Pairing properties of an odd-frequency superfluid Fermi gas

We theoretically investigate strong-coupling properties of an odd-frequency Fermi superfluid. This pairing state has the unique property that Cooper pairs are formed between fermions, not at the same time, but at different times. To see whether or not such unequal-time pairs still exhibit bosonic behavior, we examine the spacetime structure of the odd-frequency Cooper-pair wave function at T = 0, by employing the combined pathintegral formalism with the BCS-Eagles-Leggett-type superfluid theory. In the strong-coupling regime, the oddfrequency pair wave function still has different space-time structure from that in the ordinary even-frequency swave superfluid state; their magnitudes are found to become close to each other, except for the equal-time pairing component. In this regime, we also evaluate the superfluid phase transition temperature Tc within the framework of the strong-coupling theory developed by Nozi & egrave;res and Schmitt-Rink. The calculated Tc in the strong-coupling regime of the odd-frequency system is found to be well described by the Bose-Einstein condensation of tightly bound Bose molecules. Our results indicate that, in spite of vanishing equal-time pairing, odd-frequency Cooper pairs still behave like bosons in the strong-coupling regime, as in the even-frequency s-wave superfluid case.