Analytic thermodynamics and thermometry of Gaudin-Yang Fermi gases

TL;DR

This paper simplifies the thermodynamic analysis of the one-dimensional attractive Fermi gas with spin imbalance, making it more accessible for experimental applications and enabling precise thermometry.

Contribution

It reduces the complex thermodynamic Bethe ansatz solution to four algebraic equations, providing a universal and exact approach in relevant experimental regimes.

Findings

Simplified thermodynamic equations for the Gaudin-Yang model.

Qualitative analysis of finite-temperature crossover.

Practical scheme for accurate thermometry in experiments.

Abstract

We study the thermodynamics of a one-dimensional attractive Fermi gas (the Gaudin-Yang model) with spin imbalance. The exact solution has been known from the thermodynamic Bethe ansatz for decades, but it involves an infinite number of coupled nonlinear integral equations whose physics is difficult to extract. Here the solution is analytically reduced to a simple, powerful set of four algebraic equations. The simplified equations become universal and exact in the experimental regime of strong interaction and relatively low temperature. Using the new formulation, we discuss the qualitative features of finite-temperature crossover and make quantitative predictions on the density profiles in traps. We propose a practical two-stage scheme to achieve accurate thermometry for a trapped spin-imbalanced Fermi gas.