Excitations in the BCS-BEC crossover regime of a superfluid Fermi gas with a Feshbach resonance

We investigate single-particle excitations at T = 0 in the BCS-BEC crossover regime of a superfluid Fermi gas. We solve the Bogoliubov-de Gennes equations in a trap, including a tunable pairing interaction associated with a Feshbach resonance. We show that the single-particle energy gap Eg is dominated by the lowest-energy Andreev bound state localized at the surface of the gas, which is much smaller than the superfluid order parameter Δ˜(r=0) at the center of the trap. We also calculate the rf-tunneling current spectrum IF(ω). In a broad Feshbach resonance, the peak energy in IF(ω) is shown to give, not Eg, but Δ˜(r=0). In a narrow resonance, significant spectral weight coming from the low-energy Andreev states hides the appearance of the peak in IF(ω) at ω≃Δ˜(r=0). Our results for a broad resonance is in good agreement with the recent rf-tunneling measurement in a superfluid 6Li.