How to measure the free energy and partition function from atom-atom correlations

TL;DR

This paper introduces an experimental method to determine thermodynamic properties of ultracold atomic gases by measuring local atom-atom correlations and applying the Hellmann-Feynman theorem, validated on the 1D Bose gas model.

Contribution

It presents a novel approach to directly measure free energy and partition function from correlation data, applicable to ultracold atomic gases.

Findings

The method accurately estimates free energy in the 1D Bose gas.

Analytic expressions agree well with exact thermodynamic Bethe ansatz results.

The approach is promising for experimental thermodynamics in quantum gases.

Abstract

We propose an experimental approach for determining thermodynamic properties of ultracold atomic gases with short-range interactions. As a test case, we focus on the one-dimensional (1D) Bose gas described by the integrable Lieb-Liniger model. The proposed approach relies on deducing the Helmholtz or Landau free energy directly from measurements of local atom-atom correlations by utilising the inversion of a finite-temperature version of the Hellmann-Feynman theorem. We demonstrate this approach theoretically by deriving approximate analytic expressions for the free energies in specific asymptotic regimes of the 1D Bose gas and find excellent agreement with the exact results based on the thermodynamic Bethe ansatz available for this integrable model.