Geometric potentials in quantum optics: A semi-classical interpretation

¹  Laboratoire Kastler Brossel and CNRS, Ecole Normale Supérieure - 24 rue Lhomond, 75005 Paris, France
²  Institute of Theoretical Physics and Astronomy of Vilnius University - A. Gostauto 12, Vilnius 01108, Lithuania

Corresponding author: jean.dalibard@lkb.ens.fr

Received: 25 July 2008
Accepted: 6 August 2008

Abstract

We propose a semi-classical interpretation of the geometric scalar and vector potentials that arise due to Berry's phase when an atom moves slowly in a light field. Starting from the full quantum Hamiltonian, we turn to a classical description of the atomic centre-of-mass motion while still treating the internal degrees of freedom as quantum variables. We show that the scalar potential can be identified as the kinetic energy of an atomic micro-motion caused by quantum fluctuations of the radiative force, and that the Lorentz-type force appears as a result of the motion-induced perturbation of the internal atomic state. For a specific configuration involving two counter-propagating Gaussian laser beams, we relate the geometric forces to the radiation pressure and dipole forces known from quantum optics. The simple physical pictures provided by the present analysis may help for the design and the implementation of novel geometric forces.