Collapses and revivals of matter waves

TL;DR

This paper analytically studies quantum collapses and revivals in Bose-Einstein condensates using the two-site Bose-Hubbard model, providing formulas for collapse and revival times and peak shapes.

Contribution

It introduces an analytic expression valid in the weak coupling limit that accurately describes collapses and revivals in the two-site Bose-Hubbard model.

Findings

Analytic expression matches numerical results for collapse and revival dynamics.

First-order interaction calculations predict collapse and revival times.

Second-order interactions are necessary for peak shape accuracy.

Abstract

Quantum collapses and revivals are fascinating manifestations of interference. Of particular interest in recent years are macroscopic quantum interference effects in Bose-Einstein condensates. In this letter such effects will be studied for the two site Bose-Hubbard model that is a standard model for exploration of Bose-Einstein condensates. An analytic expression that is valid in the weak coupling limit for the difference in the occupation of the two sites is developed and tested numerically. It describes correctly the collapses and revivals. Moreover, it is demonstrated that a calculation to the first order in the interparticle interaction is required for the prediction of the collapse and revival times while the second order is required for the evaluation of the shape of the revival peaks. We believe that the result is relevant for a variety of situations where collapses and revivals are found.