Universal contact of strongly interacting fermions at finite temperatures

TL;DR

This paper investigates the temperature dependence of the universal contact in strongly interacting Fermi gases, providing theoretical calculations across temperature regimes and suggesting experimental approaches for measurement.

Contribution

It offers the first comprehensive theoretical analysis of the universal contact's temperature dependence in Fermi gases, including high-temperature virial expansion and low-temperature comparisons.

Findings

Contact decreases monotonically with temperature in the unitarity limit.

Virial expansion is reliable above the Fermi temperature.

Different strong coupling theories predict varying low-temperature behaviors.

Abstract

The recently discovered universal thermodynamic behaviour of dilute, strongly interacting Fermi gases also implies a universal structure in the many-body pair-correlation function at short distances, as quantified by the contact ${\cal I}$. This quantity is an excellent indicator of the presence of strong correlations in these systems, which provide a highly accessible physical model for other strongly correlated quantum fluids. Here we theoretically calculate the temperature dependence of this universal contact for a Fermi gas in free space and in a harmonic trap. At high temperatures above the Fermi degeneracy temperature, $T\gtrsim T_{F}$, we obtain a reliable non-perturbative quantum virial expansion up to third order. At low temperatures we compare different approximate strong coupling theories. These make different predictions, which need to be tested either by future experiments or advanced quantum Monte Carlo simulations. We conjecture that in the universal unitarity limit, the contact or correlation decreases monotonically with increasing temperature, unless the temperature is significantly lower than the critical temperature, $T\ll T_{c}\sim0.2T_{F}$. We also discuss briefly how to measure the universal contact either in homogeneous or harmonically trapped Fermi gases.