Non-equilibrium dynamics of a Bose-Einstein condensate in an optical lattice

TL;DR

This paper investigates the far-from-equilibrium dynamics of a strongly interacting Bose-Einstein condensate in a one-dimensional optical lattice using advanced theoretical techniques, revealing damping of oscillations and non-condensate fractions.

Contribution

It introduces a self-consistent functional integral approach beyond mean-field theory to analyze non-equilibrium dynamics in the Bose-Hubbard model.

Findings

Damped oscillations of condensate and non-condensate fractions observed.

Comparison shows improved accuracy over Hartree-Fock-Bogoliubov mean-field theory.

Results align with exact quantum dynamics for small atom numbers.

Abstract

The dynamical evolution of a Bose-Einstein condensate trapped in a one-dimensional lattice potential is investigated theoretically in the framework of the Bose-Hubbard model. The emphasis is set on the far-from-equilibrium evolution in a case where the gas is strongly interacting. This is realized by an appropriate choice of the parameters in the Hamiltonian, and by starting with an initial state, where one lattice well contains a Bose-Einstein condensate while all other wells are empty. Oscillations of the condensate as well as non-condensate fractions of the gas between the different sites of the lattice are found to be damped as a consequence of the collisional interactions between the atoms. Functional integral techniques involving self-consistently determined mean fields as well as two-point correlation functions are used to derive the two-particle-irreducible (2PI) effective action. The action is expanded in inverse powers of the number of field components N, and the dynamic equations are derived from it to next-to-leading order in this expansion. This approach reaches considerably beyond the Hartree-Fock-Bogoliubov mean-field theory, and its results are compared to the exact quantum dynamics obtained by A.M. Rey et al., Phys. Rev. A 69, 033610 (2004) for small atom numbers.