Quantum fluctuation induced time of flight correlations of an interacting trapped Bose gas

TL;DR

This study numerically analyzes momentum correlations in a 2D trapped Bose gas at zero temperature, revealing quantum fluctuation-induced anti-correlations and weak positive correlations, highlighting quantum coherence effects.

Contribution

It introduces a particle number preserving Bogoliubov approach to identify quantum fluctuation effects on momentum correlations in trapped Bose gases.

Findings

Large anti-correlation dip at wave numbers ~1/R_c due to quantum fluctuations

Weak positive correlation at larger wave numbers

Anti-correlation as a fingerprint of coherent quantum fluctuations

Abstract

We investigate numerically the momentum correlations in a two dimensional, harmonically trapped interacting Bose system at $T=0$ temperature, by using a particle number preserving Bogoliubov approximation. Interaction induced quantum fluctuations of the quasi-condensate lead to a large anti-correlation dip between particles of wave numbers $\mathbf{k}$ and $-\mathbf{k}$ for $|\mathbf{k}|\sim 1/R_c$, with $R_c$ typical size of the condensate. The anti-correlation dip found is a clear fingerprint of coherent quantum fluctuations of the condensate. In contrast, for larger wave numbers, $|\mathbf{k}| >> 1/R_c$, a weak positive correlation is found between particles of wave numbers $\mathbf{k}$ and $-\mathbf{k}$, in accordance with the Bogoliubov result for homogeneous interacting systems.