Density ripples in expanding low-dimensional gases as a probe of correlations

TL;DR

This paper provides analytical relations linking the density ripples observed during the expansion of low-dimensional ultracold Bose gases to their initial correlation functions, enabling insights into quantum and thermal fluctuations.

Contribution

It introduces simple analytical formulas for the density ripple spectrum after expansion, applicable to various regimes including 1D and 2D Bose gases, and demonstrates how to extract correlation exponents from experimental data.

Findings

Analytical expression for density ripples in weakly interacting 1D Bose gases.

Self-similar density ripple spectrum in 2D Bose gases below BKT transition.

Method to determine correlation function exponents from ripple evolution.

Abstract

We investigate theoretically the evolution of the two-point density correlation function of a low-dimensional ultracold Bose gas after release from a tight transverse confinement. In the course of expansion thermal and quantum fluctuations present in the trapped systems transform into density fluctuations. For the case of free ballistic expansion relevant to current experiments, we present simple analytical relations between the spectrum of ``density ripples'' and the correlation functions of the original confined systems. We analyze several physical regimes, including weakly and strongly interacting one-dimensional (1D) Bose gases and two-dimensional (2D) Bose gases below the Berezinskii-Kosterlitz-Thouless (BKT) transition. For weakly interacting 1D Bose gases, we obtain an explicit analytical expression for the spectrum of density ripples which can be used for thermometry. For 2D Bose gases below the BKT transition, we show that for sufficiently long expansion times the spectrum of the density ripples has a self-similar shape controlled only by the exponent of the first-order correlation function. This exponent can be extracted by analyzing the evolution of the spectrum of density ripples as a function of the expansion time.