Polarization-gradient-assisted subrecoil cooling: Quantum calculations in one dimension

We present a fully quantum-mechanical analysis of laser cooling of an angular momentum ${\mathit{J}}_{\mathit{g}}$=1 to ${\mathit{J}}_{\mathit{e}}$=1 transition in a laser configuration consisting of two counterpropagating linearly polarized laser beams. The essential feature of this configuration is the coexistence of velocity-selective coherent population trapping (VSCPT) and polarization-gradient cooling. The role of polarization-gradient cooling is to provide (i) for short interaction times ‘‘precooling’’ of the initial momentum distribution and (ii) in the long-time limit ‘‘confinement of velocities.’’ This eventually leads to a larger number of atoms being captured in the dark state when compared with the schme of Aspect et al. [Phys. Rev. Lett. 61, 826 (1988)]. We find that the optimum parameter values for polarization-gradient cooling and VSCPT are in a completely different parameter regime: polarization-gradient cooling works best off resonance and for low intensities, while VSCPT works best on resonance. We can combine the advantages of polarization-gradient cooling and VSCPT in a scheme where we cycle in time between the optimum cooling parameters for both cooling mechanisms.