A quantum degenerate Bose–Fermi mixture of ⁴¹K and ⁶Li

The lithium atomic beam is produced by the oven which consists of a heating cell and a tapered reflux nozzle. The heating cell is heated to 450 °C to generate the required vapor pressure of ⁶Li atoms. The tapered reflux nozzle collects the blocked atoms, extending the lifetime of the oven. A 150 mm long tube with 3.5 mm inner diameter is installed at the end of the reflux nozzle, serving as differential pumping tube and atomic beam collimator. After collimating, the transverse divergence of the atomic beam is reduced to 10 mrad. However, the longitudinal velocity of lithium atoms is on the order of 1000 m s⁻¹, far beyond the MOT's capture range. We adopt the standard Zeeman slowing technique to decelerate the longitudinal velocity of the ⁶Li atoms. By creating an inhomogeneous magnetic field, the frequency shift accumulated during the deceleration is compensated by the Zeeman effect, leading to a continuous deceleration.

The configuration of the spin-flip Zeeman slower is shown in figure 5(a). The magnetic coil system consists of three sections, i.e., plus-field section, spin-flip section and minus-field section. The plus-field section is a cone-shaped coil of 11 layers, having a length of 437.4 mm. The minus-field section is a concentric coil of 4 × 4 windings. The spin-flip section connects the plus- and minus-field sections with a length of 185.6 mm. The coil assembly extends over 650 mm and the minimum point of magnetic field is 110 mm away from the center of MOT chamber. To compensate the residual magnetic field created by the minus-field section, we install a concentric coil at the opposite position of the MOT chamber (see figure 5(a)). In the experiment, the currents for the plus and minus coils are optimized to be 45 and 62 A, while the current for the compensation coil is set to 23 A. The calculated and measured magnetic field of Zeeman slower are shown in figure 5(b), having a perfect agreement. The resulting magnetic field in the MOT center is calculated to be −0.03 G with a gradient of 2.16 G cm⁻¹, ignorable for 3D MOT.

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Slowing and repumping lasers are superimposed by a beam splitter and expanded by a telescope. Then the dichromatic laser beam is focused by a 500 mm achromatic lens. The 1/e² beam diameter at the center of 3D MOT is about 16 mm. The peak intensity of slowing light is 15.67 ${{I}}_{{\rm{sat}}}^{{\rm{Li}}}$ (${{I}}_{{\rm{sat}}}^{{\rm{Li}}}=2.54$ mW cm⁻² is the saturation intensity of ⁶Li), while that of repumping light is 5.49 ${{I}}_{{\rm{sat}}}^{{\rm{Li}}}.$ Both the slowing and repumping lasers are σ⁺ polarized and the optimal detuning is −80.07 Γ_Li (Γ_Li = 2π × 5.87 MHz is the D2 transition linewidth of ⁶Li). With such a Zeeman slower, we can obtain an atomic beam with 2 × 10¹⁰ atoms s^–1 flux and about 20 m s⁻¹ average velocity.

2D MOT is an efficient pre-cooling method to produce atomic beams with high flux and low velocity. However, in the conventional 2D MOT, cooling and trapping occur only in the transverse directions which makes cooling of atoms inefficient. In the case ⁴¹K atoms whose natural abundance is 6.73%, the loading rate is limited. To improve the performance of ⁴¹K pre-cooling stage, we adopt an advanced 2D⁺ MOT scheme in the experiment. The key ingredient is to applying a pair of retro-reflect cooling and repumping beams in the axial direction, leading to an axial optical molasses cooling. The atoms which are axially cooled will experience more transverse cooling time, resulting in less transverse divergence and higher density of the atomic beams.

The schematic view of our advanced 2D⁺ MOT is shown in figure 6. The 2D⁺ MOT chamber is a cuboid full glass cell with a size of 45 × 45 × 95 mm. A custom designed differential pumping tube is connected to the glass cell, onto which a mirror and an absorptive polarizer are glued. Both the polarizer and the mirror are drilled a hole in the center with a diameter of 2 mm. We wind two pairs of rectangular coils around the glass cell to generate the required cylindrical quadrupole magnetic field in the transverse directions, while the magnetic field along the axial direction is zero. Two additional coil pairs in Helmholtz configuration are used to shift the center of the 2D⁺ MOT.

