Title: Multi-particle instability in a spin-imbalanced Fermi gas,
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.