A generalized molecule approach capturing the Feshbach-induced pairing physics in the BEC–BCS crossover

Abstract

By including the effect of a trap with characteristic energy given by the Fermi temperature TF in a two-body two-channel model for Feshbach resonances, we reproduce the measured binding energy of ultracold molecules in a 40K atomic Fermi gas. We also reproduce the experimental closed-channel fraction Z across the BEC–BCS crossover and into the BCS regime of a 6Li atomic Fermi gas. We obtain the expected behavior Z ∝ √TF at unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of the Z dependency on TF on the BCS side, where a significant quantitative discrepancy between experimental data and theory’s predictions has been repeatedly reported. In order to contrast with future experiments we report the proportionality constant at unitarity between Z and √TF predicted by our model for a 40K atomic Fermi gas.