Quasiparticle disintegration in fermionic superfluids

TL;DR

This paper investigates how fermionic quasiparticles in a superfluid Fermi gas are affected by disintegration processes, including emission of one or three quasiparticles, revealing spectrum distortions and shifts near the minimum.

Contribution

It introduces a detailed analysis of quasiparticle disintegration processes beyond previous work, including the effects of three-quasiparticle emission on the spectrum.

Findings

Disintegration processes are described by a $t$-matrix self-energy.

Strong coupling causes significant spectrum distortion near the $1\to3$ threshold.

The main effect near the dispersion minimum is a Hartree shift, with small corrections to the energy gap.

Abstract

We study the fermionic quasiparticle spectrum in a zero-temperature superfluid Fermi gas, and in particular how it is modified by different disintegration processes. On top of the disintegration by emission of a collective boson ($1\to2$, subject of a previous study, PRL 124, 073404), we consider here disintegration events where three quasiparticles are emitted ($1\to3$). We show that both disintegration processes are described by a $t$-matrix self-energy (as well as some highly off-resonant vacuum processes), and we characterize the associated disintegration continua. At strong coupling, we show that the quasiparticle spectrum is heavily distorted near the $1\to3$ disintegration threshold. Near the dispersion minimum, where the quasiparticles remain well-defined, the main effect of the off-shell disintegration processes is to shift the location of the minimum by a value that corresponds to the Hartree shift in the BCS limit. With our approximation of the self-energy, the correction to the energy gap with respect to the mean-field result however remains small, in contrast with experimental measurements.