium is the fundamental state FS=5s 2 1 S0 and excited state ExS=5s5p 1 P1, which corresponds to a wavelength λc=461 nm.

[0041] In Figure 6, Nosske defines two regions of the magnetic field topology that enable a Zeeman decelerator, labeled 1 and 2 in Figure 4. In region 1, the magnetic field increases to a maximum value Bmax of 160 G, with a positive gradient; in region 2, the magnetic field decreases from Bmax, passes through zero at the center of the trap, O, and continues to decrease to a minimum value -Bmax, with a negative gradient.

[0042] In the publication Nosske considers two possibilities: using region 1, which exploits one polarization component of the cooling beam, or region 2, which exploits the other polarization component. The magnetic field gradient reaches a maximum of about 15 G / cm in region 1, and about twice as large (30 G / cm) in region 2. Nosske finds that the Zeeman deceleration is more efficient in region 2 than in region 1, and speculates that this is due to less impact from collisions with hot atoms (see §V of the publication). For strontium, Γ / 2π = 32 MHz, and the optimum offset of the cooling beam Δ z (N) is equal to -210MHz (=-6.6.Γ / 2π) (Table I of the publication).

[0043] The Lamporesi publication assumes that the cooling of the heat beam occurs in the "vanishing tail" of the magnetic field generated by the permanent magnets, i.e., in the region from the oven to the point of maximum field, which corresponds to Nosske's region 1. The gradient near the center is 0.36 T / m (equivalent to 36 G / cm). For sodium, Γ / 2.π = 9.79 MHz, and in Lamporesi the offset of the cooling beam Δz(L) is equal to -304 MHz (= -31.Γ / 2π) (Table I of the publication).

[0044] In two publications, the Zeeman decelerator beam CB, Δ z (L), and Δ z The optimal detuning of (N) is determined experimentally without any physical explanation / understanding of the effect of the detuning value.

[0045] Both Lamporesi and Nosske state that up to half of the optical power of the cooling beam can be utilized to decelerate the thermal atomic beam. The cooling beam is linearly polarized along the zero-field axis of the 2D-MOT and has two circular components σ + and σ - Utilizing half of the available optical power means that only one circular component slows down the atoms, while the other is wasted. [Prior art documents] [Non-patent literature]

[0046] [Non-Patent Document 1] Phillips et al “Laser Deceleration of an Atomic Beam” (Phys.Rev. Lett. Vol 48, n°9, 1982) [Non-patent document 2] Tiecke et al “High flux two-dimensional magneto-optical-trap source for cold lithium atoms” (Phys. Rev. A, 80, 013409, 2009) [Non-patent document 3] Raab et al, Phys.Rev. Lett., vol 59, n°23, p 2631 1987) [Non-patent document 4] Lamporesi et al (Review of scientific Instruments 84, 063102, 2013) [Non-patent document 5] Nosske et al (Physical. Review A, 96, 053415, 2017) Summary of the Invention [Problem to be solved by the invention]

[0047] The goal of the present invention is to realize an atom source that combines compactness and low energy consumption with a high flux of cold atoms. The design of the cold atom source according to the present invention has a geometry close to that described in Lamporesi / Nosske, but with modified magnetic field parameters to achieve a larger cold atom flux. [Means for solving the problem]

[0048] - a primary atom source configured to generate an atomic beam propagating along the z direction of a coordinate system xyz; - a two-dimensional magneto-optical trap called 2D-MOT, a first pair and a second pair of two counter-propagating beams, the first pair and the second pair being perpendicular to each other and lying in a plane yz, the intersection of which defines a trapping area having a center O; A magnetic device configured to generate a magnetic field, the magnetic field comprising: Null values ​​at the center O and on the x-axis at least within the trapping area, a component By along y that has a constant gradient along the z axis within the trapping region, the absolute value of said constant depending on the atomic species; A component By along the y axis that varies along the z axis between two extremes, a positive maximum and a negative minimum, where the absolute value of the extreme located on the opposite side of the primary atom source is strictly greater than the absolute value of the other extreme. a magnetic device having a two-dimensional magneto-optical trap, a cooling beam propagating counter-directionally to the direction of the atoms, with a frequency detuning Δ with respect to the frequency of the cooling transition, which has a negative value depending on the atomic species; z m, showing the cooled beam and A cold atom source is provided, comprising:

[0049] According to a further development, the absolute value of the extremum located opposite the primary source is strictly greater than the absolute value of the other extremum by a factor of at least 1.3.

[0050] According to a further development, the absolute value of the extremum located opposite the primary atomic source is strictly greater than the absolute value of the other extremum by a factor of 3 or less.

[0051] According to a further development, the magnetic device includes four sets of laminated permanent magnets arranged at the corners of a rectangle in the xz plane centered at a point O' located on the z-axis but offset from O, two sets being arranged on the primary source side and two sets arranged on the opposite side having individual magnetic dipoles oriented in opposite directions along the y-axis, and the absolute value (M2) of the magnetic dipoles of the two sets (S3, S4) arranged on the primary source side is smaller than the absolute value (M1) of the two sets (S1, S2) arranged on the opposite side.

[0052] According to the development, the cooling beam is detuned by a frequency Δ z The additional frequency detuning Δ from m is determined by z Denote m': Δ z m'=Δ z m-2μB B PSS / h-2Γ / (2π)+ / -2Γ / (2π)

[0053] μ B is the Bohr magneton, h is the Planck constant, Γ is the natural linewidth of the cooling transition, and B PSS is the absolute value of the magnetic field extremum located on the primary atom source side.

[0054] According to a development, the atomic species is selected from among strontium, ytterbium, calcium, magnesium, cadmium, sodium.

[0055] According to the developed version, the frequency detuning Δ z m is as follows: -1500MHz≦Δ z m≦-325MHz

[0056] According to a development, the primary atom source is an oven.

[0057] According to a development, the primary atom source is a solid-state atom source whose desorption is controlled by a laser source.

