Subrecoil Raman laser cooling of ⁶Li atoms

Abstract

We realize an efficient one-dimensional Raman cooling of ⁶Li atoms using 2S\to 2P Raman transition pulses and 2S\to 3P ultraviolet (UV) optical repumping. In this cooling scheme, we directly cool an initial cold atomic sample of 350 μK released from a standard magneto-optical trap down to a velocity spread of 0.8 recoil velocity, corresponding to an effective temperature of 4.5 μK, an increase of almost an order of magnitude in the phase space density with respect to ordinary laser sub-Doppler cooling. This technique may provide an ideal initial sub-recoil atomic sample for the application of the large-momentum-transfer in the recoil-sensitive lithium atom interferometers.

Graphical abstract

Keywords

cold atoms / subrecoil cooling / Raman cooling

1 Introduction

The atom/molecule cooling has been dramatically advanced in fundamental physics and application science. The well-known Doppler cooling, the foundation of laser cooling technology, relies on atoms absorbing photons due to the Doppler effect and subsequent random scattering of anti-Stokes photons. This leads to a sample with a finite, limited temperature of T_D=\hslash \mathrm{\Gamma }/(2k_B) (where \hslash, \mathrm{\Gamma }, and k_B are the reduced Planck constant, the linewidth of the atomic transition, and the Boltzmann constant, respectively). To overcome this limitation, the Sisyphus cooling is developed to cool to a lower temperature [1]. The lowest temperature achievable with the Sisyphus cooling is referred to as the single-photon recoil limit T_{rec}=m{v}_{rec}^2/k_B, where m is the atomic mass and v_{rec}=\hslash k/m is the recoil velocity. A way to break this cooling limit is so-called velocity-selective coherent population trapping (VSCPT) [2] and Raman cooling [3–12], which make the atoms with near zero velocity stay in the dark state in which atoms do not absorb light and push other atoms with small velocity drift or diffuse to v=0 in the momentum space to realize very low temperature cooling.

To further cool the atoms, one has to employ collision-based cooling methods such as evaporative and sympathetic cooling. Evaporative cooling has been widely used to attain sub-μ\mathrm{K}\sim \mathrm{n}\mathrm{K} temperature and quantum degeneracy, but is precluded in many applications, such as the optical atomic clocks and cold atom interferometers, because the cooling could cause the atom loss and require collisional thermalization with long time-consuming.

For the lightest alkali metal, lithium, although it has been intensively studied in the field of ultracold quantum gas, direct laser cooling to a very low temperature is challenging. This three-electron atom can also be used for precision measurements, such as accurately measuring the absolute frequency to test the QED theory [13–21] and the use of cold atom interferometers [22, 23] to test the standard models. However, due to the unresolved D_2 lines, it is difficult to cool a lithium atomic sample to a very low temperature with laser cooling. To resolve the near-degenerate hyperfine structure in the excited state, the ⁷Li atoms are cooled to about 40 μK with the Sisyphus cooling of lithium by using the D_1 line [24]. Gray molasses based on the 2S_{1/2}\to 2P_{1/2} transition of the D_1 line was developed to cool a lithium atomic sample to about 50 μK [25–28]. The ultraviolet magneto-optical trap (UV MOT) using the small natural linewidth of the 2S\to 3P transition of ⁶Li has also been realized [29, 30]. Recently, we have broken the Doppler cooling limit and cooled ⁶Li atoms to 16 μK by using the ultraviolet narrow transition for which the natural linewidth is comparable to the recoil frequency [31]. Based on this cooling scheme, we have realized the first cold ⁶Li atom interferometer and precisely measured the recoil frequency [22]. Although there have been many efforts to implement laser cooling to obtain a low temperature, the Raman cooling of the lithium atoms to reach the single-photon recoil temperature has not been experimentally demonstrated so far.

Here, we report an experimental realization of the one-dimensional Raman cooling of ⁶Li atoms. To overcome the severe heating caused by the large ratio of the Raman Rabi frequency to the inelastic scattering rate for the D_1 and D_2 line, we use the ultraviolet narrow transition of 2S\to 3P as the pumping field to implement the Raman cooling cycle. Using the developed two stages of the two-photon Raman momentum transfer and exchange, the ⁶Li atoms are cooled from an initial temperature of about 350 μK to about 0.8 v_{rec}, corresponding to an effective temperature of 4.5 μK. The work may provide an ideal starting point for the application of cold lithium atom interferometers to measure the fine structure constant.

