Photo-excitation measurement of Tan's contact for a strongly interacting Fermi gas

TL;DR

This paper derives an exact theoretical relation linking Tan's contact to photo-excitation rates in strongly interacting Fermi gases, enabling improved measurement of Tan's contact coefficient.

Contribution

The authors generalize previous relations between Tan's contact and molecular fractions, providing a new theoretical tool for experimental measurement in strongly interacting Fermi gases.

Findings

The derived relation agrees with recent experimental data near the unitary limit.

It offers a method to measure Tan's contact coefficient at finite temperature.

The relation extends previous models to include photo-excitation processes.

Abstract

We derive theoretically an exact relation between Tan's universal contact and the photo-excitation rate of a strongly interacting Fermi gas, in the case of optically transferring fermionic pairs to a more tightly bound molecular state. Our deviation generalizes the relation between Tan's contact and the closed-channel molecular fraction found earlier by Werner, Tarruell and Castin in Eur. Phys. J. B \textbf{68}, 401 (2009). We use the relation to understand the recent low-temperature photo-excitation measurement in a strongly interacting $^{6}$Li Fermi gas {[}Liu \textit{et al.}, arXiv:1903.12321{]} and show that there is a reasonable agreement between theory and experiment close to the unitary limit. We propose that our relation can be applied to accurately measure Tan's contact coefficient at finite temperature in future experiments.