[0058] Further objects and embodiments of the present invention and their advantages are explained in detail below with reference to the accompanying drawings. [Brief explanation of the drawings]

[0059] [Figure 1] FIG. 1, already cited, shows a cold atom source based on a Zeeman decelerator according to the prior art. [Figure 2A] FIG. 2A, already cited, shows in perspective the four-beam geometry of a two-dimensional magneto-optical trap, called MOT 2D, according to the prior art. [Figure 2B] FIG. 2B, already cited, shows the geometry in the yz plane of four beams of a two-dimensional magneto-optical trap, called MOT 2D, according to the prior art. [Figure 2C] FIG. 2C, already cited, shows a first shape of the magnet in the yz plane of the prior art. [Figure 2D] FIG. 2D, already cited, shows the magnetic field changes required to trap atoms in the prior art MOT-2D. [Figure 3] FIG. 3, already cited, shows an improved 2D-MOT configuration including a Zeeman decelerator beam according to the prior art. [Figure 4] FIG. 4, already cited, shows another magnet shape that is impossible to implement. [Figure 5] 1 shows a second magnet configuration of the prior art. [Figure 6] 1 shows the variation of the component By as a function of z according to the prior art. [Figure 7] 1 illustrates the basic principle of a cold atom source according to the present invention. [Figure 8] An example of a cold atom source that was investigated as a first step towards the present invention is shown. [Figure 9] 1 shows an example of a phase space plot of various atom velocities emitted by an oven for a prior art 2D-MOT alone. [Figure 10] For a 2D-MOT alone according to the prior art, the corresponding Maxwell-Boltzmann distribution of the velocities of atoms released by the oven (dark grey) and the distribution after taking into account the effect of the trap (light grey) are shown. [Figure 11]1 shows phase space plots of various atomic velocities in the presence of a cooled beam with a nominal detuning equal to −210 MHz of strontium and according to the prior art. [Figure 12] The velocity distribution corresponding to the case in FIG. [Figure 13] For the cold atom source in Figure 8, the atomic trajectories of atoms emitted by the oven are modified by the combined effect of a magnetic field and a cooling beam with a direction opposite to that of the atomic beam and a detuning Δz relative to the cooling transition, and the phase space plot is shown neglecting off-resonant scattering of photons. [Figure 14] Figure 8 shows atomic trajectories in phase space corresponding to the optimal parameter set for the cold atom source. [Figure 15] For the cold atom source of Figure 8, for the same set of parameters as in Figure 14, we show the corresponding Maxwell-Boltzmann distribution of the velocities of atoms emitted by the oven (dark grey), and the distribution after taking into account the effect of the trap (light grey). [Figure 16] 1 shows an example of a cold atom source according to the present invention. [Figure 17] 1 shows a phase space plot of the atomic trajectories of atoms emitted by the oven for a cold atom source according to the invention, modified by the combined effect of a magnetic field and a cooling beam that is opposite in direction to the atomic beam and has a detuning Δz relative to the cooling transition. [Figure 18] 1 shows atomic orbitals in phase space corresponding to an optimal set of parameters for a cold atom source according to the present invention. [Figure 19] 18 shows the corresponding Maxwell-Boltzmann distribution of the velocities of atoms emitted by the oven (dark grey), and the distribution after taking into account the effect of the trap (light grey), according to the present invention, for the same parameter set as in FIG. [Figure 20] 1 shows a phase space plot with atomic orbitals of an atom according to an embodiment of the present invention, where the cooling beam exhibits an initial detuning Δz and a properly chosen additional detuning Δz′ with respect to the cooling transition. [Figure 21]1 shows a calculated trajectory in phase space corresponding to an embodiment of the present invention, where the cooling beam exhibits an initial detuning Δz and a properly chosen additional detuning Δz′ with respect to the cooling transition. [Figure 22] 21 shows the corresponding Maxwell-Boltzmann distribution of the velocities of atoms emitted by the oven (dark grey), and the distribution after taking into account the effect of the trap (light grey), according to the present invention, for the same parameter set as in FIG. DETAILED DESCRIPTION OF THE INVENTION

[0060] Starting from the Lamporesi / Nosske configuration, our approach is to understand in detail the physical effects involved in this trap, which combines a 2D-MOT and a non-optimized Zeeman decelerator, in order to improve its performance by modifying the parameters of interest.

[0061] The numerical simulations used in Lamporesi considered the atomic dynamics from the oven to the 2D MOT region and within the 2D MOT separately and did not identify specific features of atomic trajectories (e.g., that atoms can be trapped by the 2D-MOT as they pass through the trapping region twice), nor the operation and efficiency of the trap (e.g., that both polarization components of the Zeeman-cooled beam can be used simultaneously to decelerate atoms).

[0062] A cold atom source according to the invention is shown in Figure 7. The cold atom source comprises a primary atom source PAS configured to generate an atomic beam AtB propagating along the z-axis of a coordinate system xyz.

[0063] According to one embodiment, the primary source is an oven, the output of which can be a single aperture or can be filled with an array of microtubes to increase the collimation of the source.

[0064] According to another embodiment, the primary source is a solid-state atom source, the desorption of which is controlled by a laser source, with a thermal jet of atoms being obtained by laser ablation, preferably in the ultraviolet range, as reported by Kock et al., "Laser controlled atom source for optical clocks," Scientific Reports 6, 37321 (2016).

[0065] The cold atom source also includes a two-dimensional magneto-optical trap, called 2D-MOT, which contains two counter-propagating beams, a first pair (LB1, LB1') and a second pair (LB2, LB2'). The two pairs are perpendicular to each other and lie in the plane yz, and their intersection defines a trapping volume ZTr with center O. The size of the trap along the z axis is Trz. The four beams LB1, LB1', LB2, and LB2' trap and cool the atoms, and the four-beam configuration is identical to the Lamporesi / Nosske configuration.

[0066] The 2D-MOT also includes a magnetic device MD configured to generate a magnetic field having a null value at least at the center O within the trapping region and on the x-axis. Furthermore, the component By of the magnetic field along y has an approximately constant gradient along the z-axis within the trapping region, the value of the constant depending on the atomic species: ∇B=δBy / δz≒constant

[0067] In Nosske, Lamporesi, and Figure 7, the value of the magnetic field gradient is negative. According to another embodiment, the gradient is positive, which requires reversing the polarization of the 2D MOT beam and exchanging the role of each polarization component in the Zeeman decelerator.

[0068] The cold atom source according to the present invention also includes a cooling beam CBm propagating counter-directionally to the direction of the atoms. The cooling beam CBm has a linear polarization along the x-axis, which is a right-handed circular polarization σ + component and left circularly polarized σ -It is decomposed into a balanced sum of components. Note that circular polarization along the y-axis determines only the π transitions of the atoms and is not useful in the Zeeman decelerator.

[0069] The cooling beam is generated by a laser (not shown in Fig. 7). The cooling beam CBm is a negative value Δ from the frequency fc of the cooling transition of the atomic species in the beam AtB. z has a frequency fcb detuned by m: fcb=fc-|Δ z m| (1)

[0070] The inventors have investigated the frequency detuning Δ for the operation of the 2D-MOT in order to better understand the behavior of the cold atom source with the aim of improving its performance. z The effect of the value of m was particularly studied.

[0071] All beams are located in interconnected vacuum chambers.

[0072] As a starting point for the development of the present invention, a studied cold atom source 10 based on the Nosske configuration is shown in Figure 8. The trap configuration is shown in A, the applied magnetic field By is plotted in B, and the configuration of the four magnet sets in the xz plane is shown in C.

