Comparative Study of BCS-BEC Crossover Theories above $T_c$: the Nature of the Pseudogap in Ultra-Cold Atomic Fermi Gases

摘要

This paper presents a comparison of two finite-temperature BCS-Bose Einsteincondensation (BEC) crossover theories above the transition temperature:Nozieres Schmitt-Rink (NSR) theory and finite $T$-extended BCS-Leggett theory.The comparison is cast in the form of numerical studies of the behavior of thefermionic spectral function both theoretically and as constrained by(primarily) radio frequency (RF) experiments. Both theories include pairfluctuations and exhibit pseudogap effects, although the nature of thispseudogap is very different. The pseudogap in finite $T$-extended BCS-Leggetttheory is found to follow a BCS-like dispersion which, in turn, is associatedwith a broadened BCS-like self energy, rather more similar to what is observedin high temperature superconductors (albeit, for a d-wave case). The fermionicquasi-particle dispersion is different in NSR theory and the damping isconsiderably larger. We argue that the two theories are appropriate indifferent temperature regimes with the BCS-Leggett approach more suitablenearer to condensation. There should, in effect, be little difference at higher$T$ as the pseudogap becomes weaker and where the simplifying approximationsused in the BCS-Leggett approach break down. On the basis ofmomentum-integrated radio frequency studies of unpolarized gases, it would bedifficult to distinguish which theory is the better. A full comparison forpolarized gases is not possible since there is claimed to be inconsistencies inthe NSR approach (not found in the BCS-Leggett scheme). Future experimentsalong the lines of momentum resolved experiments look to be very promising indistinguishing the two theories.