The paper is organized as follows: In Section 2, we give a simple Raman cooling theory and present the experimental details, with an emphasis on the fine-tuning of the excitation spectra of the Raman pulses. Section 3 provides the results obtained from our experiments in terms of final velocity distribution and cooling dynamics. In the conclusion, we summarize and discuss our results and their applications.

2 Experiments

Our experimental setup is similar to that described in our previous work [22]. Here, we just briefly present the experimental procedure. An atomic beam of lithium from the hot oven is decelerated by the Zeeman slower. The standard MOT is used to obtain about 1.5\times {10}^8 atoms with an initial temperature of 350 μK and a radius of about 1 mm. Subsequently, the repump beams of the MOT and magnetic field are turned off, while cooling beams last for 200 μs to pump all atoms to the hyperfine ground state |2S_{1/2},F=1/2⟩. Then, the Raman cooling cycle sequence is followed to perform the cooling.

The one-dimensional Raman cooling consists of the velocity-selective Raman transitions, optical repumping, and the repetition of the sequence of pulses, as shown in Fig.1. The orthogonally polarized Raman beams counter-propagate along the z-axis. The gravity and the magnetic field are along the x-axis and the y-axis, respectively. The Zeeman sublevels with magnetic quantum number m_F can be ignored for the very small magnetic field. The atoms are initially distributed in the hyperfine state |2S_{1/2},F=1/2⟩ of the ground state of ⁶Li. They are illuminated by the two counter-propagating laser beams with the higher frequency {\omega }_1 and the lower frequency {\omega }_2 with orthogonal polarizations. The Raman single photon detuning \mathrm{\Delta } of each beam is large enough to suppress the resonant excitation. When the frequency difference between two beams {\omega }_{12}={\omega }_1-{\omega }_2 is close to the split of the two hyperfine ground states {\omega }_{HFS}, the atoms are coherently transferred to the hyperfine ground state |2S_{1/2},F=3/2⟩. The two-photon frequency detuning \delta felt by the atoms in this Raman transition is given by

(1)\delta ={\omega }_{12}-{\omega }_{HFS}-{\delta }_{AC}-{\mathit{k}}_{eff}\cdot \mathit{v}-4{\omega }_r,

where {\delta }_{AC} is the ac Stark light shift caused by two Raman beams, {\mathit{k}}_{eff}\cdot \mathit{v} is the Doppler shift of the atoms with velocity \mathit{v}, {\mathit{k}}_{eff}={\mathit{k}}_1-{\mathit{k}}_2\approx 2{\mathit{k}}_1 is the effective wavevector and the single photon recoil frequency {\omega }_r=\hslash k_1^2/(2m), respectively. Note that the Doppler shift has the same value as the four times {\omega }_r for atoms with a velocity v_{rec}. For the atoms with zero velocity v=0, an effective resonance frequency {\omega }_0={\omega }_{HFS}+{\delta }_{AC}+4{\omega }_r. Consequently, the resonant condition for atoms with any velocity is

(2)\begin{array}{r}{\mathit{k}}_{eff}\cdot \mathit{v}={\omega }_{12}-{\omega }_0.\end{array}

Eq. (2) shows clearly that atoms with opposite velocities will be resonantly transferred in the Raman process when {\omega }_{12} is red detuning to the {\omega }_0. The velocity span of the transferred atoms is related to the Fourier spectrum width of the pulse duration by \left|\mathrm{\Delta }v\right|\sim 1/(\tau k_{eff}), where \tau is the duration of the pulse. Notably, the atoms are coherently transferred to the |2S_{1/2},F=3/2⟩ state while changing their velocities by twice the recoil velocity in the direction of the effective wavevector. In the experiment, {\omega }_{12} is chosen to make its detuning with {\omega }_0 scanning from far to close resonance and alternately changes the effective wavevector direction to work on the atoms with the opposite velocity direction.

