Coexistence of superfluid gap and pseudogap in the BCS-BEC crossover regime of a trapped Fermi gas below $T_{\rm c}$

TL;DR

This paper explores how strong pairing fluctuations create a shell structure in a trapped ultracold Fermi gas below the superfluid transition temperature, revealing coexistence of superfluid gap and pseudogap in the BCS-BEC crossover.

Contribution

It introduces a combined T-matrix and local density approximation approach to analyze inhomogeneous pairing fluctuations and their effects on local properties in a trapped Fermi gas.

Findings

Shell structure of superfluid and pseudogap regions identified

Spatial extent of BCS superfluid density increases below T_c

Impacts on photoemission spectrum and local pressure analyzed

Abstract

We investigate strong pairing fluctuations and effects of a harmonic trap in the superfluid phase of an ultracold Fermi gas. Including amplitude and phase fluctuations of the inhomogeneous superfluid order parameter $\Delta(r)$ in a trap within a combined $T$-matrix theory with the local density approximation, we examine local properties of single-particle excitations and a thermodynamic quantity in the BCS-BEC crossover region. Below the superfluid phase transition temperature $T_{\rm c}$, we show that inhomogeneous pairing fluctuations lead to a shell structure of the gas cloud in which the spatial region where the ordinary BCS-type superfluid density of states appears is surrounded by the region where the pseudogap associated with strong pairing fluctuations dominates single-particle excitations. The former spatial region enlarges to eventually cover the whole gas cloud far below $T_{\rm c}$. We also examine how this shell structure affects the photoemission spectrum, as well as the local pressure. Since a cold Fermi gas is always trapped in a harmonic potential, our results would be useful for the study of strong-coupling superfluid physics, including this realistic situation.