A new perturbation theory for the superfluid Fermi gas in the molecular Bose-Einstein condensed state

TL;DR

This paper introduces a novel perturbation theory for superfluid Fermi gases in the molecular BEC state, combining perturbative and nonperturbative quantum scattering physics to improve predictions of observable properties.

Contribution

It develops a new diagrammatic wave function approach that incorporates nonperturbative scattering physics, extending beyond mean-field approximations for superfluid Fermi gases.

Findings

Computed parameters in the BEC limit beyond mean-field

Predicted superfluid pairing function and correlation functions

Provided accurate momentum distribution and density matrices

Abstract

We demonstrate how solutions to quantum few-fermion scattering problems can be the point-of-departure of a new treatment of a generalized many-body wave function. Our focus is on a particular ansatz for the ground state wave function of a superfluid Fermi gas introduced earlier (cond-mat/0506293). Our method is perturbative in the sense that the probability amplitudes for few-fermion scattering processes are treated as small quantities; it is also NONPERTURBATIVE in the sense that whenever such scattering events occur, nonperturbative quantum few-fermion scattering physics dominates. This approach can be viewed as a new diagrammatic methodology, based on a wave function as distinct from a perturbation series in the interparticle interactions. Some generic properties of the wave function are studied, and its parameters in the Bose-Einstein condensed limit are computed beyond mean-field. These results enable us to predict many observable properties of this Fermi gas with well-controlled accuracy, such as the superfluid pairing function, the four-fermion and six-fermion correlation functions, the momentum distribution, and the two-body reduced density matrix, etc.