Laser cooling and trapping of neutral atoms: theory

Abstract

The purpose of this report is to present a survey of recent theoretical advances in the field of Laser Cooling and Trapping of Neutral Atoms and to point out a few general trends. The subsequent report, by Aspect, will cover the experimental developments. It is of course impossible, in a short time, to present an exhaustive review. Several important works will not even be mentioned. I apologize in advance for the incompleteness of this presentation. I have chosen here to put the emphasis on general questions such as: — What are the physical mechanisms allowing one to manipulate the velocity and the position of an atom? — What are the fundamental limits for the lowest temperatures which can be achieved by these methods? — What can we learn from this field? Are there any new concepts, new points of view, new approaches which could be useful for other branches of Physics? We begin this report by recalling the basic physical processes, which consist of resonant exchanges of energy and momentum between photons and atoms in elementary emission and absorption processes. The atom falls from the excited state e to the ground state g by emitting a photon k, the atomic momentum changing from p to p — Ilk. Or, it can absorb a photon k and jump from g to e, gaining a momentum Ilk. The important point is that the momentum change is always connected with a change of internal state. There is therefore a strong interplay between these two types of atomic degrees of freedom. The description of their coupled evolution involves a lot of characteristic times, such as the radiative lifetime TR of the excited state e, which is also the inverse of the spontaneous emission rate F; the optical pumping time r~between the ground state Zeeman sublevels; the velocity damping time Text,. . . And this raises the important question of finding the slow variables of the problem, which “slave” the other ones. Another very important point is that spontaneous emission introduces fluctuations and dissipation in the atomic evolution. This is not surprising, since spontaneous emission results from the coupling of the atom with a large reservoir, which is the quantum radiation field in its vacuum state. The interest of spontaneous emission is that it provides a simple basic model of a quantum dissipative process. In a certain sense, laser cooling and trapping can be considered as a continuation of Einstein’s pioneering work of 1917, showing for the first time how atoms could reach thermal equilibrium by exchanging