Homoclinic signatures of dynamical localization

Departamento de Física Aplicada, Escuela de Ingenierías Industriales, Universidad de Extremadura, Apartado Postal 382, E-06071 Badajoz, Spain

Received: 29 August 2006
Accepted: 28 November 2006

Abstract

It is demonstrated that the oscillations in the width of the momentum distribution of atoms moving in a phase-modulated standing light field, as a function of the modulation amplitude , are correlated with the variation of the chaotic layer width in energy of an underlying effective pendulum. The maximum effect of dynamical localization and the nearly perfect delocalization are associated with the maxima and minima, respectively, of the chaotic layer width. It is also demonstrated that kinetic energy is conserved as an almost adiabatic invariant at the minima of the chaotic layer width, and that the system is accurately described by delta-kicked rotors at sufficiently large zeros of the Bessel functions and . Numerical calculations of kinetic energy and Lyapunov exponents confirm all the theoretical predictions.