Quantum Fluctuations in the Superfluid State of the BCS-BEC Crossover

TL;DR

This paper investigates quantum fluctuations in the superfluid state of the BCS-BEC crossover, providing analytical and numerical results that align well with experiments and quantum Monte Carlo simulations, and discusses methods for self-consistent calculations.

Contribution

It offers a comprehensive analysis of quantum fluctuations in the BCS-BEC crossover, including effects on measurable properties and a new approach for self-consistent calculations.

Findings

Excellent agreement with quantum Monte Carlo and experimental results at unitarity.

Analytical derivation of Fermi liquid corrections in the BCS limit.

Description of reduction in scattering length and quantum depletion in the BEC limit.

Abstract

We determine the effects of quantum fluctuations about the T=0 mean field solution of the BCS-BEC crossover in a dilute Fermi gas using the functional integral method. These fluctuations are described in terms of the zero point motion of collective modes and the virtual scattering of gapped quasiparticles. We calculate their effects on various measurable properties, including chemical potential, ground state energy, the gap, the speed of sound and the Landau critical velocity. At unitarity, we find excellent agreement with quantum Monte Carlo and experimental results. In the BCS limit, we show analytically that we obtain Fermi liquid interaction corrections to thermodynamics including the Hartree shift. In the BEC limit, we show that the theory leads to an approximate description of the reduction of the scattering length for bosonic molecules and also obtain quantum depletion of the Lee-Yang form. At the end of the paper, we describe a method to include feedback of quantum fluctuations into the gap equation, and discuss the problems of self-consistent calculations in satisfying Goldstone's theorem and obtaining ultraviolet finite results at unitarity.