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Physical Review A

Scaling laws in velocity-selective coherent-population-trapping laser cooling

Giovanna Morigi, Bruno Zambon, Norbert Leinfellner, E. Arimondo

Published Apr 1, 1996• 11 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.53.2616

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•May 8, 1994•1 citation
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 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.
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.
ABSTRACT In this work we present an investigation of velocity-selective coherent population trapping (VSCPT) in asym- metric three-level schemes. The light force in such schemes is of an intrinsically transient character and shouldnot be described in a quasiclassical approach. Instead, results of the full quantum-mechanical calculations are presented with emphasis on their meaning to the efficiency of subrecoil laser cooling. 1 INTRODUCTION Laser cooling of neutral atoms has received significant advances by the introduction of velocity-selectivecoherent population trapping ((VSCPT) some years ago.1 Since it leads to atomic temperatures well below therecoil limit, studies of ultracold atoms and atomic interactions may be improved by magnitudes.The effect of VSCPT relies on optical pumping of atoms into a state WNC) which is a trap state for a certaincenter-of-mass velocity vO. This trap state is created by a destructive superposition of atomic states within amultilevel quantum system. Once being in such a state LWNC) the laser light does not interact anymore with theatom which leads to a decoupling with the rest of the system at vo. Atoms located outside this small velocityregion get a chance to be trapped by the momentum diffusion due to spontaneous emission of photons. Aftera sufficient long interaction time nearly all atoms are trapped inside a narrow momentum distribution whichcan be interpreted as cooling. The theoretical and experimental investigation of VSCPT is usually consideredby use of a three-level A-system as shown in Fig.1. Such a system can be found for example in a symmetrical
We have demonstrated velocity-selective coherent population trapping (VSCPT) in a two-level system created by circularly polarized light driving the $2{}^{3}{S}_{1}\ensuremath{\rightarrow}3{}^{3}{P}_{2}$ transition in metastable helium. It is quite different from the usual VSCPT because there need be no consideration of selection rules, polarization, or internal atomic states. This most primitive case elicits the simple nature of VSCPT as a special kind of quantum interference, and demonstrates the presence of VSCPT in a system that has only two internal levels. It is readily observed for this transition because the ratio of the recoil frequency to the natural linewidth is 0.22, two orders of magnitude larger than for most laser cooling experiments. Our trapped state is fed by Doppler cooling, which is unusually effective here because of the large recoil, and is totally absent in previously described VSCPT experiments.
In recent years, there has been a great deal of interest in velocity selective coherent population trapping (VSCPT).1 However, since VSCPT occurs via a random walk in momentum space, in order to achieve significant VSCPT in three dimensions, it is necessary to precool and confine atoms dose to the recoil momentum. Shahriar et al.2 recently predicted that this type of cooling and velocity confinement assisted VSCPT can be achieved in one, two, or three dimensions when a Λ-system atom is excited by a pair of blue detuned Raman resonant standing waves, with a phase difference of θ = π/4.