# Universal contact of strongly interacting fermions at finite temperatures - Condensed Matter > Quantum Gases

Abstract: The recently discovered universal thermodynamic behaviour of dilute, stronglyinteracting Fermi gases also implies a universal structure in the many-bodypair-correlation function at short distances, as quantified by the contact${\cal I}$. This quantity is an excellent indicator of the presence of strongcorrelations in these systems, which provide a highly accessible physical modelfor other strongly correlated quantum fluids. Here we theoretically calculatethe temperature dependence of this universal contact for a Fermi gas in freespace and in a harmonic trap. At high temperatures above the Fermi degeneracytemperature, $T\gtrsim T {F}$, we obtain a reliable non-perturbative quantumvirial expansion up to third order. At low temperatures we compare differentapproximate strong coupling theories. These make different predictions, whichneed to be tested either by future experiments or advanced quantum Monte Carlosimulations. We conjecture that in the universal unitarity limit, the contactor correlation decreases monotonically with increasing temperature, unless thetemperature is significantly lower than the critical temperature, $T\llT {c}\sim0.2T {F}$. We also discuss briefly how to measure the universalcontact either in homogeneous or harmonically trapped Fermi gases.

Author: Hui Hu, Xia-Ji Liu, Peter D. Drummond

Source: https://arxiv.org/