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

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