Our experiments use a second-harmonic generation Raman amplified laser with a 1342 nm external cavity diode laser (ECDL) seed light to generate 671 nm Raman light sources. It is frequency-offset locked to the crossover peak of the D_1−D_2 line of ⁶Li through the saturated absorption spectrum, leading that the single photon detuning is \mathrm{\Delta } = −4.88 GHz relative to the D_2 line. The locked linewidth of the light is about 700 kHz. The laser is split into two paths by a polarizing beam splitter (PBS). One of the beams passes through an acousto-optic modulator (AOM). Two Raman beams with a frequency difference close to the ground state hyperfine splitting of about 2\pi \times 228.205 MHz. The two Raman beams continue to pass through the same AOM used as a light switch and then enter two optical fibers respectively, propagating in opposite directions near the cavity. In the experiment, the zero-order and first-order diffracted lights of an AOM are used to prepare the switching between two Raman beams with opposite effective wave vectors. The effective Raman Rabi frequency in a Raman transition is given by {\mathrm{\Omega }}_R=\sum {\mathrm{\Omega }}_{1i}{\mathrm{\Omega }}_{2i}/(2{\mathrm{\Delta }}_i), where {\mathrm{\Omega }}_{1i} and {\mathrm{\Omega }}_{2i} are the Rabi frequencies of high-frequency and low-frequency transition, respectively, and i denotes for the possible intermediate states |i⟩. Typically, for a 200 mW light intensity, an effective Rabi frequency {\mathrm{\Omega }}_R=2\pi \times 750 kHz, leading to the peak light shift between two ground hyperfine states is about 2\pi \times 30\mathrm{k}\mathrm{H}\mathrm{z}\approx 0.1|{\mathit{k}}_{eff}\cdot {\mathit{v}}_{rec}|. Therefore, the ac light shift can be negligible.

The second step for the Raman cooling requires that the atoms in the |2S_{1/2},F=3/2⟩ state need to be pumped back to the initial ground state |2S_{1/2},F=1/2⟩. Typically, it is employed by a resonant light through the spontaneous radiation to complete such a cycle. The leading velocity change of the atoms is the sum of the single-photon recoil velocity of the absorbed pump light and the random velocity projection due to the spontaneous radiation. For ⁶Li, the ground hyperfine state splitting is about 228 MHz, and the spin is half-integer. We observed that the repumping light coupled with D_1 or D_2 lines resonant with the |2S_{1/2},F=3/2⟩ state causes a severe heating effect on |2S_{1/2},F=1/2⟩ and greatly degrades the cooling. Therefore, we instead use a 323 nm laser to couple the transition |2S_{1/2},F=3/2⟩\to |3P_{3/2}⟩ with a narrower natural linewidth {\mathrm{\Gamma }}_{\mathrm{U}\mathrm{V}} (2\pi \times 754 kHz) to achieve the recovery of the atomic ground state. The UV laser is generalized by a fourth harmonic generation with a 1293 nm seed laser locked to an ultrastable optical frequency comb (OFC) with a stability of 3\times {10}^{-16} @1299 nm in 1 s. High-precision frequency locking makes it possible to tune the single-photon detuning of the ultraviolet light in the scale of UV natural linewidth. Subsequent experimental results show that when the single-photon detuning of the repump light is lower than {\mathrm{\Gamma }}_{\mathrm{U}\mathrm{V}}, the cooling effect with sub-recoil velocities occurs. This repumping light is 20° off the optical axis of Raman light propagation and is reflected by a mirror to coincide with the incident light to improve the efficiency of the repump and balance the optical radiation pressure on the atoms from the lights.

