Coherence time of a Bose-Einstein condensate in an isolated harmonically trapped gas

TL;DR

This paper investigates the phase coherence dynamics of a Bose-Einstein condensate in an isolated, harmonically trapped gas, revealing universal long-time behavior characterized by ballistic and diffusive growth of phase variance.

Contribution

It provides analytical expressions for the phase variance growth in the collisionless, ergodic regime, highlighting a new universality class distinct from homogeneous gases.

Findings

Phase variance exhibits ballistic and diffusive growth at long times.

Universal functions describe the phase dynamics when scaled by temperature and chemical potential.

The universality class differs from that of homogeneous Bose gases.

Abstract

We study the condensate phase dynamics in a low-temperature equilibrium gas of weakly interacting bosons, harmonically trapped and isolated from the environment. We find that at long times, much longer than the collision time between Bogoliubov quasiparticles, the variance of the phase accumulated by the condensate grows with a ballistic term quadratic in time and a diffusive term affine in time. We give the corresponding analytical expressions in the limit of a large system, in the collisionless regime and in the ergodic approximation for the quasiparticle motion. When properly rescaled, they are described by universal functions of the temperature divided by the Thomas-Fermi chemical potential. The same conclusion holds for the mode damping rates. Such universality class differs from the previously studied one of the homogeneous gas.