[0073] In the cold atom source 10, the magnetic device MD is configured so that the component B along y varies along z between two extremes: a positive maximum and a negative minimum, as shown in Figure 8B. In the cold atom source 10, the positive maximum Bmax and the negative minimum Bmin have the same absolute value: |Bmin| = Bmax, as shown in Figure 8B.

[0074] To have the zero value of By at O, the two extrema are symmetrically placed with respect to the center O.

[0075] Note that for positive gradient values, the respective positions of the maxima and minima of the magnetic field By are reversed.

[0076] According to one example, as shown in FIG. 2C, the magnetic device MD includes two sets of laminated permanent magnets (S1t, S2t) arranged symmetrically on either side of the z-axis, with their individual magnetic dipoles oriented in opposite directions along the y-axis.

[0077] According to another example, the magnetic device MD includes four sets of laminated permanent magnets arranged at the corners of a rectangle R in the xz plane centered at O. Two sets (S3, S4) arranged on the primary source side and two sets (S1, S2) arranged on the opposite side have individual magnetic dipoles oriented in opposite directions along the y axis as shown in FIG. 8C.

number

[0078] In this non-limiting example, the primary source is a strontium oven located at z = -15 cm from the center O. The trap size along z (overlap of the four MOT beams) is Trz = + / - 2 cm. A sapphire viewport SW located at z = +35 cm allows the Zeeman laser light to be directed towards the oven and in the opposite direction to the thermal atomic beam produced by the oven. The viewport is heated, e.g., to about 300 °C for strontium, to avoid rapid metallization caused by the strontium thermal beam.

[0079] Distance d between the primary source and the trap center O ps-O Many design and physical constraints are taken into account when determining the size of the atom source. This distance should be as short as possible, but currently cannot be made less than 10 cm. A distance of 15 cm is the current standard for cold atom source design.

[0080] Maximum value B of the magnetic field on the z-axis at the position of the magnet stack max (Minimum value B min ) is set by the magnet configuration (i.e., magnet position and required gradient ∇B).

[0081] In the case of strontium, at the negative gradient ∇B=δBy / δz=-Gr≒-40G / cm, B at -z0=-5cm max is approximately 160 G, and at z0=+5 cm, Bmin is approximately −160 G (see FIG. 8B).

[0082] Figure 8(A) also shows the two regions 1 and 2 already identified by Nosske, as well as two additional regions 3 and 4. Region 3 begins at the center O and ends at the magnetic field minimum +z0, while region 4 begins at the end of region 3 and ends at the sapphire window at z = 35 cm.

[0083] To better understand the atomic dynamics along z in regions 1 and 2 before and within the trap up to O, as well as in regions 3 and 4 located after the center O, we developed a numerical simulation to calculate the trajectories of atoms from the oven to the end of the trajectory. This simulation uses a fourth-order Runge-Kutta algorithm to calculate the atomic dynamics in the presence of i) the magnetic fields generated by four stacks of permanent magnets, ii) the laser beam of the 2D-MOT, and iii) the Zeeman cooling beam. This simulation is based on the configuration shown in Figure 8(A).

[0084] The first simulation considers the 2D-MOT alone, without the Zeeman cooling beam, with an applied magnetic field as in Figure 8(B) using magnets as in Figure 8(C). Figure 9 shows a phase space plot of the various atomic velocities emitted by the oven. It shows the trajectories of atoms along z as a function of their initial velocity along z, vz, at the oven exit at 585 °C. The white lines / curves correspond to trajectories that are not trapped within the 2D-MOT, and the black lines correspond to trajectories that are trapped by the 2D-MOT at the origin.

[0085] The background color is the atomic acceleration a MAXThe values ​​correspond to the acceleration values ​​of a, where gray is no acceleration, white is negative acceleration, and black is positive acceleration. Atoms are slowed down to diffract photons, and the amount of photons they can diffract depends on the atomic species, and more specifically on their natural linewidth Γ, as well as the intensity and frequency of the laser light. The maximum acceleration a MAX is given by the following formula:

number

[0086] where k is the wavenumber associated with the cooling beam,

number

[0087] The acceleration is a vector quantity whose direction is defined by k, which in the case of a Zeeman-cooled beam is directed towards the oven, i.e., towards the direction of propagation of the atoms emitted by the oven. The maximum acceleration is achieved when the laser beam is set in resonance with the cooling transition and has an intensity much higher than the saturation intensity Isat, defined as the intensity required to reduce the absorption coefficient of the atomic medium to half its value.

[0088] There is no Zeeman cooling beam, so the trajectory is only modified within the 2D-MOT region by acceleration by the 2D-MOT beam, which determines the central force that steers the atoms along the x-axis as well as the frictional force that slows down the atoms' motion.

[0089] This simulation only considers the one-dimensional propagation of the atoms along z, and does not initially consider the radial spread of the heat beam. It can be seen that only atoms with a positive initial velocity less than 70 m / s are trapped.

[0090] Figure 10 shows the Maxwell-Boltzmann distribution (dark gray) of the velocities of atoms released by the oven (almost completely covered by the modified distribution except for low velocities) and the distribution after accounting for the effect of the trap (light gray). Only small velocities in the range [0, 70] m / s are trapped (left side of the distribution), which corresponds to a very small number of atoms. The peak at 0 velocities 90 represents the fraction of atoms trapped by the 2D MOT and is equal to 0.45%.

[0091] Atoms reaching the HV chamber surface 80 at radius r=19 mm thermalize along with the HV chamber surface and are lost to the cooling and trapping process. The trapping efficiency is corrected to account for the radial spreading of atoms during their motion and is calculated according to Greenland et al., Journal of Physics D: Applied Physics 18, 1223 (1985), "Atomic beam velocity distributions." When losses due to the radial spreading of the thermal beam are considered, this trapping efficiency drops to 0.25%.

[0092] Figure 11 shows the best configuration, Δ, defined by Nosske et al. z Phase space plots of various atomic velocities in the presence of a cooling beam with a nominal detuning equal to (N) = -210 MHz (equivalent to -6.6Γ / (2π) for strontium). The background color indicates the acceleration experienced by the atom at each position and velocity; in addition to the acceleration due to the 2D MOT, there is now also the acceleration determined by the Zeeman cooling beam, which is always pointed towards the oven (hence white). σ of the Zeeman beam along z + Velocities resonant with the polarization component reproduce the shape of the magnetic field in the phase plot, while velocities resonant with the σ-polarization component of the Zeeman beam z reproduce the opposite shape of the magnetic field. The two shapes overlap at z=0, where the magnetic field is null, at a velocity set by the detuning of the Zeeman beam.

