Quasicondensation in Two-Dimensional Fermi Gases

Abstract

In this paper we follow the analysis and protocols of recent experiments, combined with simple theory, to arrive at a physical understanding of quasi-condensation in two dimensional Fermi gases. We find that quasi-condensation mirrors Berezinskiȋ-Kosterlitz-Thouless behavior in many ways, including the emergence of a strong zero momentum peak in the pair momentum distribution. Importantly, the disappearance of this quasi-condensate occurs at a reasonably well defined crossover temperature. The resulting phase diagram, pair momentum distribution, and algebraic power law decay are compatible with recent experiments throughout the continuum from BEC to BCS.Understanding two dimensional (2D) fermionic superfluidity has a long history relating to the Mermin- Thus recent reports [9, 10] of a form of pair condensation in 2D fermionic gases are particularly exciting. These follow earlier work addressing the ground state [11] and the higher temperature regime, away from condensation [12]. These experiments [9,10] show that strong normal state pairing is an essential component of 2D Fermi superfluids, even in the BCS regime. In fact, much of the theory invoked to explain these experiments was based upon true Bose systems. A characteristic feature of 2D superfluidity at finite T is the presence of narrow peaks in the momentum distribution of the pairs, without macroscopic occupation of the zero momentum state. Throughout the paper this will be our definition of "quasi-condensation." This quasi-condensation in momentum space is associated with algebraic decay of coherence in real space. Importantly, the BKT-related transition temperature is manifested as a sudden change in slope of a normalized peak momentum distribution for pairs.In this paper we present a theory of a 2D Fermi gas near quantum degeneracy and show how it reproduces rather well the results of these recent experiments [9,10] through an analysis of the phase diagram, the pair momentum distribution and algebraic power laws. Given the ground breaking nature of the experiments, it is important to have an accompanying theoretical study which follows exactly the same protocols without any adjustments or phenomenology. Our approach is to be distinguished from other studies of 2D Fermi gases [4,[13][14][15][16][17][18][19][20][21][22][23]. In particular, those addressing BKT physics [4,[13][14][15][16]20], use existing formulae [24,25] and determine the unknown parameters to obtain T BKT c . By contrast here we reverse the procedure and follow experimental protocols to thereby provide a new formula, involving composite bosons, for the transition temperature associated with quasi-condensation. In the homogeneous case, this is analytically tractable and presented as Eq. (6) below.Importantly, there is a rather abrupt crossover out of a quasi-condensed phase at a fairly well defined temperature T qc . In the BEC regime this matches earlier theoretical estimates of the BKT transition temperature which are based on different theoretical formalisms [4,[13][14][15][16]. We ...

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