Geometric potentials for subrecoil dynamics

Abstract

Quantum motion of atoms in light fields is described on the basis of adiabatic internal states. Forces arise due to the spatial variation of these states, which is determined by the electric field polarization. In a dark state, these are the only forces present. They are described by a geometric vector and a scalar potential. We give analytical expressions for the geometric potentials in the dark states of a driven $\stackrel{\ensuremath{\rightarrow}}{j}j\ensuremath{-}1$ transition and the dark state in the $\stackrel{\ensuremath{\rightarrow}}{1}1$ system, for arbitrary electromagnetic fields. For systems with velocity selective trapping states, the scalar geometric potential is inversely proportional to the field intensity squared. When the field has nodes the potential diverges. In one dimension, this constitutes an exact realization of the Kronig-Penney model.