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The cooling and repumping lasers are superimposed by a polarizing beam splitter (PBS). The resulting dichromatic laser beam is separated into 3 beams and expanded by spherical and/or cylindrical telescopes to create the transverse and axial beams. Two transverse beams have an elliptical cross section (1/e² diameters: 30 and 90 mm). They are σ⁺ polarized and retro-reflected by two custom designed right-angle prisms with phase compensation coatings. The axial laser beam is linearly polarized with a 1/e² diameter of 20 mm. It passes through the absorptive polarizer and then retro-reflected by the mirror. The intensity ratio between the inward and outward beams can be freely tuned by a half wave plate (HWP). Additionally, an independent blue detuned push beam is applied to increase probability of atoms passing through the differential pumping tube and reaching the 3D MOT chamber. The push beam contains both the cooling and repumping frequencies with a 1/e² diameter of 1.2 mm, which can fully pass through the 2 mm hole. Finally, with the optimization of magnetic field gradient (11.2 G cm⁻¹) and other parameters (see table 1), a maximum loading rate of 2.2 × 10⁹ atoms s^–1 for the single species ⁴¹K 3D MOT is achieved, which is more than one order of magnitude larger in comparison with the conventional 2D MOT [36, 37].

Table 1.  Optimal parameters of the advanced 2D⁺ MOT.

	Transverse cooling	Axial cooling	Push
Icool (${{I}}_{{\rm{sat}}}^{{\rm{K}}}=1.75$ mW cm−2)	5	30.77	50.55
Irep $({{I}}_{{\rm{sat}}}^{{\rm{K}}})$	5	30.77	50.55
Δωcool (ΓK = 2π × 6.04 MHz)	−3.64	−3.64	+6.11
Δωcool (ΓK)	−2.15	−2.15	+6.06

3D MOT is a standard technique to obtain cold atom clouds. It consists of six counter-propagating laser beams and a quadrupole magnetic field. The magnetic field gradient for loading the two-species is optimized to be 13 G cm⁻¹. For simultaneously manipulating the ⁶Li and ⁴¹K lasers, broadband PBS, dual-wavelength HWPs and quarter-wave plate are used. Each 3D MOT laser beam contains four frequencies, i.e. cooling and repumping frequencies of ⁴¹K and ⁶Li atoms. The 1/e² beam diameter is 18 mm, other parameters such as the laser intensity and detuning are shown in figure 7. We mention that due to the unresolved excited hyperfine structure, there's no cycling transition for both ⁴¹K and ⁶Li atoms. Therefore, the repumping laser also contribute to the cooling process that requires large intensity. Figure 7 shows the optimized loading parameters for the two-species 3D MOT. With a 2 s MOT loading phase, a total number of 4 × 10^{9 41}K atoms and 3 × 10^{9 6}Li atoms can be obtained simultaneously. The temperature of ⁴¹K atoms is 5.6 mK while that of ⁶Li atoms is 2.9 mK.