[0093] Compared to the configuration where only the 2D-MOT operates, this configuration traps atoms at a faster velocity, although the initial velocity window is of similar size, and the Maxwell-Boltzmann distribution is larger in that velocity range, resulting in a higher trapping efficiency, as shown in Figure 12.

[0094] Figure 12 shows how this experimental configuration modifies the velocity distribution: a larger proportion of the initial Maxwell-Boltzmann velocity distribution now ends up at the zero velocity peak: 9.2% (peak 120), which decreases to 4.1% when radial losses are taken into account.

[0095] As reported by Nosske and thanks to the interaction with the σ+ polarization component of the Zeeman beam, it can be seen from Figure 11 that only atoms with an initial velocity of 170 m / s are “directly” trapped in the 2D-MOT, i.e., decelerated in region 1 or region 2.

[0096] Slow atoms (see velocity section 103) are not trapped because they are decelerated to the reversal point before entering the 2D-MOT.

[0097] Atoms with initial velocities between 180 m / s and 220 m / s are again subjected to the σ + The beam interacts with the polarization components, slowing down in regions 2 and 3, and is trapped after passing through the origin. The utilization of region 3 has never been reported or recognized before, and is one of the results of numerical simulations (trajectory 101 in Figure 11).

[0098] An atom with an initial velocity of approximately 230-240 m / s passes through the 2D-MOT almost unaffected, is decelerated along the magnetic field gradient in region 4 by the σ-polarized component of the Zeeman beam, and is finally captured by the 2D-MOT after its motion is reversed thanks to off-resonance scattering caused by the Zeeman beam (trajectory 102 in Figure 11). The utilization of region 4 has never been reported before and is one of the results of numerical simulations.

[0099] Next, for the cold atom source 10 in FIG. 8, the polarization component σ of the cooled beam CBm + and σ - In order to use both z Explain how the optimal range for m can be determined.

[0100] speed v z and the magnetic field is B y The effective detuning Δ observed by an atom at a position (z) eff is equivalent to: Δ eff =Δ Z -(kv z ) / 2.π+(μ B g F m F B y (z)) / h (3) where: - k=2π / λc is the wave number associated with the cooling beam, λ c is the transition wavelength, - μ B is the Bohr magneton, -g F is the Landé factor, - h is Planck's constant, - Δ Z is the nominal detuning for the resonance condition, - -kv z / 2.π is the atomic velocity v z is the Doppler shift determined by - + μ B g F m F B y (z)) / h is the local magnetic field B y Each sublevel m is determined by (z) F is the Zeeman shift of

[0101] Therefore, two terms are added to the nominal laser detuning for each sublevel m F are the Doppler shift and Zeeman shift of

[0102] Figure 13 shows the atomic orbit of the atoms emitted by the oven at z = -15 for the cooling atomic source in Fig. 8, with the magnetic field generating the linear quadrupole of the 2D-MOT along the y-axis at z = 0 and in the opposite direction to the atomic beam and the detuning Δ z from the cooling transition. The phase space plot corrected by the combined effect with the Zeeman decelerated beam CBm having

[0103] For the atoms to be captured by the 2D-MOT, they must enter the overlap region (-2.0 cm < z < 2.0 cm in the case we consider) defined by the MOT beam at an absolute velocity less than the value vc that the 2D MOT can capture. The gray area CR indicates the capture region of the 2D-MOT, which is determined by the size of the MOT beam and the velocity capture v c of the MOT. For strontium and the parameters of the 2D-MOT in this example, the velocity capture is vc = 70 m / s.

[0104] As shown in Fig. 13, when using circularly polarized light opposite to the light irradiated in the opposite direction to the atomic beam, the magnetic field generated by the permanent magnet for the 2D-MOT has two gradients that can be utilized for cooling the thermal beam provided by the oven. The first magnetic field gradient is within region 1 of Fig. 13, and the second gradient is within regions 2 and 3 of the same figure.

[0105] For strontium, especially 88 in the case of Sr (the most abundant isotope), the cooling transition is at 461 nm 1 S0- 1 P1, with a linewidth Γ = 2π x 30.5 MHz and a saturation intensity I sat = 42.5 mW / cm 2 . It is recalled that

[0106] It is also recalled that the magnetic field gradient ∇B at z = 0 is set by the atomic species as a requirement for realizing the 2D MOT (for strontium, it is about 40 G / cm). The magnetic maximum B on the z-axis at the position of the magnet stack near the oven maxis set by the magnet configuration (i.e., magnet position and desired ∇B), and for strontium and ∇B of approximately 40 G / cm, B at z = -z = -5 cm max The minimum value B on the z-axis at the position of the magnet stack away from the oven is about 160G. min is the opposite of Bmax, so at z=z0=5cm, B min is equal to approximately -160G (see Figure 8, B and C).

[0107] In Fig. 13, for simplicity, only the action of the cooling beam is considered, and the trajectory of the point where the cooling beam resonates with the atomic beam is expressed as σ + The dashed line indicates the polarized light, and σ - The polarized case is shown by the dotted line, and the off-resonance scattering caused by the presence of the Zeeman and 2D-MOT beams is neglected. The atomic velocity window for effective cooling and the final velocity at which the atoms are focused vary with the detuning Δ z and the configuration of the magnetic field.

[0108] Curve 5 is the σ of the cooled beam + Polarization component (detuning Δ z ) in phase space, and curve 6 represents the σ - Atoms in resonance with the polarization components are shown in phase space. Region 8 shows atoms emitted by the oven whose velocity (at the oven exit) is contained within the first interval IS1, so that the atoms are in a σ - The atoms enter into resonance with the Zeeman beam component, where they are decelerated to z = -z = -5 cm. Section 9 shows the atoms emitted by the oven whose velocity is contained within the second interval IS2, so that the atoms are within σ + It enters into resonance with the Zeeman beam component and is decelerated there and in region 3 to z = z0 = 5 cm.

[0109] Detuning Δ zThe Zeeman cooled beam at resonates with atoms moving along the z-axis with a velocity of -2πΔz / k, and this resonance is observed where the B field is null, at z=0 (i.e., the location of the 2D MOT), and is well approximated far from the magnet configuration (i.e., in the oven and where the cooled beam enters the setup).

[0110] Elsewhere, the cooling beam resonates with a velocity that depends on the local magnetic field that shifts the atomic levels. More precisely, the cooling beam resonates with: - its σ in region 1 - via polarization components

number

number

[0111] Two groups of atoms cooled by oppositely polarized light are bundled together at the end of each gradient with velocity: - Atoms cooled in region 1 are at -z0=-5cm (the position of the magnet stack close to the oven),

number

number

[0112] The effect of off-resonant photon scattering, neglected in Figure 13, is an additional acceleration of the atoms in the -z direction, which reduces the velocity obtained in the Zeeman cooling process and ultimately reverses the atomic motion. This effect is taken into account in the simulation of atomic trajectories to determine whether they are trapped by the 2D-MOT in operation.