A highly efficient Raman cooling requires the ultralow excitation probability for zero-velocity atoms during the cooling process. The Raman cooling experiment is conducted after the MOT phase, and the 10 A current that generates a 20 G/cm spatial magnetic field gradient in the anti-Helmholtz coils is turned off within 200 μs. The eddy currents induced in the coils interact with the surrounding environment, leading to both temporal and spatial magnetic hysteresis effects. The residual magnetic field decays over time and tends to stabilize after a waiting time before Raman cooling, depending on the various experimental systems. In order to observe the effect of time-decayed magnetic field on the pulse excitation spectrum, the velocity-insensitive Raman excitation spectra with the \pi pulses of the duration \tau =45 μs are shown in Fig.3 for different waiting time t_0=1.2 ms, 1.5 ms, and 1.8 ms after turning off the MOT, respectively. For the square Raman pulses, the transition probability is described as P={\mathrm{\Omega }}_R^2/\left({\mathrm{\Omega }}_R^2+{\delta }^2\right)\mathrm{s}\mathrm{i}{\mathrm{n}}^2(\sqrt{{\mathrm{\Omega }}_R^2+{\delta }^2}t/2). The excitation spectrum of the square pulse is characterized by the many side bands and zero-excitation points. The nth zero-excitation points of the spectrum can be expressed as {\delta }_{n0}=1/T\sqrt{n^2-k^2/4}, where k={\mathrm{\Omega }}_{R}T/\pi is related to the area of the pulse and k=1 denotes the \pi pulse. Atoms with zero-velocity can stay in the dark state as long as {\omega }_{12}-{\omega }_0={\delta }_{n0} is satisfied for Raman cooling pulses. For previous Raman cooling experiments with square wave pulses the 1st zero-excitation conditions are satisfied, i.e., {\omega }_{12}-{\omega }_0={\delta }_{10}. The 1st zero-excitation spectrum width for a \pi pulse is {\delta }_{10}=\sqrt{3}/(2T). However, the residual magnetic field could degrade the Raman transition, leading to the non-zero-excitation of the 1st zero position. As shown in Fig.3, the position of the 1st zero at t_0=1.2 ms (the residual background magnetic field 50 mG) cannot be well defined, and the excitation probability is as high as 20%, which is fatal in the Raman cooling. On the contrary, at 1.8 ms with the minimum magnetic field gradient, the profile of the 1st zero-excitation at t_0=1.8 ms (less than 1 mG) is obvious. However, the excitation probability is still higher than 10%. In these excitation spectra, we note that the robustness of the zero-excitation positions is improved under the different decoherence mechanisms for the higher order of zeros. Therefore, in the subsequent experiments, we tune the detuning of the Raman cooling pulses to the 2nd zeros of the excitation spectrum, i.e., {\omega }_{12}-{\omega }_0={\delta }_{20}.

3 Results and discussion

The full Raman cooling in the experiment consists of two stages, as displayed in Fig.4. In the first stage, a pulse sequence consists of 3 pairs of square pulses alternating in the positive and negative direction along the z-axis. A repumping pulse with a duration of 50 μs is followed for each cooling pulse. The AOM controls the wave vector to switch within 1 μs.

The initial atomic samples released from the MOT have a velocity spread of about 10 v_{rec}. To make the Raman cooling as efficient as possible, the profile, duration, and detuning of the pulses are designed carefully for optimal cooling performance. Three cooling pulses with two-photon red detuning are tuned around 9 v_{rec}, 5 v_{rec}, and 3 v_{rec}, respectively, to transfer as many atoms with large initial velocities as possible. The maximum available light intensity with a \pi pulse time of 0.6 μs is used to rapidly cool the atoms to 15 μK with a duration of 1.2 ms, corresponding to a 1/\sqrt{\mathrm{e}} velocity of 1.4v_{rec}.

After the first stage, the Raman-precooled atoms are used as a starting point for further deep cooling. In the second stage, we reduce the Raman light intensity and design three pairs of square pulses with two-photon red detuning of about 3 v_{rec}, 2 v_{rec}, and 1 v_{rec}, respectively, the \pi pulse time of each cooling pulse is carefully controlled to make sure that the second zeros of the excitation spectrum keep alignment with the resonance conditions of atoms with zero velocity.

After these two stages of Raman cooling, the one-dimensional velocity distribution of the atoms is determined by scanning the two-photon detuning of the opposite Raman lights. The atoms with different velocities are selected to transfer from |2S_{1/2},F=1/2⟩ to |2S_{1/2},F=3/2⟩ to obtain the excitation spectrum. We use a 15 μs Raman pulse ({\mathrm{\Omega }}_R=2\pi \times 33\mathrm{k}\mathrm{H}\mathrm{z}) during the scanning spectrum. The measured velocity resolution is less than the recoil velocity to reflect the velocity distribution accurately. Another resonant light coupling |2S_{1/2},F=3/2⟩\to 2P_{3/2} is used to calculate the number of atoms in the state of |2S_{1/2},F=3/2⟩ by using the absorption imaging. Each Raman cooling cycle with six pulses and optical pumping spends 1.8 ms.

