Harmonically trapped Fermi gas: Temperature dependence of the Tan contact

TL;DR

This paper investigates how the Tan contact in small harmonically trapped Fermi gases varies with temperature, using a cluster expansion approach and comparing different quantum statistics to understand universal relations in ultracold gases.

Contribution

It introduces a cluster expansion method to accurately compute the Tan contact across temperature regimes and quantifies finite-range effects in trapped Fermi gases.

Findings

Cluster expansion accurately describes high-temperature Tan contact.

Finite-range corrections are quantitatively characterized.

Fermi statistics influence the Tan contact compared to Bose and Boltzmann statistics.

Abstract

Ultracold atomic gases with short-range interactions are characterized by a number of universal species-independent relations. Many of these relations involve the two-body Tan contact. Employing the canonical ensemble, we determine the Tan contact for small harmonically trapped two-component Fermi gases at unitarity over a wide range of temperatures, including the zero and high temperature regimes. A cluster expansion that describes the properties of the N-particle system in terms of those of smaller subsystems is introduced and shown to provide an accurate description of the contact in the high temperature regime. Finite-range corrections are quantified and the role of the Fermi statistics is elucidated by comparing results for Fermi, Bose and Boltzmann statistics.