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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Pulsed sub-recoil laser cooling of atoms

Huang Wu, E. Arimondo, Christopher J. Foot

Published Oct 1, 1996• 6 citations
Publisher

Abstract

In this paper we propose a new and simple velocity selective method, which combines the velocity selective coherent population trapping of atoms in a light field and the kinetic energy coupling between the dark state and coupled state(s) during free flight, in order to reach a very narrow momentum distribution in a short period of time. This technique combined with force-assisted velocity selective coherent population trapping can produce very efficient cooling and trapping. It can also be used to overcome the cooling limit caused by the leakage of the dark state.

DOI
10.1088/1355-5111/8/5/004

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In this paper we propose a new and simple velocity selective method, which combines the velocity selective coherent population trapping of atoms in a light field and the kinetic energy coupling between the dark state and coupled state(s) during free flight, in order to reach a very narrow momentum distribution in a short period of time. This technique combined with force-assisted velocity selective coherent population trapping can produce very efficient cooling and trapping. It can also be used to overcome the cooling limit caused by the leakage of the dark state.
We have theoretically studied a one-dimensional light field configuration which combines velocity-selective coherent-population trapping with the action of a novel kind of sub-Doppler force providing efficient cooling below the recoil limit. The force is based on velocity-induced non-adiabatic passage of atomic population from the non-coupling state to the light-shifted coupling state. We show for 87Rb that within 0.88 ms 35% of an initial distribution of 12k width can be cooled into a 0.5k momentum interval, and that more than 90% of the initial distribution are still confined to 12k width.
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.
Velocity-selective coherent population trapping is a technique for laser-cooling atoms to below the recoil limit where the momenta of the atoms and photons in the light field are equal. We have studied this mechanism using an efficient simulation model, which both simplifies the calculations and gives a physical insight into the dynamics of the anomalous diffusion process. Our calculations have been carried out for transitions in which the total atomic angular momentum is F=1 to 1 in both one and two dimensions and F=2 to 2 in one dimension. In the latter case, no exact dark state exists, and the momentum distribution tends towards a Lorentzian in the steady state.
Atoms can be accumulated by velocity-selective coherent population trapping (VSCPT) in dark states of very highly monovelocity, resulting in very narrow distributions. The optical pumping process that permits the population accumulation proceeds by random walk in momentum space and is of limited efficiency. Several authors have predicted that damping forces can enhance VSCPT in carefully chosen laser fields. We present corroboration of this idea with measurements showing increased efficiency for VSCPT.
We present a theoretical analysis of a new one-dimensional laser-cooling scheme that was recently demonstrated on a beam of metastable 4He atoms. Both internal and translational degrees of freedom are treated quantum mechanically. Unlike semiclassical approaches, such a treatment can be applied to situations in which the atomic coherence length is of the same order of or larger than the laser wavelength, which is the case for atoms cooled below the one-photon recoil energy. We introduce families of states that are closed with respect to absorption and stimulated emission, and we establish the generalized optical Bloch equations that are satisfied by the corresponding matrix elements. The existence of velocity-selective trapping states that are linear combinations of states with different internal and translational quantum numbers is demonstrated, and the mechanism of accumulation of atoms in these trapping states by fluorescence cycles is analyzed. From a numerical solution of the generalized optical Bloch equations, we study in detail how the final atomic-momentum distribution depends on the various physical parameters: interaction time, width of the initial distribution, laser detuning, laser power, and imbalance between the two counterpropagating waves. We show that the final temperature decreases when the interaction time increases, so that there is no fundamental limit to the lowest temperature that can be achieved by such a method. Finally, possible extensions of this method to two-dimensional cooling are presented.