Multi-particle instability in a spin-imbalanced Fermi gas

TL;DR

This paper investigates a multi-particle instability in a spin-imbalanced Fermi gas with weak attractive interactions, revealing how multiple fermions bind together and extending the concept of Cooper pairing to imbalanced systems.

Contribution

It derives the optimal ratio of spin populations for maximum binding energy and verifies this using exact diagonalization, extending the understanding of pairing in imbalanced Fermi gases.

Findings

Maximum binding energy per particle occurs at a specific spin ratio.

Analytical derivation matches exact diagonalization results.

Multi-particle instability generalizes Cooper pairing to imbalanced systems.

Abstract

Weak attractive interactions in a spin-imbalanced Fermi gas induce a multi-particle instability, binding multiple fermions together. The maximum binding energy per particle is achieved when the ratio of the number of up- and down-spin particles in the instability is equal to the ratio of the up- and down-spin densities of states in momentum at the Fermi surfaces, to utilize the variational freedom of all available momentum states. We derive this result using an analytical approach, and verify it using exact diagonalization. The multi-particle instability extends the Cooper pairing instability of balanced Fermi gases to the imbalanced case, and could form the basis of a many-body state, analogously to the construction of the Bardeen-Cooper-Schrieffer theory of superconductivity out of Cooper pairs.