Exploring the Thermodynamics of a Universal Fermi Gas

TL;DR

This paper develops a precise method to determine the equation of state of a uniform unitary Fermi gas, providing new insights into its thermodynamics, phase transitions, and quasiparticle behavior in strongly interacting quantum systems.

Contribution

It introduces a novel approach for measuring the equation of state of a uniform Fermi gas at unitarity, enabling detailed comparison with theories and revealing new physical phenomena.

Findings

The low-temperature thermodynamics of the normal phase aligns with Fermi liquid theory.

The superfluid transition is precisely localized.

The normal phase behaves as a mixture of a Fermi gas and fermionic polarons.

Abstract

From sand piles to electrons in metals, one of the greatest challenges in modern physics is to understand the behavior of an ensemble of strongly interacting particles. A class of quantum many-body systems such as neutron matter and cold Fermi gases share the same universal thermodynamic properties when interactions reach the maximum effective value allowed by quantum mechanics, the so-called unitary limit [1,2]. It is then possible to simulate some astrophysical phenomena inside the highly controlled environment of an atomic physics laboratory. Previous work on the thermodynamics of a two-component Fermi gas led to thermodynamic quantities averaged over the trap [3-5], making it difficult to compare with many-body theories developed for uniform gases. Here we develop a general method that provides for the first time the equation of state of a uniform gas, as well as a detailed comparison with existing theories [6,14]. The precision of our equation of state leads to new physical insights on the unitary gas. For the unpolarized gas, we prove that the low-temperature thermodynamics of the strongly interacting normal phase is well described by Fermi liquid theory and we localize the superfluid transition. For a spin-polarized system, our equation of state at zero temperature has a 2% accuracy and it extends the work of [15] on the phase diagram to a new regime of precision. We show in particular that, despite strong correlations, the normal phase behaves as a mixture of two ideal gases: a Fermi gas of bare majority atoms and a non-interacting gas of dressed quasi-particles, the fermionic polarons [10,16-18].