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

TL;DR

This study numerically demonstrates that the Goldstone mode in a confined ultracold Fermi gas can be directly observed through the dynamics of single-particle excitations following an interaction quench, revealing low-frequency oscillations.

Contribution

It introduces a microscopic time-dependent density-matrix approach within the Bogoliubov-de Gennes formalism to simulate and identify the Goldstone mode in a 3D confined Fermi gas.

Findings

Goldstone mode visible in single-particle excitation dynamics

Low-frequency in-phase oscillations observed after quench

Complete inversion of occupations in lowest-lying states

Abstract

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.