Finally, after a total of ten cycles and 60 pulses lasting for 3 ms, the velocity distributions of the atoms before and after Raman cooling are shown in Fig.5. The scale of the x-axis is converted from two-photon detuning \delta to velocity v according to \delta ={\mathit{k}}_{eff}\cdot \mathit{v}. The measured data are fitted well with the curve of Gaussian and bimodal Gaussian for the initial and final velocity distribution respectively. The 1/\sqrt{\mathrm{e}} velocity spread of the velocity distribution is reduced from 8.5 v_{rec} to a subrecoil velocity of 0.8 v_{rec}. The atomic sample is cooled by two orders of magnitude from 350 to 4.5 μK corresponding to 0.64 T_{rec}, a decrease of almost two orders of magnitude in the temperature. The ratio of the area enclosed by the two curves relative to the x-axis implies that nearly 80% of the atoms are involved in the cooling process.

In Fig.6, we experimentally investigate the final temperature of the sample for the different single-photon detuning {\delta }_{\mathrm{U}\mathrm{V}} of the UV repumping beams. It explicitly shows that when {\delta }_{\mathrm{U}\mathrm{V}} is smaller than 0.35 {\mathrm{\Gamma }}_{\mathrm{U}\mathrm{V}}, the final temperature breaks into the recoil temperature 7 μK. The final temperature decreases as the UV single-photon detuning {\delta }_{\mathrm{U}\mathrm{V}} is close to zero and reaches the limit temperature of 4.0 μK. However, the number of atoms decreased sharply if the , resulting from the near resonance excitation and poor signal-to-noise ratio, causing a significant statistical error.

We investigate the final velocity spread \delta v (half-width at 1/\sqrt{\mathrm{e}}) as a function of the cooling time \mathrm{\Theta } during the second stage, as shown in Fig.7 and find that the velocity spread obeys very well with a power law \delta v\sim {\mathrm{\Theta }}^{-1/\alpha }. It clearly shows that velocity spread \delta v gradually tends to a stable value around 0.8 v_{rec} within 1.5 ms. The fit to the data with a function of {\mathrm{\Theta }}^{-1/\alpha } gives the exponent \alpha =2, directly determining the cooling efficiency. This is also related to \gamma (v)=(v/v_0{)}^{\alpha }, which reveals the v dependence of the excitation spectrum of the cooling pulse around the zero-point, where v_0 is the selected velocity corresponding to the detuned pulse. An excitation spectrum of the square pulse around the first zero corresponds to a power law with \alpha =2 [4]. Our experiment uses the second zero of the square pulse \pi excitation spectrum to satisfy the Raman resonance condition for v=0. The corresponding \alpha is about 1.93 in a narrower interval of v/v_0\sim 0-0.2, consistent with the basic physical description of the Lévy statistical model.

Although we have cooled the ⁶Li atomic sample to sub-recoil temperature, the final cooling effect still differs from the very low temperature of the Raman cooling effect in other cesium or rubidium atoms. Experimentally, even when a narrower cooling pulse with a long \pi pulse duration, typically involving Raman Rabi frequencies in the kHz range, is used around v=0, no further cooling effect is accomplished as predicted by the theory. As highlighted in theoretical studies [32], under weak magnetic fields and Raman Rabi frequency, {}^6\mathrm{L}\mathrm{i} — owing to its coupling with multiple excited states — exhibits a significantly enhanced inelastic scattering rate {\mathrm{\Gamma }}_{\mathrm{i}\mathrm{n}} compared to heavier atoms like {}^{87}\mathrm{R}\mathrm{b} or {}^{133}\mathrm{C}\mathrm{s}. This scattering rate introduces pronounced heating: it alters the asymptotic behavior of the velocity-dependent photon scattering rate R\left(v\right) around v=0, disrupting the delicate balance between cooling and diffusion of velocity. Consequently, cooling efficiency diminishes, preventing {}^6\mathrm{L}\mathrm{i} from reaching the 0.1 v_{rec} routinely achieved in Raman cooling of heavier atoms. The light mass of {}^6\mathrm{L}\mathrm{i} also exacerbates this issue by amplifying velocity diffusion due to photon recoil, further destabilizing momentum accumulation at low velocities.

4 Conclusions

In summary, we reported the one-dimensional subrecoil Raman cooling for ⁶Li for the first time. Engineering the cooling pulses in two stages, the temperature of atoms is cooled from 350 to 4.5 μK in the time of 3 ms with the Raman lasers. The UV narrow transition is used as the repumping beams to overcome the partially resolved excited state energy levels and significant heating from the small ground state hyperfine splitting. The final cooling with Lévy flight statistics is demonstrated. Our work could provide a good starting point for precision measurement experiments requiring subrecoil temperature atomic samples with fast cooling.

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