$\Lambda$-enhanced sub-Doppler cooling of lithium atoms in $D_1$ gray molasses

Following the bichromatic sub-Doppler cooling scheme on the $D_1$ line of ${}^{40}$K recently demonstrated in  Fernandes et al. [Europhys. Lett. 100, 63001 (2012)], we introduce a similar technique for ${}^7$Li atoms and obtain temperatures of $60\mu \mathrm{K}$ while capturing all of the $5\times {10}^8$ atoms present from the previous stage. We investigate the influence of the detuning between the the two cooling frequencies and observe a threefold decrease of the temperature when the Raman condition is fulfilled. We interpret this effect as arising from extra cooling due to long-lived coherences between hyperfine states. Solving the optical Bloch equations for a simplified $\Lambda$-type three-level system we identify the presence of an efficient cooling force near the Raman condition. After transfer into a quadrupole magnetic trap, we measure a phase space density of $\sim$${10}^{-5}$. This laser cooling offers a promising route for fast evaporation of lithium atoms to quantum degeneracy in optical or magnetic traps.

Figure 1

The $D_1$ line for ${}^7$Li. The cooling scheme has a strong coupling laser (principal beam, black solid arrow) ${\delta }_2$ blue detuned from the $|F=2\rangle \to |F^{\prime }=2\rangle$ transition and a weak coupling laser (repumper, gray solid arrow) ${\delta }_1$ blue detuned from the $|F=1\rangle \to |F^{\prime }=2\rangle$ transition. The repumper is generated from the principal beam by an electro-optical modulator operating at a frequency $803.5+\delta /2\pi \mathrm{MHz}$, where $\delta ={\delta }_1-{\delta }_2$.

Figure 2

(a) Typical temperature of the cloud as a function of the repumper detuning for a fixed principal beam detuned at ${\delta }_1=4.5\Gamma =2\pi \times 26.4$ MHz. The dashed vertical line indicates the position of the resonance with transition $|F=2\rangle \to |F^{\prime }=2\rangle$, the dotted horizontal line shows the typical temperature of a MOT. (b) Magnification of the region near the Raman condition with well-aligned cooling beams and zeroed magnetic offset fields. (c) Minimum cloud temperature as a function of repumper power.

Figure 3

The $\Lambda$ level scheme. An intense standing wave with Rabi frequency ${\Omega }_2$ and a weaker standing wave with Rabi frequency ${\Omega }_1$, detuning ${\delta }_1$, illuminate an atom with three levels in a $\Lambda$ configuration.

Figure 4

Comparison of experimental data with the perturbative approach results for a detuning of the pump ${\delta }_2=2\pi \times 26.4\mathrm{MHz}=4.5\Gamma$. (a) Temperature versus repumper detuning, experiment; we indicate the MOT temparature by the dotted line. Panels (b) and (c) show, respectively, the friction coefficient $\alpha$ and photon scattering rate ${\Gamma }^{\prime }$ for ${\Omega }_2=3.4\Gamma$ (red dashed curve) and $2.1\Gamma$ (blue solid curve). The intensity ratio ${({\Omega }_1/{\Omega }_2)}^2$ is 0.02. The vertical dashed line indicates the position of ${\delta }_1=0$.

Figure 5

The cascade of levels dressed by transition 2 with a schematical representation of state $|1\rangle$. Traces show typical cycles of atoms pumped from $|1\rangle$ and back depending on the detuning of wave 1. The detuning of the repumper modulates the entry point into the cascade of the dressed states, leading either (a) heating or (b) cooling processes.

Figure 6

Comparison of results using the perturbative calculation (dashed), and the continued fractions (solid) for the $\varphi =0$ case, with the same parameters as in Fig. 4 and ${\Omega }_2=2.1\Gamma$.

Figure 7

${\langle \mathcal{F}\rangle }_{\varphi }$ in units of $1/\hslash k\Gamma$ as a function of $v$ for different values of $\delta$ around $\delta =0$. The horizontal scale is in units of the thermal velocity at $T=200\mu \mathrm{K}$, $v_{th}=\sqrt{k_{\mathrm{B}}T/m}$.

Figure 8

Continued fractions solution of the photon scattering rate ${\Gamma }^{\prime }=\Gamma {\rho }_{33}$ averaged over all relative phases of the repumper and principal standing waves as a function of the two-photon detuning $\delta$. Velocity-dependent effects are taken into account here by computing an average of ${\langle {\Gamma }^{\prime }\rangle }_{\varphi }\left(v\right)$ weighed by a Maxwell-Boltzmann velocity distribution at 200 $\mu$K.