Mean-field model for the interference of matter waves from a three-dimensional optical trap

TL;DR

This paper models the interference patterns of Bose-Einstein condensates in combined optical and harmonic traps using the Gross-Pitaevskii equation, matching experimental observations and predicting long-lived oscillations.

Contribution

It introduces a mean-field model that accurately reproduces experimental interference patterns and predicts their long-term oscillations in 2D and 3D traps.

Findings

Interference patterns of 27 bright spots in 3D and 9 in 2D are observed.

Patterns can form upon removal of optical lattice only.

Oscillations of the interference pattern can persist for a long time.

Abstract

Using the mean-field time-dependent Gross-Pitaevskii equation we study the formation of a repulsive Bose-Einstein condensate on a combined optical and harmonic traps in two and three dimensions and subsequent generation of the interference pattern upon the removal of the combined traps as in the experiment by Greiner {\it et al.} [Nature (London) {\bf 415}, 39 (2002)]. For optical traps of moderate strength, interference pattern of 27 (9) prominent bright spots is found to be formed in three (two) dimensions on a cubic (square) lattice in agreement with experiment. Similar interference pattern can also be formed upon removal of the optical lattice trap only. The pattern so formed can oscillate for a long time in the harmonic trap which can be observed experimentally.