This paper has been withdrawn by the authors as the recent measurement of the closed channel population for Li6 [Partridge et al., cond-mat/0505353] indicates that the cutoff energy is still much larger than any other relevant energy scales for this broad Feshbach resonance.
We present the random phase approximation (RPA) theory of the Bose-Einstein-condensation-Bardeen-Cooper-Schrieffer crossover in an atomic Fermi gas near a Feshbach resonance that includes the relevant two-body atomic physics exactly. This allows us to determine the probability for the dressed molecules in the Bose-Einstein condensate to be in the closed channel of the Feshbach resonance and to compare with the recent experiments of Partridge et al. [95, 020404 (2005)10.1103/PhysRevLett.95.020404] with , who have measured the same quantity.
We study a polarized Fermi gas and demonstrate that Fano-Feshbach (FF) resonances lead to the pairing of fermions and holes into long living massive bosonic modes (bifermions and biholes), which can be viewed as signatures of a first order quantum phase transition. These modes, which are neither conventional Cooper pairs nor closed channel bosonic dimers, have a peculiar dispersion relation and appear already in the weak coupling limit, i.e. for large FF detunings. Our result is in accord with claims of Schunck \emph{et al.} [cond-mat/0702066] that by stabilizing the normal state the population imbalance still allows effect of s-wave fermionic pairing.
We compute the fraction of closed-channel molecules in trapped atomic Fermi gases, over the entire range of accessible fields and temperatures. We use a two-channel model of Bardeen-Cooper-Schrieffer-Bose-Einstein-condensation crossover theory at general temperature , and show that this fraction provides a measure of the T-dependent pairing gap. Our calculations, containing no free parameters, are in good quantitative agreement with recent low- measurements in (6)Li. We present readily testable predictions for the dependencies of the closed-channel fraction on temperature and Fermi momentum.