Quench dynamics of a confined ultracold Fermi gas: Direct visibility of the Goldstone mode in the single-particle excitations

We present a numerical study of a confined ultracold Fermi gas showing that the Goldstone mode of the BCS gap is directly visible in the dynamics of the single-particle excitations. To this end, we investigate the low-energy dynamic response of a confined Fermi gas to a rapid change of the scattering length (i.e., an interaction quench). Based on a fully microscopic time-dependent density-matrix approach within the Bogoliubov-de Gennes formalism that includes a 3D harmonic confinement we simulate and identify the emergence of the Goldstone mode in a cigar-shaped $^6$Li gas. We show that the quench leads to a low-frequency in-phase oscillation of the single-particle occupations. Complete inversion is achieved for occupations corresponding to the lowest-lying single-particle states.