Disorder-Induced Shift of Condensation Temperature for Dilute Trapped Bose Gases

TL;DR

This paper investigates how weak disorder affects the Bose-Einstein condensation temperature in ultracold dilute gases trapped in harmonic potentials, revealing a non-monotonic shift depending on disorder correlation length.

Contribution

It provides a detailed analysis of the leading order shift in condensation temperature caused by disorder with different spatial correlations, highlighting a maximum at a critical correlation length.

Findings

Positive shift of condensation temperature increases then decreases with correlation length.

Maximum temperature shift occurs at a specific correlation length.

Disorder correlation length critically influences the condensation temperature shift.

Abstract

We determine the leading shift of the Bose-Einstein condensation temperature for an ultracold dilute atomic gas in a harmonic trap due to weak disorder by treating both a Gaussian and a Lorentzian spatial correlation for the quenched disorder potential. Increasing the correlation length from values much smaller than the geometric mean of the trap scale and the mean particle distance to much larger values leads first to an increase of the positive shift to a maximum at this critical length scale and then to a decrease.