Spin1/2Fermions in the Unitary Regime: A Superfluid of a New Type

Abstract

We have studied, in a fully non-perturbative calculation, a dilute system of spin 1/2 interacting fermions, characterized by an infinite scattering length at finite temperatures. Various thermodynamic properties and the condensate fraction were calculated and we have also determined the critical temperature for the superfluid-normal phase transition in this regime. The thermodynamic behavior appears as a rather surprising and unexpected mélange of fermionic and bosonic features. The thermal response of a spin 1/2 fermion at the BCS-BEC crossover should be classified as that of a new type of superfluid. The unitary regime is commonly referred to as the situation in which the scattering length a greatly exceeds the average inter-particle separation, thus n|a| 3 ≫ 1, where n is the particle number density [1,2]. It is widely accepted by theorists that at T = 0 these systems are superfluid and that in the unitary regime the coherence length is comparable in magnitude with the average interparticle separation. At T = 0 this problem has been considered by a number of authors [3] and the most accurate results so far have been reported in Refs. [4,5,6]. In 2002 it was shown experimentally that such systems are (meta)stable, and they have been studied extensively experimentally ever since [7,8].The typical theoretical treatment of such systems is based on the idea put forward by Eagles, Leggett and others [9], and used subsequently by most authors [10,11]. The form of the many-body wave function is as in the weak coupling BCS limit and is used for all values of the scattering length a. The particle number projected BCS wave function has the functional formwhere odd subscripts refer to spin-up particles and even subscripts to spin-down particles, A is the antisymmetrization operator, r 12 = |r 1 − r 2 | and φ(r) is either the Cooper pair wave function in the BCS limit, or the two-bound state wave function in the BEC limit. The main difficulty with this approach becomes evident when one tries to use this kind of wave function in the unitary regime, where n|a| 3 ≫ 1. In the extreme BEC limit, this wave function describes a state with all bosons (dimers) at rest, in the condensed state. The fraction of non-condensed bosons (dimers) is known to be small thenwhere n d = n/2 and a dd = 0.6a is the dimer-dimer scattering length [6,12]. When one approaches the unitary regime, the fraction of non-condensed bosons becomes of order one [13], which resembles qualitatively the situation in superfluid 4 He, and then a meanfield description (with or without fluctuations) becomes questionable. In order to calculate the thermal properties of a system of fermions in the unitary regime, we have placed them on a 3D-spatial lattice and used a path integral representation of the partition function. We start fromwhere β = 1/T = N τ τ andÔ is a quantity of interest. T stands for the temperature and µ for the chemical potential, andĤ andN are the Hamiltonian and the particle number operators respectively.Since the system under consideration is di...

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