Beliaev damping of the Goldstone mode in atomic Fermi superfluids

TL;DR

This paper extends the theoretical understanding of Beliaev damping in superfluids by including nonlinear spectrum effects, deriving a decay rate formula, and applying it to Fermi gases across the BCS-BEC crossover, revealing significant deviations from standard results.

Contribution

It introduces a modified decay rate formula accounting for spectrum nonlinearities and applies it to Fermi superfluids, enhancing the understanding of collective excitation damping.

Findings

Nonlinear spectrum effects significantly alter decay rates.

Derived a new formula for Beliaev damping with spectrum nonlinearities.

Applied the theory to Fermi gases, matching experimental observations.

Abstract

Beliaev damping in a superfluid is the decay of a collective excitation into two lower frequency collective excitations; it represents the only decay mode for a bosonic collective excitation in a superfluid at T = 0. The standard treatment for this decay assumes a linear spectrum, which in turn implies that the final state momenta must be collinear to the initial state. We extend this treatment, showing that the inclusion of a gradient term in the Hamiltonian yields a realistic spectrum for the bosonic excitations; we then derive a formula for the decay rate of such excitations, and show that even moderate nonlinearities in the spectrum can yield substantial deviations from the standard result. We apply our result to an attractive Fermi gas in the BCS-BEC crossover: here the low-energy bosonic collective excitations are density oscillations driven by the phase of the pairing order field. These collective excitations, which are gapless modes as a consequence of the Goldstone mechanism, have a spectrum which is well established both theoretically and experimentally, and whose linewidth, we show, is determined at low temperatures by the Beliaev decay mechanism.