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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Force in velocity-selective coherent population trapping: full quantum-mechanical description

Norbert Leinfellner, Eugeny Korsunsky, Laurentius Windholz

Published May 6, 1996• 0 citations
Publisher

Abstract

In this work we present an investigation of velocity-selective coherent population trapping (VSCPT) in asymmetric three-level schemes. The light force in such schemes is of an intrinsically transient character and should not 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.

DOI
10.1117/12.239866

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In this work we present an investigation of velocity-selective coherent population trapping (VSCPT) in asymmetric three-level schemes. The light force in such schemes is of an intrinsically transient character and should not 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.
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 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 study a class of laser cooling schemes that combine velocity-selective coherent population trapping (VSCPT) with Doppler cooling mechanisms. The Doppler mechanism prevents the atoms from diffusing into the region of high momentum, thereby removing the characteristic long-time asymptotic behaviour of VSCPT where, in the end, all the atoms escape from the trap. It is shown that the transition Jg = 2 to Je = 1 while maintaining the simple field configuration present in the original VSCPT case provides the additional Doppler mechanism and leads to virtually zero temperature without the loss of atoms that characterize the original VSCPT dynamics.
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.