Strong-coupling limit in the evolution from BCS superconductivity to Bose-Einstein condensation

Abstract

We consider the problem of the crossover from BCS superconductivity to Bose-Einstein condensation in three dimensions for a system of fermions with an attractive interaction, for which we adopt the simplifying assumption of a suitably regularized point-contact interaction. We examine in a critical way the fermionic (self-consistent) T-matrix approximation which has been widely utilized in the literature to describe this crossover above the superconducting critical temperature, and show that it fails to yield the correct behaviour of the system in the strong-coupling limit, where composite bosons form as tightly bound fermion pairs. We then set up the correct approximation for a "dilute" system of composite bosons and show that an entire new class of diagrams has to be considered in the place of the fermionic T-matrix approximation for the self-energy. This new class of diagrams correctly describes both the weak-and strong-coupling limits, and consequently results into an improved interpolation scheme for the intermediate (crossover) region. In this context, we provide also a systematic mapping between the corresponding diagrammatic theories for the composite bosons and the constituent fermions. As a preliminary result to demonstrate the numerical effect of our new class of diagrams on physical quantities, we calculate the value of the scattering length for composite bosons in the strong-coupling limit and show that it is considerably modified with respect to the result obtained within the self-consistent fermionic T-matrix approximation.

Dimer-dimer scattering length for fermions with different masses: Analytical study for large mass ratio

“…We indeed find that the Pieri and Strinati [9] approximation is asymptotically correct for large mass ratio. Taken with the fact that their result for a 4 is also a quite good approximation when the two different fermions have equal mass, we come to the conclusion that their approximation is quite good for any mass ratio.…”

“…(14) are the same as those appearing in Eq. (9). Hence the only difference is that we have now to calculate the kernel K(q, 0; Q, 0) for r → ∞.…”

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

“…(2.16) is characteristic of the NSR treatment of fluctuations [3]. The correct result a M = 0.6a s [28] requires going past the Gaussian approximation [27,29]. In this paper, in contrast, we only treat pairing fluctuations within NSR.…”

Time-dependent density-functional theory for trapped strongly interacting fermionic atoms

“…While the BCS mean-field theories [30] predict a m =2a [31], a solution of four-fermion problem for contact scattering provided the value a m Ϸ 0.6a [32]. Very little is known about the correct form of ⑀͑n͒ in the intermediate range.…”