The uncertainty product of an out-of-equilibrium many-particle system

TL;DR

This paper shows that the uncertainty product in an out-of-equilibrium Bose-Einstein condensate can deviate from mean-field predictions due to many-body correlations, even with an infinite number of particles.

Contribution

It demonstrates the necessity of many-body theories to accurately describe out-of-equilibrium BECs, highlighting deviations from Gross-Pitaevskii dynamics.

Findings

Uncertainty product deviates from GP predictions during dynamics

Many-body correlations influence the reduced two-body density matrix

Deviations occur even in the infinite particle limit

Abstract

In the present work we show, analytically and numerically, that the variance of many-particle operators and their uncertainty product for an out-of-equilibrium Bose-Einstein condensate (BEC) can deviate from the outcome of the time-dependent Gross-Pitaevskii dynamics, even in the limit of infinite number of particles and at constant interaction parameter when the system becomes 100% condensed. We demonstrate our finding on the dynamics of the center-of-mass position--momentum uncertainty product of a freely expanding as well as of a trapped BEC. This time-dependent many-body phenomenon is explained by the existence of time-dependent correlations which manifest themselves in the system's reduced two-body density matrix used to evaluate the uncertainty product. Our work demonstrates that one has to use a many-body propagation theory to describe an out-of-equilibrium BEC, even in the infinite particle limit.