[0113] For the 2D-MOT to capture atoms decelerated along both magnetic field gradients, the atoms must reach the MOT's capture velocity v c (approximately 70 m / s for Sr and the MOT beam parameters adopted in this example) into the 2D-MOT region.

[0114] The velocity of the cooled atoms in region 1 is

number

[0115] Cooling occurs in regions 2 and 3, and the rate at z=5 cm

number

[0116] Contrary to the case of Fig. 11 (Nosske), in the studied cold atom source of Fig. 8, the slow atoms contained within section IS1 (atoms in area 8) are slowed down so as to be trapped within the 2D-MOT.

[0117] In this way, the frequency detuning Δ zm is determined so that a first set of atoms exhibiting a velocity within a first velocity interval IS1 and a second set of atoms exhibiting a velocity within a second velocity interval IS2 at the outlet of the primary atom source are decelerated by resonance with the first and second circularly polarized components of the cooling beam, respectively. The second velocity interval IS2 is continuous with the first velocity interval IS1.

[0118] For negative gradients, IS1 is σ - and IS2 is σ + In the case of a positive gradient, IS2 is σ - and IS1 resonates with σ + It resonates with me.

[0119] The atomic orbitals in phase space corresponding to the optimum result for the parameter set considered above (with the Zeeman beam saturation intensity set to 1.4) were determined by simulation and are shown in Figure 14. The optimum result is as follows: -2.π.Δ z / k=about 190m / s

[0120] For strontium, k = 2π / 461 nm = 1.36 × 10 for the blue cooling transition 7 m -1 This means that the detuning Δ z This means that m(opt) = -414MHz = -13.6 × Γ / 2π.

[0121] To trap two classes of atoms decelerated using opposite polarization components of the cooling beam in the 2D MOT, we set the detuning Δ z It has been determined by simulation that must lie within the interval: -414MHz≦Δ z m≦-364MHz (4)

[0122] This corresponds to -13.6 × Γ / 2π ≤ Δ ≤ -11.9 × Γ / 2π in terms of the linewidth of the cooling transition used for Sr.

[0123] Compared to Figure 11 (Nosske), it can be seen in Figure 14 that a much wider velocity interval of the atoms released by the oven is trapped in the 2D-MOT. This result is clearly visible in Figure 15, which shows the velocity distribution of atoms released by the oven at 585 °C (dark grey) and the velocity distribution after taking into account the effect of the trap (light grey). The fraction of the Maxwell-Boltzmann initial velocity distribution captured by the 2D-MOT corresponds to 26.9% (peak 150).

[0124] This result decreases to 9.3% when considering radial losses (compared to 4.1% for Nosske in Figure 12). Indeed, it can be seen from Figure 14 that the trajectory 140 is quite long and proceeds almost to the limit of region 4. The long section required to travel such a long distance determines a high radial spread of the atomic beam, which significantly reduces the flux of atoms that can be effectively captured by the 2D-MOT.

[0125] The section I0 of equation (4) for detuning the cooled beam Sr =[-414MHz;-364MHz] has been determined by simulation using the following parameters: - Atomic species = Strontium: ∇B = -40 G / cm; a max =9.3 10 5 m / s 2 - Saturation parameter of the cooling beam s = 1.4 (ratio of the optical intensity of the cooling beam to the saturation intensity of the corresponding atomic transition) - 2D-MOT parameters for this example.

[0126] These parameters are subject to change.

[0127] Detuning of the cooling beam Δ z The limits of the frequency interval of m are, in a first approximation, determined mainly by the atomic species (required nominal magnetic field gradient, a max depends on the value of , the properties of the cooling transition, and in particular the wave vector k).

[0128] At the second level, when the atomic species are fixed, the interval depends on the parameter s: shifts in absolute value towards higher frequencies as s increases.

[0129] This interval also depends on the value of the gradient: taking the gradient at +100% / -50% of the nominal value still gives acceptable (but not optimized) results, e.g., for strontium, 40G / cm + 40G / cm / 20G / cm.

[0130] The 2D-MOT parameters (acquisition speed, size, beam intensity and divergence) only slightly affect the interval limits.

[0131] For strontium, various simulations have established that the frequency interval for realistic values ​​of the s-parameter and detuning values ​​considering ∇B=-40G / cm is as follows: s=1:-400MHz≦Δ z m≦-350MHz s=2:-430MHz≦Δ z m≦-380MHz s=3:-460MHz≦Δ z m≦-405MHz s=4:-480MHz≦Δ z m≦-425MHz s=5:-500MHz≦Δ z m≦-445MHz s=10:-530MHz≦Δ z m≦-480MHz

[0132] This global section I Sr Detuning at [-530 MHz; -350 MHz] allows good trapping of atoms for reasonable values ​​of s.

[0133] That is, the frequency detuning Δ z m must be contained within the interval I, which depends on the atomic species.

[0134] Δ for s=1.2 published by Nosske zThe detuning value of (N)=-210 MHz is outside this interval and is smaller in absolute value.

[0135] In the publication by Li et al., "Bi-color atomic beam slower and magnetic field compensation for ultracold gases," doi.org / 10.1116 / 5.0126745, a strontium detuning value of -380 MHz is described for a cold atom source with a configuration similar to that shown in Figure 8. Sr Although the detuning values ​​in the trap have been identified by Li et al., the behavior of the atoms in the trap has not been analyzed in detail, contrary to what has been mentioned above.

[0136] Examples of atomic species of interest are listed below in Table I, along with various key parameters.

[0137] [Table 1]

[0138] For each atomic species of interest in Table I, in conjunction with the possible s coefficients and gradient values, the inventors determine the cooling beam detuning Δ z The relevant interval I relative to m is established by simulation.

[0139] For sodium and the saturation parameter s = 6.5 used in Lamporesi, this interval is calculated by simulation and the interval [-362 MHz; -333 MHz] is obtained, which deviates from the detuning value of -304 MHz published by Lamporesi, but is smaller in magnitude.

[0140] Saturation parameters below s = 5 are not suitable because the high atomic velocities that must be initially slowed down in region 2 do not scatter enough photons along the magnetic field gradient to maintain resonance and subsequently are not finally trapped by the 2D MOT.

[0141] Let ∇B=-40G / cm: s=5:-350MHz≦Δzm≦-325MHz s=6:-355MHz≦Δzm≦-330MHz s=7:-360MHz≦Δzm≦-335MHz s=10:-375MHz≦Δzm≦-350MHz

[0142] This global section I Na Detuning at [-360 MHz; -325 MHz] allows good trapping of atoms for reasonable values ​​of s.

