Number fluctuations in cold quantum gases

TL;DR

This paper investigates quantum number fluctuations in ultracold gases at zero temperature, revealing non-extensive scaling behaviors and analyzing fluctuations across different quantum regimes.

Contribution

It provides a systematic analysis of zero-temperature number fluctuations in homogeneous quantum gases, including the BEC-BCS crossover, with new calculations of subleading terms.

Findings

Fluctuations scale as R^2 ln R in 3D and as ln R in 1D.

Zero-temperature fluctuations are non-extensive.

The study covers both superfluid and Fermi gases across the BEC-BCS crossover.

Abstract

In ultracold gases many experiments use atom imaging as a basic observable. The resulting image is averaged over a number of realizations and mostly only this average is used. Only recently the noise has been measured to extract physical information. In the present paper we investigate the quantum noise arising in these gases at zero temperature. We restrict ourselves to the homogeneous situation and study the fluctuations in particle number found within a given volume in the gas, and more specifically inside a sphere of radius $R$. We show that zero-temperature fluctuations are not extensive and the leading term scales with sphere radius $R$ as $R^2\ln R$ (or $\ln R$) in three- (or one-) dimensional systems. We calculate systematically the next term beyond this leading order. We consider first the generic case of a compressible superfluid. Then we investigate the whole Bose-Einstein-condensation (BEC)-BCS crossover crossover, and in particular the limiting cases of the weakly interacting Bose gas and of the free Fermi gas.