Pure Goldstone mode in the quench dynamics of a confined ultracold Fermi gas in the BCS-BEC crossover regime

TL;DR

This paper numerically investigates the emergence of a pure, gapless Goldstone mode in a confined ultracold Fermi gas following an interaction quench, revealing its dependence on quench details and superfluid resonances.

Contribution

It demonstrates the existence of a pure Goldstone mode in a 3D confined Fermi gas that remains gapless and is influenced by the quench parameters and superfluid resonances.

Findings

Goldstone mode is gapless and determined by quench details.

Superfluid resonances affect the Goldstone mode.

Interaction quench causes in-phase oscillations of single-particle states.

Abstract

We present a numerical study of the dynamic response of a confined superfluid 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 full Bogoliubov-de Gennes formalism that includes a 3D harmonic confinement we simulate and identify the emergence of a Goldstone mode of the BCS gap in a cigar-shaped $^6$Li gas. By analyzing this Goldstone mode over a wide range of parameters, we show that its excitation spectrum is gapless and that its main frequency is not fixed by the trapping potential but that it is determined by the details of the quench. Thus, we report the emergence of a pure Goldstone mode of the BCS gap that --in contrast to situations in many previous studies-- maintains its gapless excitation spectrum predicted by the Goldstone theorem. Furthermore, we observe that the size-dependent superfluid resonances resulting from the atypical BCS-BEC crossover have a direct impact on this Goldstone mode. Finally, we find that the interaction quench-induced Goldstone mode leads to a low-frequency in-phase oscillation of the single-particle occupations with complete inversion of the lowest-lying single-particle states which could provide a convenient experimental access to the pure gapless Goldstone mode.