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Quantum Electronics and Laser Science Conference

Realistic theory of laser cooling

Juha Javanainen

Published May 12, 1991• 0 citations
OpenAlex

Abstract

We present a theory of laser cooling and trapping that applies to an atom with an arbitrary level structure moving at a (nearly) arbitrary velocity in a (nearly) arbitrary three-dimensional light field.

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A review is presented of some of the principal techniques of laser cooling and trapping that have been developed during the past 20 years. Its approach is primarily experimental, but its quantitative descriptions are consistent in notation with most of the theoretical literature. It begins with a simplified introduction to optical forces on atoms, including both cooling and trapping. Then its three main sections discuss its three selected features, (1) quantization of atomic motion, (2) effects of the multilevel structure of atoms, and (3) the effects of polychromatic light. Each of these features is an expansion in a different direction from the simplest model of a classical, two-level atom moving in a monochromatic laser field.
In this work Matlab simulation of the atomic Liouville equation for spontaneous emissions was developed for laser cooling of Radium atoms. The atomic decay time driven was determined according to the photon account. The theory includes the mechanical light effect for to atomic structure. The study followed the stimulating solution of Optical Bloch Equations (OBE’s) for four levels system in an atom trap, where the center of mass motion is described quantum mechanically. The results showed that the laser cooling approach to Maxwell’s law, the reduction of the velocity leads to new distribution of velocities and the atoms moving towards the light source will resonate the light field (crossing resonance).
In the limit of asymptotically small photon momentum, a Fokker–Planck equation for the center-of-mass Wigner function suffices to describe laser cooling of an atom. We have devised a procedure to compute the light pressure force and the diffusion tensor for an atom with an arbitrary level structure, traveling with an arbitrary velocity in any given three-dimensional light field. The scheme is based on solving a set of differential equations closely related to the density matrix equations of motion encountered in conventional recoilless laser spectroscopy. Computer programs have been written that automatically construct and solve the required equations from broad specifications of the problem, such as energies and angular momenta of the atomic levels. A Langevin equation stochastic simulation has been implemented to solve the Fokker-Planck equation of laser cooling using the computed force and diffusion. Comparisons of optical-molasses experiments and simulations carried out for a model sodium atom with a J = 2→J = 3 transition show qualitative similarities such as sub-Doppler limit temperatures, but the quantitative agreement of theory and experiment is not satisfactory.