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To increase the PSD, we perform two different CMOT for ⁴¹K and ⁶Li atoms simultaneously. During the CMOT phase, the magnetic field gradient is linearly ramped from 13 G cm⁻¹ to 20.8 G cm⁻¹ in 10 ms. For ⁶Li atoms, the peak intensity of 3D cooling and repumping laser beams are suddenly set to 0.75 ${{I}}_{{\rm{sat}}}^{{\rm{Li}}}$ and 1.16 ${{I}}_{{\rm{sat}}}^{{\rm{Li}}},$ respectively. Then both of them are linearly ramped to 0.05 ${{I}}_{{\rm{sat}}}^{{\rm{Li}}}$ in 10 ms. Similarly, the frequencies of cooling and repumping light are suddenly shifted to −4.09 Γ_Li and −0.99 Γ_Li, respectively. Then they are linearly ramped to −1.70 Γ_Li and −1.67 Γ_Li in 10 ms, respectively (see figure 7). After the CMOT, the temperature of ⁶Li atoms reduces to 284 μK with an atom number of 2.9 × 10⁹, resulting a PSD of 5.2 × 10⁻⁷. For ⁴¹K atoms, a novel D1–D2 CMOT technique [27] is adopted. Comparing with the ⁶Li CMOT, the D1 cooling transition ∣F = 2〉 to ∣F' = 2〉 of ⁴¹K is used instead of the D2 cooling transition. In order to suppress the light-assisted collisions, cooling (repumping) peak intensity is linearly reduced from 27.10 ${{I}}_{{\rm{sat}}}^{{\rm{K}}}$ (6.06 ${{I}}_{{\rm{sat}}}^{{\rm{K}}}$) to 0.50 ${{I}}_{{\rm{sat}}}^{{\rm{K}}}$ (4.04 ${{I}}_{{\rm{sat}}}^{{\rm{K}}}$) while the detuning is ramped from +3.6 Γ_K (−3.85 Γ_K) to +4.5 Γ_K (−1.65 Γ_K) in 10 ms, respectively. With this technique, the temperature of ⁴¹K atoms is reduced to 247 μK. The atom number of D1–D2 CMOT is 2.6 × 10⁹ and PSD is 1.13 × 10⁻⁷.

In a MOT, the lowest achievable temperature is Doppler temperature ${{T}}_{D}=\hslash {\rm{\Gamma }}/(2{{k}}_{{\rm{B}}}\,)$ (where $\hslash$ is the Plank constant divided by 2π, Γ is the linewidth of transition and ${{k}}_{{\rm{B}}}$ is the Boltzmann constant). Sub-Doppler cooling well below T_D is generally achieved with Sisyphus cooling in optical molasses. However, due to the unresolved excited-state hyperfine structure of the D2 transition, standard molasses cooling of ⁶Li and ⁴¹K are inefficient. In order to further increase the PSD, we adopt an advanced cooling scheme, where sub-Doppler cooling in gray molasses for ⁴¹K atoms [27] and UV MOT for ⁶Li atoms are employed, respectively. In order to combine the two different laser cooling technique, tremendous efforts have been devoted to optimize the relevant experimental parameters (see figure 7). As more ⁴¹K atoms are required, we suddenly switch off the magnetic gradient field after the CMOT phase to perform the gray molasses of ⁴¹K. The UV MOT of ⁶Li is applied at the residual magnetic field.

D1 line gray molasses is a newly developed laser cooling technique based on the combination of D1 line Sisyphus cooling and velocity-selective-coherent-population-trapping in a ${\rm{\Lambda }}$-type three-level system. In order to implement gray molasses, cooling and repumping lasers with frequencies blue detuned from the ⁴¹K D1 transition line are required (see figure 2). As described in the third section, the same optical setup is used for both D1 line gray molasses and D2 MOT, which greatly reduces the experimental complexity. At the beginning of the gray molasses, the D2 repumping laser and magnetic field are switched off while the input signal of EOM is turned on, generating the required cooling and repumping frequencies. Experimentally, we use the same detuning of +5.3 Γ_K for the two lasers to fulfill the Raman condition and the cooling/repumping intensity ratio is fixed at about 5:1. To achieve high capture efficiency of the gray molasses, maximum laser intensity is applied in the first 2 ms, which is 17.29 ${{I}}_{{\rm{sat}}}^{{\rm{K}}}$ and 3.46 ${{I}}_{{\rm{sat}}}^{{\rm{K}}}$ for the cooling and repumping light, respectively. Then we simultaneously ramp the laser intensity down to 5.76 ${{I}}_{{\rm{sat}}}^{{\rm{K}}}$ (1.15 ${{I}}_{{\rm{sat}}}^{{\rm{K}}}$) in the following 7 ms. With the gray molasses cooling, the temperature of ⁴¹K atoms is reduced to 42 μK and the PSD is increased to 5.4 × 10⁻⁶, providing an excellent starting point for further magnetic trapping and evaporative cooling.

