Quantum fluctuations in the image of a Bose gas

TL;DR

This paper investigates the quantum and thermal fluctuations in ultracold Bose gas density profiles, analyzing how these fluctuations influence measurement precision and potentially enhance soliton position detection.

Contribution

It introduces a method to compute the Fisher information from density correlations, extending previous work on soliton measurements to a broader class of solutions.

Findings

Quantum and thermal fluctuations affect image noise.

Fluctuations can improve soliton position estimation.

Derived sensitivity bounds for measuring observables in Bose gases.

Abstract

We analyze the information content of density profiles for an ultracold Bose gas of atoms and extract resolution limits for observables contained in these images. Our starting point is density correlations that we compute within the Bogoliubov approximation, taking into account quantum and thermal fluctuations beyond mean-field theory. This provides an approximate way to construct the joint counting statistics of atoms in an array of pixels covering the gas. We derive the Fisher information of an image and the associated Cramer-Rao sensitivity bound for measuring observables contained in the image. We elaborate on our recent study on position measurements of a dark soliton [Negretti et al., Phys. Rev. A 77, 043606 (2008)] where a sensitivity scaling with the atomic density as n^{-3/4} was found. We discuss here a wider class of soliton solutions and present a detailed analysis of the Bogoliubov excitations and the gapless (Goldstone) excitation modes. These fluctuations around the mean field contribute to the noise in the image, and we show how they can actually improve the ability to locate the position of the soliton.