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We report on simultaneous sub-Doppler laser cooling of fermionic $^6$Li and$^{40}$K using the D$_1$ optical transitions. We compare experimental resultsto a numerical simulation of the cooling process applying a semi-classicalMonte Carlo wavefunction method. The simulation takes into account the threedimensional optical molasses setup and the dipole interaction between atoms andthe bichromatic light field driving the D$_1$ transitions. We discuss thephysical mechanisms at play, we identify the important role of coherencesbetween the ground state hyperfine levels and compare D$_1$ and D$_2$sub-Doppler cooling. In 5 ms, the D$_1$ molasses phase largely reduces thetemperature for both $^6$Li and $^{40}$K at the same time, with a finaltemperature of 44 $\mu$K and 11 $\mu$K, respectively. For both species thisleads to a phase-space density close to $10^{-4}$. These conditions are wellsuited to directly load an optical or magnetic trap for efficient evaporativecooling to quantum degeneracy.

Simultaneous sub-Doppler laser cooling of fermionic $^6$Li and $^{40}$K on the D$_1$ line: Theory and Experiment