Cold Atoms in Driven Optical Lattices

TL;DR

This paper analyzes the dynamics and stability of cold atoms and Bose-Einstein condensates in one-dimensional driven optical lattices, providing analytical and numerical insights into recurrence times, energy spectra, and the effects of external forcing across different interaction regimes.

Contribution

It develops an analytical formalism for both deep and shallow optical lattices and explores the stability and recurrence behavior of condensates under external driving forces.

Findings

Analytical expressions for energy spectrum and recurrence times in different regimes.

Good agreement between analytical and numerical stability analyses.

Identification of conditions for delicate and robust recurrences in driven lattices.

Abstract

The center of mass dynamics of cold atoms and the Bose-Einstein condensate in one dimensional optical lattice is considered both in the absence and in the presence of external forcing. We discuss three situations for matter waves: first, the cold atoms; second, sufficiently dilute condensate where the dynamics are governed by the single particle wave packet dynamics; third, strong interaction regime, where, inter-atomic interaction can no longer be ignored. The analytical formalism developed for the two regimes, namely, deep optical lattice and shallow optical lattice. Parametric dependencies of energy spectrum and classical period, revival time and super revival are explained for the two regimes. The dynamics of condensate in driven optical lattice crystal are analyzed by studying dynamical stability of the condensate. The stability is determined by the dispersion behavior of the condensate excited in driven optical lattice. The recurrence behavior of the condensate close to the nonlinear resonances is analyzed as a function of time for delicate recurrences which take place for instance when lattice is weakly perturbed and robust recurrences which may manifest themselves for sufficiently strong external driving force. The analysis is not only valid for dilute condensate but also applicable for strongly interacting homogeneous condensate provided, the external modulation causes no significant change in density profile of the condensate. We explain parametric dependence of the dynamical recurrence times which can easily be realized in laboratory experiments. In addition, we find a good agreement between the obtained analytical results and numerical calculations. The stability of condensate is also explored in driven optical lattice numerically.