Bose-Einstein condensation in an optical lattice: A perturbation approach

TL;DR

This paper derives analytical expressions for the properties of a Bose-Einstein Condensate in a one-dimensional optical lattice under weak interactions, validating the approach against numerical calculations.

Contribution

It presents a perturbative analytical method for describing BECs in optical lattices, identifying conditions where the ground state simplifies to a harmonic oscillator wave function.

Findings

Analytical expressions match numerical results within certain parameter ranges.

Optical lattice can counteract interaction effects, simplifying the ground state.

The approach delineates the validity range of perturbative solutions.

Abstract

We derive closed analytical expressions for the order parameter $\Phi (x)$ and for the chemical potential $\mu $ of a Bose-Einstein Condensate loaded into a harmonically confined, one dimensional optical lattice, for sufficiently weak, repulsive or attractive interaction, and not too strong laser intensities. Our results are compared with exact numerical calculations in order to map out the range of validity of the perturbative analytical approach. We identify parameter values where the optical lattice compensates the interaction-induced nonlinearity, such that the condensate ground state coincides with a simple, single particle harmonic oscillator wave function.