Two-channel models of the BEC/BCS crossover

By including the effect of a trap with characteristic energy given by the Fermi temperature $T_F$ in a two-body two-channel model for Feshbach resonances, we reproduce the experimental closed-channel fraction $Z$ across the BEC-BCS crossover and into the BCS regime of a $^6$ Li atomic Fermi gas. We obtain the expected behavior $Z \propto \sqrt{T_F}$ at unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of the $Z$ dependency on $T_F$ on the BCS side, where a significant discrepancy between experiments and theory has been repeatedly reported.By including the effect of a trap with characteristic energy given by the Fermi temperature $T_F$ in a two-body two-channel model for Feshbach resonances, we reproduce the experimental closed-channel fraction $Z$ across the BEC-BCS crossover and into the BCS regime of a $^6$Li atomic Fermi gas. We obtain the expected behavior $Z \propto \sqrt{T_F}$ at unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of the $Z$ dependency on $T_F$ on the BCS side, where a significant discrepancy between experiments and theory has been repeatedly reported.

arXiv:2007.10901Jul 21, 20200 citations

The BEC–BCS Crossover

R. Combescot

Cambridge University Press eBooksMar 10, 20220 citations

Broad vs. narrow Fano-Feshbach resonances in the BCS-BEC crossover with trapped Fermi atoms

Stefano Simonucci, P. Pieri, Giancarlo Calvanese Strinati

With reference to the broad and narrow Fano-Feshbach resonances of 6 Li at about 822 G and 543 G, we show that for the broad resonance a molecular coupled-channel calculation can be mapped with excellent accuracy onto an effective single-channel problem with a contact interaction. This occurs for a wide enough range of the magnetic field that the full BCS-BEC crossover can be realized with a typical trap. For the narrow resonance, the mapping onto a single-channel problem and the realization of the BCS-BEC crossover are restricted to too narrow a range of the magnetic field to obtain them in practice. A general criterion is also formulated for deciding whether the BCS-BEC crossover can be exhausted within the single-channel model for any specific Fano-Feshbach resonance. In this way, the BCS-BEC crossover for Fermi atoms with the broad resonance is placed on the same footing as the corresponding crossover for different physical systems.With reference to the broad and narrow Fano-Feshbach resonances of 6 Li at about 822 G and 543 G, we show that for the broad resonance a molecular coupled-channel calculation can be mapped with excellent accuracy onto an effective single-channel problem with a contact interaction. This occurs for a wide enough range of the magnetic field that the full BCS-BEC crossover can be realized with a typical trap. For the narrow resonance, the mapping onto a single-channel problem and the realization of the BCS-BEC crossover are restricted to too narrow a range of the magnetic field to obtain them in practice. A general criterion is also formulated for deciding whether the BCS-BEC crossover can be exhausted within the single-channel model for any specific Fano-Feshbach resonance. In this way, the BCS-BEC crossover for Fermi atoms with the broad resonance is placed on the same footing as the corresponding crossover for different physical systems.

arXiv:cond-mat/0407600Europhysics Letters (EPL)Feb 1, 200552 citations

By including the effect of a trap with characteristic energy given by the Fermi temperature

T_F

in a two-body two-channel model for Feshbach resonances, we reproduce the experimental closed-channel fraction

Z

across the BEC-BCS crossover and into the BCS regime of a

^6

Li atomic Fermi gas. We obtain the expected behavior

Z \propto \sqrt{T_F}

at unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of the

Z

dependency on

T_F

on the BCS side, where a significant discrepancy between experiments and theory has been repeatedly reported.