The motivation for implementing a ⁶Li UV MOT is simple: the linewidth of UV transition for ⁶Li is much narrower than that of D2 transition, lead to a lower Doppler temperature. For example, the overall linewidth of the 2s–3p transition of ⁶Li is Γ_3P = 2π × 754 kHz, corresponding to a Doppler temperature of 18 μK which is much lower than that of D2 transition (141 μK). In the experiment, the UV MOT is performed in parallel with the gray molasses of ⁴¹K (see figure 7). The cooling and repumping lasers are superimposed by a PBS and then divided into six balanced laser beams by a series of PBSs and HWPs. The UV laser beams are superimposed with the red MOT laser beams through custom designed dichroic mirrors, where the 323 nm lasers are transmitted while the 671, 767 and 770 nm are reflected. The 1/e² beam diameter is 9.4 mm with maximum intensity of 1.15 ${{I}}_{{\rm{sat}}}^{{\rm{uv}}}$ (where ${{I}}_{{\rm{sat}}}^{{\rm{uv}}}=13.8$ mW cm⁻² is the saturation intensity of ⁶Li UV transition). The weak magnetic confinement is provided by the residual magnetic field gradient after switching off the current of the MOT coils. At the first 2 ms of the UV MOT, maximum intensity and largest detuning of the cooling (repumping) lasers are used to collect as many atoms as possible. Next, we ramp down the cooling (repumping) intensity of each beam from 1.08 ${{I}}_{{\rm{sat}}}^{{\rm{uv}}}$ (0.07 ${{I}}_{{\rm{sat}}}^{{\rm{uv}}}$) to 0.54 ${{I}}_{{\rm{sat}}}^{{\rm{uv}}}$ (0.01 ${{I}}_{{\rm{sat}}}^{{\rm{uv}}}$) in 3.5 ms. The cooling (repumping) detuning are decreased from −5.70 Γ_3P (−4.60 Γ_3P) to −2.10 Γ_3P (−1.10 Γ_3P) at the same time. This step is analog with a red CMOT, where the light-assisted collisions are suppressed. By holding these parameters for another 3.5 ms, a cloud of 1.24 × 10⁹ atoms with a temperature of 62 μK is obtained. The calculated PSD is 5.5 × 10⁻⁵, which is two orders of magnitude larger than that of CMOT.

Magnetic trap is state selective, in which only the atoms at low-field-seeking states can be captured. However, the atoms are depolarized after the laser cooling phase as they stay in both hyperfine states (F states) and distribute randomly in all the Zeeman states (${m}_{F}$ states). Therefore, atoms which occupy high field seeking states or states which are susceptible to undergo spin relaxation will loss from the magnetic trap. Moreover, heating and atom loss induced by the interspecies spin-exchange collisions will significantly reduce the lifetime of atoms in the magnetic trap. Therefore, it is necessary to pump all the atoms into the stretched states before the magnetic trap is switched on.

In the experiment, we implement a high field D1 optical pumping for both species to achieve high efficiency transfer and perfect spin purification. The target states are ∣F = 2, m_F = 2〉 of ⁴¹K and ∣F = 3/2, m_F = 3/2〉 of ⁶Li, respectively, as there's no channel for interspecies spin-exchange collision and both of the states have the strongest confinement in the magnetic trap. The advantage of D1 optical pumping is that the target states are dark states at the same time. For instance, if we drive ∣F = 2〉 to ∣F' = 2〉 transition of ⁴¹K, the atoms which are pumped into the m_F = 2 state will not absorb any photons and thus they are protected against further heating.

At the end of laser cooling phase, a homogeneous magnetic field of 15 G is turned on in 0.75 ms, providing large separation of different Zeeman states which is essential for the spin purification. Then, a pair of balanced counter-propagating light beams containing D1 pumping and repumping frequencies with a duration of 50 μs are applied to both species. Both of the pumping and repumping lasers are ${\sigma }^{+}$ polarized. With optimized parameters (see table 2), we obtain 70% and 90% pumping efficiency for ⁴¹K and ⁶Li atoms, respectively. By using RF spectroscopy, we also verify that nearly all the atoms are populated in the target states.

Table 2.  Optimal parameters for D1 optical pumping.