[0143] Similarly, for ytterbium, a saturation parameter below s=5 is not appropriate because the high atomic velocities that must be initially slowed down in region 2 do not scatter enough photons along the magnetic field gradient to maintain resonance and subsequently be ultimately trapped by the 2D MOT.

[0144] Let ∇B=-60G / cm: s=5:-560MHz≦Δ z m≦-520MHz s=6:-575MHz≦Δ z m≦-535MHz s=7:-590MHz≦Δ z m≦-550MHz s=10:-620MHz≦Δ z m≦-565MHz

[0145] This global section I Yb Detuning at: [-620 MHz; -520 MHz] allows good trapping of atoms for reasonable values ​​of s.

[0146] For calcium, a saturation parameter below s = 0.7 is not appropriate because the high atomic velocities that must be initially slowed down in region 2 do not scatter enough photons along the magnetic field gradient to maintain resonance and subsequently are not finally trapped by the 2D MOT.

[0147] Let ∇B=-40G / cm: s=1:-610MHz≦Δ z m≦-525MHz s=2:-660MHz≦Δ z m≦-575MHz s=3:-695MHz≦Δ z m≦-610MHz s=5:-750MHz≦Δ z m≦-660MHz

[0148] This global section I Ca Detuning at: [-695 MHz; -525 MHz] allows good trapping of atoms for reasonable values ​​of s.

[0149] For magnesium, a saturation parameter less than s = 0.1 is not appropriate because the high atomic velocities that must be initially slowed down in region 2 do not scatter enough photons along the magnetic field gradient to maintain resonance and subsequently are not finally trapped by the 2D MOT.

[0150] Let ∇B=-100G / cm: s=0.1:-970MHz≦Δ z m≦-875MHz s=0.2:-1075MHz≦Δ z m≦-945MHz s=0.3:-1155MHz≦Δ z m≦-1000MHz s=0.5:-1271MHz≦Δ z m≦-1070MHz

[0151] This global interval I Mg Detuning at: [-1271 MHz; -875 MHz] allows good trapping of atoms for reasonable values ​​of s.

[0152] For cadmium, saturation parameters below s = 0.1 are not appropriate because the high atomic velocities that must be initially slowed down in region 2 do not scatter enough photons along the magnetic field gradient to maintain resonance and then be ultimately trapped by the 2D MOT. Given the very high saturation intensity Isat = 1005 mW / cm2, it is not interesting to evaluate the case for s > 0.3.

[0153] Let ∇B=-80G / cm: s=0.1:-810MHz≦Δ z m≦-720MHz s=0.2:-910MHz≦Δ z m≦-790MHz s=0.3:-970MHz≦Δ z m≦-835MHz

[0154] This global section I Cd Detuning at: [-720 MHz; -970 MHz] allows good trapping of atoms for reasonable values ​​of s.

[0155] 8 and taking into account the atomic species of interest, is contained within the global interval [-1271 MHz; -325 MHz]. Taking into account the variation of the slope around the nominal value (above the nominal value, which is mainly more interesting from the point of view of the trapped atomic flux), the global interval becomes: I G ≒[-1500MHz;-325MHz]

[0156] For other atomic species of interest with physical parameters of the same order as those listed above, the interval values ​​are also I G This becomes:

[0157] The simulations presented above to determine the frequency intervals in which the detuning can occur were performed with a detailed understanding of the physics within the trap as explained above.

[0158] It is not necessary to resort to the sophisticated simulations described above to experimentally implement the cold atom source shown in Figure 8, including determining the value of the detuning frequency. As an example, for a cold strontium atom source, the frequency detuning along with the simulations is disclosed in the Li publication mentioned above.

[0159] The inventors have G We also demonstrated that the frequency detuning within the trap induces a lateral spatial shift of the atomic beam AtB exiting the trap. In Figure 8, a flux of atoms exits the 2D MOT and enters the 3D MOT through an exit hole located at z = 0. The atomic beam exits the 2D MOT in the x direction, perpendicular to the plane of the drawing, by being pushed by a pusher beam, also in the x direction. This spatial shift is in the negative z direction and has the effect of restricting the flow of atoms through the small exit hole toward the 3D MOT. This effect makes it difficult to experimentally determine the optimal detuning by placing a sensor outside the 2D MOT. To experimentally determine the optimized value of detuning, direct measurement of the atomic flux within the 2D MOT is required. To achieve this, the pusher beam PB can be removed within the 2D MOT and replaced by a photodetector or camera (e.g., a CCD camera) to observe the fluorescence of the 2D MOT. Placing the sensor within the 2D MOT eliminates the effect of the lateral beam offset. Once the sensor is inside the trap, the frequency of the cooled beam is varied until the optimized frequency detuning value corresponds to maximum detection. Once the frequency detuning value is determined, the sensor is removed and the extruded beam is reintroduced into the setup.

[0160] The claimed cold atom source stems from the above mentioned physical considerations: the basic idea behind the invention is that in order to minimize the atom loss caused by the radial spreading of the thermal atomic beam, the previously long reversed trajectories in region 4 need to be significantly shortened (see trajectory 140 in Figure 14). This is achieved by making the magnetic field maxima and minima asymmetric.

[0161] The magnetic device MD of the cold atom source according to the present invention is configured to generate a magnetic field By that varies along the z axis between two extrema: a positive maximum and a negative minimum, with the absolute value of the extrema located opposite the primary source of atoms being strictly greater than the absolute value of the other extrema. With such asymmetric values ​​of the magnetic field, the position on the z axis of the extrema located opposite the primary atom source must be determined in order to maintain a null value at the center O. An example of a cold atom source 11 according to the present invention is shown in FIG. 16. A of FIG. 16 shows the setup configuration.

[0162] In the example of Figure 16 for strontium, where the negative gradient ∇B is about -40 G / cm, at -z0 = -5 cm, B max is approximately 160 G, and at z0=6.23 cm Bmin is approximately -230 G (see Figure 16B). This is the minimum value located on the opposite side of the oven, and the conditions are as follows: |Bmin|>Bmax

[0163] In the case of a positive gradient ∇B of about +40 G / cm, the positive maximum is located on the opposite side of the oven. In this case, the conditions are: Bmax>|Bmin|

[0164] In the embodiment of the present invention shown in FIG. 16B, the magnetic device MD includes four sets of laminated permanent magnets. To maintain the null value at O, the four sets are arranged at the corners of a rectangle R' in the xz plane, centered at a point O' located on the z-axis but offset from O. Two sets (S3, S4) are arranged on the primary source side, and two sets (S1, S2) are arranged on the opposite side. The two sets (S3, S4) and the two sets (S1, S2) have their individual magnetic dipoles pointing in opposite directions along the y-axis. The absolute value M2 of the magnetic dipole of (S3, S4) is smaller than the absolute value M1 of the two sets (S1, S2) (see FIG. 16C).

