Comparison of Different Pairing Fluctuation Approaches to BCS-BEC Crossover

摘要

The subject of BCS - Bose Einstein condensation (BEC) crossover isparticularly exciting because of its realization in ultracold Fermi gases andits possible relevance to high temperature superconductors. In the paper wereview that body of theoretical work on this subject which represents a naturalextension of the seminal papers by Leggett and by Nozieres and Schmitt-Rink(NSR). The former addressed only the ground state, now known as the"BCS-Leggett" wave-function and the key contributions of the latter pertain tocalculations of the superfluid transition temperature $T_c$. These two papershave given rise to two main and, importantly, distinct, theoretical schools inthe BCS-BEC crossover literature. The first of these extends the BCS-Leggettground state to finite temperature and the second extends the NSR scheme awayfrom $T_c$ both in the superfluid and normal phases. It is now rather widelyaccepted that these extensions of NSR produce a different ground state thanthat first introduced by Leggett. Our analysis shows how the NSR-based approachviews the bosonic contributions more completely but it treats the fermions as"quasi-free". By contrast, the BCS-Leggett based approach treats the fermioniccontributions more completely but it treats the bosons as "quasi-free". The NSRbased schemes approach the crossover between BCS and BEC by starting from theBEC limit and the BCS-Leggett based scheme approaches this crossover bystarting from the BCS limit. Ultimately, one would like to combine these twoschemes. In this paper we review the strengths and weaknesses of bothapproaches. To reach a full understanding, it is important in the future toinvest effort in investigating in more detail the T=0 aspects of NSR-basedtheory and the $T \neq 0$ aspects of BCS-Leggett theory.