	41K optical pumping	6Li optical pumping
Icool $({{I}}_{{\rm{sat}}}^{{\rm{K}}/{\rm{Li}}})$	1.3	0.5
Irep $({{I}}_{{\rm{sat}}}^{{\rm{K}}/{\rm{Li}}})$	35.9	3.9
Δωcool(ΓK/Li)	+5.3	−0.68
Δωrep(ΓK/Li)	−0.1	−2.38

After loading both the species into the magnetic trap, they are magnetically transported to a glass cell with an extreme high vacuum environment and good optical accesses. The principle of magnetic transport is create a moving quadrupole potential which adiabatically displace the magnetic field center and thus the position of atom cloud. This can be done by installing the anti-Helmholtz coils in a movable stage or by applying time-varying currents in a series of overlapping fixed coils [38]. Although the first method is simple, it introduces unwanted noises such as mechanical turbulence and Foucault currents created by the movable stage. In the experiment, we adopt the latter one for the magnetic transport.

During the transport phase, one should keep the aspect ratio of magnetic field gradient in the x and y direction (see figure 8) as a constant, since the change of aspect ratio will heat the atom clouds. To achieve this goal, a 3-coil transport scheme is implemented as shown in figure 8. At the beginning (see figure 8(a) left), currents run through the first two coil pairs. The atom cloud is confined in the center of the first two coil pairs with an elongated shape. Next, the current is decreased in the first coil pair and simultaneously increased in the third coil pair so that the cloud moves to the center of the second coil pair with the shape unchanged (see figure 8(a) middle). Finally, as the current in the first coil pair decreases to zero and the current in the third coil pair reaches its maximum value, the cloud smoothly moves to the center of the last two coil pairs with a constant shape (see figure 8(a) right). However, due to the large distance between the MOT coils and the first transport coil pair, the aspect ratio of the magnetic field gradient is very large at the beginning of the transport phase. The same situation happens at the end of transport, where the overlap of the quadrupole coils and last transport coil pair is limited. These problems can be solved by using an additional push coil or a pair of push coils which provides an additional magnetic field gradient along the y direction to control the aspect ratio.

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A sketch of the coil assembly is shown in figure 8(b), including one push coil, one pair of MOT coils, 12 pairs of transport coils, one pair of quadrupole coils and one pair of final push coils. The atom clouds are transported over a total distance of 537 mm with an angle of 135°, providing an additional optical access along the final transport direction and large operating space around the science chamber. In the first transport section (section 1), the magnetic field gradient in z direction is 200 G cm⁻¹, then it is gradually decreased to 120 G cm⁻¹ in the section 2. By using a series of insulated gate bipolar translators and PID control loops, controllable time-varying currents running in the coils are generated. With optimized parameters, such as currents, mechanical position of the coils and transport time etc, we can obtain an overall efficiency of about 47% (51%) for ⁴¹K (⁶Li) atoms in a 3 s transport process. Considering the collisional loss during the transport and loss of atoms passing through the small aperture differential pumping tube (24%), the resulted two-species transport efficiencies are rather high.

Magnetic quadrupole trap is widely used in the ultracold atom experiment as it provides both large trapping volume and strong confinement. However, at the zero point of the magnetic field, Majorana spin-flip [39] occurs which lead to atom loss, heating and thus a limited lifetime of the atom clouds. The spin-flip region can be estimated by a simple model [40]. By substituting the experimental parameters for the two-species, the estimated Majorana spin-flip radius are 2.2 μm for ⁶Li atoms and 1.5 μm for ⁴¹K atoms, respectively. To prevent this loss mechanism, we apply an optical-plug as a repulsive barrier that repels the atoms from the spin-flip region.

In the experiment, we use 532 nm light as the optical-plug, which is far blue detuned for both ⁴¹K and ⁶Li atoms. The 532 nm light is provided by a single frequency high power solid laser. To achieve better beam profile and stability, high power fiber coupling is implemented. Finally, an 11 W laser beam is tightly focused to the center of the atom clouds with a 1/e² beam diameter of 38 μm. The resulting repulsive barriers for ⁴¹K and ⁶Li atoms are 1.15 mK and 1.19 mK, respectively. The alignment of the focused beam position is very critical, which is achieved by a pico-motor based mirror mount. With the presence of an optical-plug, the measured lifetime of atom clouds in the magnetic trap are more than 1 min.