Equation of state of a superfluid Fermi gas in the BCS-BEC crossover

Abstract

PACS. 03.75.Hh -Static properties of condensates; thermodynamical, statistical and structural properties. PACS. 03.75.Ss -Degenerate Fermi gases. PACS. 05.30.Fk -Fermion systems and electron gas.Abstract. -We present a theory for a superfluid Fermi gas near the BCS-BEC crossover, including pairing fluctuation contributions to the free energy similar to that considered by Nozières and Schmitt-Rink for the normal phase. In the strong coupling limit, our theory is able to recover the Bogoliubov theory of a weakly interacting Bose gas with a molecular scattering length very close to the known exact result. We compare our results with recent Quantum Monte Carlo simulations both for the ground state and at finite temperature. Excellent agreement is found for all interaction strengths where simulation results are available.The recent experimental realization of strongly interacting Fermi gases of 6 Li and 40 K atoms near a Feshbach resonance has opened up the exciting possibility of investigating the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC) [1][2][3][4][5]. In these systems, the inter-atomic interaction strength can be varied by tuning the energy of a near-resonant molecular state with a magnetic field.Below resonance where the s-wave scattering length a is positive, stable diatomic molecules are observed to form a BEC at low temperatures. Above resonance, with a < 0, the molecules dissociate and form a BCS superfluid of fermionic pairs. In the crossover region where the scattering length a is large one can access a new, strongly correlated regime known as the unitary limit [6]. Recent experiments in the crossover regime have found evidence for this transition by measuring low-lying collective modes [2,7,8] and heat capacity [4,9]. These rapid experimental developments constitute an ideal testing ground for theoretical studies of the BCS-BEC crossover. However, theoretical results available in the literature are limited in the strongly correlated unitary regime. The first systematic study of the crossover at zero temperature was provided by Eagles and Leggett based on BCS mean-field equations [10,11]. Later, the effects of pair fluctuations were considered by Nozières and Schmitt-Rink (NSR) at temperatures above the superfluid transition [12,13]. This was recently extended to the superfluid phase by Strinati et al. using finite temperature Green functions [14,15].Extensions of these approaches to take into account the bare Feshbach molecule have also been presented [16,17], with the conclusion that additional two-channel effects can be c EDP Sciences

Superfluid density and condensate fraction in the BCS-BEC crossover regime at finite temperatures

“…We plot our calculated results for ρ s close to T c , in spite of this problem. In particular, we note that the predicted value of T c in the NSR theory of the BCS-BEC crossover is a good approximation [21]. The NSR bendover is much less in evidence in the case of a narrow Feshbach resonance, as considered in Ref.…”

“…, MC results [12,22] give µ/ε F = 0.44 ∼ 0.49, and an improved version of NSR theory [21] gives µ/ε F = 0.4 ∼ 0.47 just below T c .…”

“…The thermodynamic potential Ω = Ω F + Ω B consists of the mean-field part Ω F due to Fermi quasiparticles and the correction term Ω B due to boson fluctuations. The mean-field contribution Ω F is given by [4,21] …”

Thermodynamics of Ultracold Fermi Gases

“…• double-dot-dashed line: BCS mean eld theory • open circles: Diagrammatic Monte Carlo calculations [113] • open squares: Quantum Monte Carlo calculations [136] • dotted line: GG perturbation theory [137,138] • dashed line: GG 0 perturbation theory [139] • triple-dot-dashed line: Ladder diagrams approximation [140] • dot-dashed line: Pseudogap theory [139] • solid line: Gaussian pair uctuation/Nozières-Schmitt Rink theory [141] Our data clearly discriminates between these theories. We observe that none of them account for our data over their full range.…”

“…This intuitively explains why collective modes do not easily discriminate between theories. [141] (gray squares), a quantum Monte-Carlo calculation from [173] (gray open circles) and a diagrammatic approach from [138] (gray crosses). The dashed line is calculated from a t of the Fixed-Node data [67].…”