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Physical Review A

Scaling laws in velocity-selective coherent population trapping in the presence of polarization-gradient cooling

C. Menotti, Giovanna Morigi, Jörg Helge Müller, E. Arimondo

Published Nov 1, 1997• 5 citations
Publisher

Abstract

One-dimensional laser cooling based on velocity-selective coherent population trapping (VSCPT) on a ${2}_{g}\ensuremath{\rightarrow}{1}_{e}$ transition has been investigated numerically through the solution of the optical Bloch equations. As in the work of G. Morigi et al. [Phys. Rev. A 53, 2616 (1996)], it has been found that for a large set of atomic and laser parameters, the VSCPT cooling process may be described through scaling-law relations. The scaling laws are based on the relations between the loss rates at large atomic momentum and their dependence on the momentum around zero value. The role of the laser detuning on the VSCPT trapping efficiency has been examined and scaling laws including the detuning have been derived.

DOI
10.1103/physreva.56.4327

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One-dimensional laser cooling based on velocity-selective coherent population trapping (VSCPT) on a 2g\ensuremath→1e{2}_{g}\ensuremath{\rightarrow}{1}_{e}2g​\ensuremath→1e​ transition has been investigated numerically through the solution of the optical Bloch equations. As in the work of G. Morigi et al. [Phys. Rev. A 53, 2616 (1996)], it has been found that for a large set of atomic and laser parameters, the VSCPT cooling process may be described through scaling-law relations. The scaling laws are based on the relations between the loss rates at large atomic momentum and their dependence on the momentum around zero value. The role of the laser detuning on the VSCPT trapping efficiency has been examined and scaling laws including the detuning have been derived.
One-dimensional laser cooling based on velocity-selective coherent population trapping (VSCPT) has been investigated numerically through the solution of the optical Bloch equations and through a Monte Carlo analysis. The 1\ensuremath{\rightarrow}1 and 2\ensuremath{\rightarrow}2 transitions have been examined as a function of the atomic recoil frequency, the spontaneous-emission decay rate, and the Rabi frequency of the cooling laser. It has been found that for a large set of those parameters, the VSCPT cooling process may be described through scaling-law relations. The scaling laws are not valid at long atom-laser interaction times or large Rabi frequencies, where the atomic Doppler shift plays a significant role in the atomic motion evolution. Similar results for two atomic transitions suggest the validity of the scaling law for any one-dimensional VSCPT process. \textcopyright{} 1996 The American Physical Society.
One-dimensional velocity-selective coherent population trapping (VSCPT) in a cascade atomic configuration, with the second excited level a Rydberg state, is investigated through numerical calculations. The trapping efficiency for the case of travelling wave lasers is derived from the solution of the optical Bloch equations. For excitation by bichromatic standing waves, the energy-band approach is applied. Although the cooling process is limited by the spontaneous emission decay of the Rydberg state, the coexistence of polarization-gradient cooling and VSCPT in the case of standing waves allows the preparation of the majority of the atomic population in a cold Rydberg state.
We present a fully quantum-mechanical analysis of laser cooling of an angular momentum Jg{\mathit{J}}_{\mathit{g}}Jg​=1 to Je{\mathit{J}}_{\mathit{e}}Je​=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.
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 et al. (1992) 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.
We show that polarization-gradient cooling occurs in the \ensuremath{\Lambda} system, simultaneously with velocity-selective coherent population trapping (VSCPT). Starting with a Doppler temperature sample, this process precools atoms and contains them, to within twice the recoil velocity, a range efficiently capturable by VSCPT. For sodium, this cooling may enhance the rate of three-dimensional VSCPT by 200 times over the rate achievable from Doppler precooling alone. We estimate that in 8 msec, for example, the atoms would be cooled in three dimensions to one-fourth the recoil temperature.