Universal contact of strongly interacting fermions at finite temperatures

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 $\mathcal{I}$. 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, $T\ll T_c\sim 0.2T_F$. We also discuss briefly how to measure the universal contact either in homogeneous or harmonically trapped Fermi gases.

15 pages, 10 figures

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Cited by in corpus (23)

• Measurement of the Homogeneous Contact of a Unitary Fermi gas
• Precise determination of the structure factor and contact in a unitary Fermi gas
• Spectral response and contact of the unitary Fermi gas
• Momentum Distribution and Contact of the Unitary Fermi gas
• Universal contact for a Tonks-Girardeau gas at finite temperature
• Contact and sum-rules in a near-uniform Fermi gas at unitarity
• High-momentum tails as magnetic structure probes for strongly-correlated $SU(\kappa )$ fermionic mixtures in one-dimensional traps
• Making statistics work: a quantum engine in the BEC-BCS crossover
• Universal pair-polaritons in a strongly interacting Fermi gas
• Critical behaviours of contact near phase transitions
• Expansion of harmonically trapped interacting particles and time dependence of the contact
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• The fourth- and fifth-order virial coefficients from weak-coupling to unitarity
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• Tan's adiabatic sweep theorem from the variational theorem for the scattering length
• Temperature dependence of $p$-wave contacts in a harmonically trapped Fermi gas
• Measurement of $p$-wave contacts in an ultracold Fermi gas of ${}^6$Li atoms
• Toward an automated-algebra framework for high orders in the virial expansion of quantum matter