Absorption and emission of a collective excitation by a fermionic quasiparticle in a Fermi superfluid

TL;DR

This paper derives a general expression for the coupling amplitude of collective excitations and fermionic quasiparticles in a superfluid, analyzing their interactions and calculating the excitations' lifetime across wave numbers.

Contribution

It provides a novel, non-resonant, and long-wavelength independent expression for the coupling amplitude using RPA and functional integral methods.

Findings

Coupling amplitude expression valid beyond resonant and long wavelength limits.

Calculated the lifetime of bosonic excitations across wave numbers.

Identified the mode quality factor behavior and its vanishing at the pair-breaking continuum.

Abstract

We study the process of absorption or emission of a bosonic collective excitation by a fermionic quasiparticle in a superfluid of paired fermions. From the RPA equation of motion of the bosonic excitation annihilation operator, we obtain an expression of the coupling amplitude of this process which is limited neither to resonant processes nor to the long wavelength limit. We confirm our result by independently deriving it in the functional integral approach using the gaussian fluctuation approximation, and by comparing it in the long wavelength limit to the quantum hydrodynamic result. Last, we give a straightforward application of the coupling amplitude we obtain by calculating the lifetime of the bosonic excitations of arbitrary wave number. We find a mode quality factor that decreases from its maximum at low wave numbers and vanishes when the bosonic branch hits the pair-breaking continuum.