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We investigate strong pairing fluctuations and effects of a harmonic trap inthe superfluid phase of an ultracold Fermi gas. Including amplitude and phasefluctuations of the inhomogeneous superfluid order parameter $\Delta(r)$ in atrap within a combined $T$-matrix theory with the local density approximation,we examine local properties of single-particle excitations and a thermodynamicquantity in the BCS-BEC crossover region. Below the superfluid phase transitiontemperature $T_{\rm c}$, we show that inhomogeneous pairing fluctuations leadto a shell structure of the gas cloud in which the spatial region where theordinary BCS-type superfluid density of states appears is surrounded by theregion where the pseudogap associated with strong pairing fluctuationsdominates single-particle excitations. The former spatial region enlarges toeventually cover the whole gas cloud far below $T_{\rm c}$. We also examine howthis shell structure affects the photoemission spectrum, as well as the localpressure. Since a cold Fermi gas is always trapped in a harmonic potential, ourresults would be useful for the study of strong-coupling superfluid physics,including this realistic situation.

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