[0165] In the example of FIG. 16, the pair (S1, S2) is located at z1=+6.23 mm, and the pair (S3, S4) is located at −z0=−5 cm.

[0166] The cold atom source according to the present invention also includes a cooling beam CBm propagating in a direction counter to that of the atoms, as shown in Figure 7. The cooling beam has a negative value Δ z The frequency detuning with respect to the frequency of the cooling transition with m is shown (see further).

[0167] FIG. 17 shows the atomic orbitals of atoms emitted by the oven at z=-15 for the cold atom source according to the present invention, with the magnetic field that generates the linear quadrupole of the 2D-MOT along the y-axis at z=0, in the opposite direction to the atomic beam and with a detuning Δ z Figure 14 shows the phase space plot modified by the combined effect of the cooling beam with . In this simulation, the parameters are the same as in Figure 13 except for the magnetic field configuration.

[0168] Curve 15 is the σ of the cooled beam + Polarization component (detuning Δ z ) in phase space, and curve 14 represents the σ - Atoms in resonance with the polarization components are shown in phase space. Region 12 shows atoms emitted by the oven whose velocity (at the oven exit) is included in the first interval IS1′, so that the atoms are in a σ - The atoms enter into resonance with the Zeeman beam component, where they are decelerated to z = -z = -5 cm. Section 13 shows the atoms emitted by the oven whose velocity is contained within the second interval IS2', so that the atoms are within σ + It enters into resonance with the Zeeman beam component and is decelerated there and in region 3 to z = z0 = 6.23 cm.

[0169] Again, the frequency detuning Δ z m is determined such that a first set of atoms exhibiting a velocity within a first velocity interval IS1′ at the outlet of the primary atom source and a second set of atoms exhibiting a velocity within a second velocity interval IS2′, which is greater than the velocity of IS1′, are decelerated by resonance with the first and second circularly polarized components of the cooling beam, respectively. In the negative gradient case described here, IS1′ is σ -and IS2' is σ + The two sections IS1' and IS2' are also consecutive.

[0170] Here, the cooling beam at detuning Δz resonates with atoms moving with velocity −2.π.Δz / k along the z-axis, and this resonance is found where the B-field is null, z=0 (i.e., the location of the 2D MOT), and is well approximated far from the magnet configuration (i.e., in the oven and where the cooling beam enters the setup).

[0171] Elsewhere, the cooling beam resonates with a velocity that depends on the local magnetic field, shifting the atomic levels.

[0172] More precisely, the cooling beam is - via polarization components

number

number

[0173] Two groups of atoms cooled by oppositely polarized light are bundled together at the same velocity at the end of each gradient: - Atoms cooled in region 1 are at z=-5 cm (the position of the magnet stack closest to the oven),

number

number

[0174] The main difference between the claimed cold atom source and the cold atom source with a symmetric configuration (FIG. 8) relates to the lower output velocity of the atoms, which are slowed down in regions 2 and 3, allowing the atoms to reach the 2D MOT trapping region without long trajectories in region 4. As a result, the efficiency of this configuration is higher in terms of atom losses, given the lower impact of the radial beam divergence.

[0175] The atomic orbitals in phase space corresponding to the optimum result for the parameter set considered above (and the saturation intensity of the Zeeman beam equal to s = 1.4) were determined by simulation and are shown in Figure 18. The optimum result is -2.π.Δ z / k=approximately 205 m / s.

[0176] For strontium, k = 2π / 461 nm = 1.36 × 10 for the blue cooling transition 7 m -1 and Δ z This means a detuning of m(opt)=-445MHz=-14.5×Γ / 2π.

[0177] In order to trap two classes of atoms in a 2D MOT that are decelerated using opposite polarization components of the cooling beam, the atom source according to the present invention is detuned by Δ z It has been determined by simulation that m must lie within the interval: I0 Sr * =-445MHz≦Δ z m≦-365MHz

[0178] This corresponds in terms of the linewidth of the cooling transition used for Sr to: -14.6×Γ / 2π≦Δ≦-12×Γ / 2π

[0179] Section I0 Sr * The minimum value of the limit (-445 MHz in [-445 MHz; -365 MHz]) is the minimum value obtained for the cold atom source in Fig. 8 (I0 Sr= [-414 MHz; -364 MHz]), but generally the values ​​of the detuning frequencies that allow proper operation of the system are very close for both cold atom sources.

[0180] Similar to the cold atom source of FIG. 8, and as explained above, in the claimed cold atom source, the detuning Δ z Determining the optimized value of m can be done experimentally.

[0181] It can be seen from Figure 18 that the trajectories previously located in region 4 (see trajectory 140 in Figure 14) are now reduced (see trajectory 180). The asymmetric magnetic field has the effect of shortening atomic trajectories that end up in the 2D-MOT after being slowed down in regions 2 and 3.

[0182] Figure 19 shows the velocity distribution of atoms released by the oven at 585 °C (dark gray) and the velocity distribution of atoms after accounting for the trapping effect (light gray). The fraction of the Maxwell-Boltzmann initial velocity distribution that is captured by the 2D-MOT is 26.9% (see peak 190). Given that it takes these atoms a shorter distance to travel from the oven to the final trapping region, and a smaller fraction is lost due to the radial expansion of the atomic beam, i.e., after accounting for losses, the fraction of atoms captured by the 2D-MOT drops from 26.9% to 14.8%, which is about 60% (=14.8% / 9.3%) more than the setup with the symmetric field configuration.

[0183] The inventors have also established through simulations that good results are obtained with |Bmin| / Bmax=K (negative gradient) or Bmax / |Bmin|=K (positive gradient), with K≧1.3 and K≦3, i.e., K is between 1.3 and 3.

[0184] In other words, the absolute value of the magnetic field on the opposite side of the primary atom source must be equal to K times the absolute value of the magnetic field on the primary atom source side.

[0185] The lower limit is set to affect the atomic flux, so in one embodiment, K is greater than or equal to 1.3: K≧1.3.

[0186] The upper limit is set by the encumbrance of the permanent magnet stacks and the interference dictated by the large magnetic field on the rest of the instrument. In one embodiment, K is less than or equal to 3: K≦3. In other words, the upper limit is set at a ratio of 3. It should be noted that a ratio of 5 would provide an atom source according to the present invention, but having such a large and unnecessary magnetic field is less suitable for cold atom experiments.

[0187] For each species, section I of the claimed cold atom source * The limiting values ​​of σ differ slightly in frequency for interval I determined for the cold atom source of Figure 8. Each interval can be determined by simulation or experimentally.

