Uncertainty product of an out-of-equilibrium Bose-Einstein condensate

TL;DR

This paper investigates the uncertainty product of position and momentum in an out-of-equilibrium Bose-Einstein condensate, revealing non-monotonous behavior and differences from mean-field predictions during dynamics and fragmentation.

Contribution

It provides the first analysis of uncertainty products in out-of-equilibrium BECs, highlighting deviations from mean-field results during interaction quenches and fragmentation.

Findings

Uncertainty product exhibits non-monotonous behavior during fragmentation.

Differences from mean-field quantities emerge even with slight depletion.

Position variance decreases while density broadens during fragmentation.

Abstract

The variance and uncertainty product of the position and momentum many-particle operators of structureless bosons interacting by a long-range inter-particle interaction and trapped in a single-well potential are investigated. In the first example, of an out-of-equilibrium interaction-quench scenario, it is found that, despite the system being fully condensed, already when a fraction of a particle is depleted differences with respect to the mean-field quantities emerge. In the second example, of the pathway from condensation to fragmentation of the ground state, we find out that, although the cloud's density broadens while the system's fragments, the position variance actually decreases, the momentum variance increases, and the uncertainty product is not a monotonous function but has a maximum. Implication are briefly discussed.