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

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.