Force-assisted velocity selective coherent population trapping

We present a fully quantum analysis of velocity selective coherent population trapping (VSCPT) in two schemes for which there is a force which assists in the accumulation of atoms in the trapping state. In the first scheme, the F-g = 2 to F-e = 2 transition was Studied where the existence of a semiclassical polarization gradient force even for a pure sigma(+)-sigma(-) configuration has been demonstrated which gives cooling for blue detuning. We also verify that cooling may be obtained for the F = 2 to 1 and F = 3 to 2 transitions; our fully quantum mechanical calculations yield a result which is consistent with recent experimental results of Valentin er al but differ from previous semiclassical calculations. Secondly, we discuss a scheme of force assisted VSCPT which combines VSCPT on the F-g = 1 to F-e = 1 transition with the coupling to another transition for which a strong sub-Doppler cooling force is present. This scheme allows velocity selective coherent population trapping and the polarization-gradient force to work under optimum conditions simultaneously. We find that both of these two schemes lead to efficient cooling of atoms.