[0188] More broadly, the detuning according to the invention and taking into account the atomic species of interest is contained within the global interval of [-1330 MHz; -325 MHz]. Taking into account variations in slope around the nominal value (above the nominal value, which is mainly more interesting from the point of view of the trapped atomic flux), the global interval becomes: I G * ≒[-1500MHz;-325MHz]

[0189] For other atomic species of interest with physical parameters of the same order as those listed above, the interval values ​​are also I G* This becomes:

[0190] Therefore, global interval I G and I G * The assessment of the limits is similar.

[0191] To further increase the velocity interval captured in the 2D-MOT according to one embodiment of the present invention, the cooled beam CBm is detuned at a frequency Δ zAdditional frequency detuning Δ determined from m z Denote m'.

[0192] 20 shows a phase space plot with atomic trajectories of atoms according to this embodiment. The trajectories of atoms released by the oven at z=-15 are modified by the combined effect of the magnetic field that generates the linear quadrupole of the 2D-MOT along the y-axis at z=0, and the Zeeman deceleration beam CBm in the opposite direction to the atomic beam, which has an initial detuning Δ z m, and a properly chosen additional detuning Δ z m'. Therefore, the cooling beam CBm has a detuning Δ z beam with m and detuning Δ z is a superposition of beams with m'.

[0193] Curve 16 shows the detuning Δ z σ of the cooled beam + The atoms in resonance with the polarization components are shown in phase space, and curve 17 represents the detuning Δ z σ of the cooled beam of m' - Atoms resonating with the polarization components are shown in phase space. A third set of atoms is captured by the 2D-MOT with velocities falling within a third velocity interval, IS3'. IS3' is continuous with IS2'.

[0194] FIG. 21 shows the calculated trajectories in phase space corresponding to the optimum results for the parameter set considered above (saturation intensity of the Zeeman beam equal to s=1.4) for a cold atom source according to the invention.

[0195] The first detuning is Δ z m = -445 MHz (equivalent to -14.5Γ / (2π) for strontium), and an additional second detuning is Δ z m' = -884 MHz (equivalent to -29.0Γ / (2π) for strontium). Atoms with velocities between 330 m / s and 550 m / s are cooled by the second cooling beam frequency (detuning Δ z σ with frequency ' -The polarization components are decelerated by interacting with the first cooling beam frequency (detuning Δ z σ of the frequency + It joins atoms with velocities in section IS2' that are slowed down by interacting with the polarized component.

[0196] Figure 22 shows the corresponding velocity distribution of atoms released by the oven at 585 °C (dark gray) and the corresponding velocity distribution after considering the combined action of the Zeeman decelerator and the 2D-MOT (light gray). The fraction of the initial Maxwell-Boltzmann velocity distribution at T = 585 °C trapped by the 2D-MOT corresponds to 52.8%, which is reduced to 26.4% due to radial losses. The atomic flux trapped by the 2D-MOT increases compared to the case without detuning.

[0197] Initial detuning value Δ z It has been established that starting from m, the additional detuning is calculated by the following formula: Δ z m0'=Δ z m-2μB B PSS / h-2Γ / (2π) (5)

[0198] μ B is the Bohr magneton, h is the Planck constant, Γ is the natural linewidth of the cold atomic transition, and B PSS is the absolute value of the magnetic field extremum located on the primary atom source side.

[0199] B for negative gradients PSS = Bmax, and for positive gradients B PSS = |Bmin|.

[0200] However, there is a tolerance, and the additional detuning Δ z m' can be selected: Δ z m'=Δ z m0'+ / -2Γ / (2π)=Δ z m-2μ B B PSS / h-2Γ / (2π)+ / -2Γ / (2π) (6)

Claims

1. a primary atom source (PAS) configured to generate an atomic beam (AtB) propagating along the z direction of a coordinate system xyz; a two-dimensional magneto-optical trap called 2D-MOT, a first pair (LB1, LB1') and a second pair (LB2, LB2') of two counter-propagating beams, said two pairs being perpendicular to each other and lying in a plane yz, the intersection of which defines a trapping region (ZTr) having a centre O; A magnetic device (MD) configured to generate a magnetic field, said magnetic field comprising: a null value at least at the center O within the trapping area and on the x-axis; a component By along y that has a constant gradient along the z-axis within the trapping region, the absolute value of the constant depending on the atomic species; the component By along y that varies along the z axis between two extremes, a positive maximum and a negative minimum, the absolute value of the extreme located on the opposite side of the primary atomic source being strictly greater than the absolute value of the other extreme; A magnetic device (MD) having a two-dimensional magneto-optical trap, a cooling beam (CBm) propagating counter-directionally to the direction of the atoms, with a frequency detuning Δ with respect to the frequency of the cooling transition, which has a negative value depending on the atomic species; ｚ m, and the cooled beam (CBm) A cold atom source (11) comprising:

2. 2. The cold atom source of claim 1, wherein the absolute value of the extremum located on the opposite side of the primary atom source is strictly greater than the absolute value of the other extremum by a factor (K) of 1.3 or greater.

3. 3. The cold atom source according to claim 1, wherein the absolute value of the extremum located on the opposite side of the primary atom source is strictly greater than the absolute value of the other extremum by a factor (K) of 3 or less.

4. 4. The cold atom source according to claim 1, wherein the magnetic device comprises four sets of laminated permanent magnets arranged at corners of a rectangle (R′) in an xz plane centered at a point O′ located on the z-axis but offset from O, two sets (S3, S4) being arranged on the primary source side and two sets (S1, S2) arranged on the opposite side having individual magnetic dipoles oriented in opposite directions along the y-axis, and wherein an absolute value (M2) of the magnetic dipoles of the two sets (S3, S4) arranged on the primary source side is smaller than an absolute value (M1) of the two sets (S1, S2) arranged on the opposite side.

5. The cooling beam (CBm) is ｚ The additional frequency detuning Δ from m is determined by the following equation: ｚ Let m' be: D ｚ m'=D ｚ m-2μB B ＰＳＳ / h-2C / (2π)+ / -2C / (2π) μ Ｂ is the Bohr magneton, h is the Planck constant, Γ is the natural linewidth of the cooling transition, and B ＰＳＳ 5. The cold atom source according to claim 1, wherein ∇ ...

6. 6. The cold atom source according to claim 1, wherein the atomic species is selected from the group consisting of strontium, ytterbium, calcium, magnesium, cadmium, and sodium.

7. The frequency detuning Δ ｚ m is, -1500MHz≦Δ ｚ m≦-325MHz 7. A cold atom source according to claim 1, wherein:

8. 8. The cold atom source according to claim 1, wherein the primary atom source is an oven.

9. 8. The cold atom source according to claim 1, wherein the primary atom source is a solid-state atom source in which desorption is controlled by a laser source.

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