Stability of Inhomogeneous Multi-Component Fermi Gases

TL;DR

This paper investigates the stability and properties of multi-component Fermi gases with short-range interactions, revealing conditions for stability, collapse, and formation of weakly-bound trimers through theoretical and computational methods.

Contribution

It extends the understanding of multi-component Fermi gases by analyzing stability criteria and the effects of multiple interspecies interactions using hyperspherical and Monte Carlo techniques.

Findings

Three- and four-component Fermi gases become unstable under certain conditions.

The collapse is driven by the interspecies scattering length, similar to Bose gases.

Stable trimer states can form in specific parameter regimes.

Abstract

Two-component equal-mass Fermi gases, in which unlike atoms interact through a short-range two-body potential and like atoms do not interact, are stable even when the interspecies s-wave scattering length becomes infinitely large. Solving the many-body Schroedinger equation within a hyperspherical framework and by Monte Carlo techniques, this paper investigates how the properties of trapped two-component gases change if a third or fourth component are added. If all interspecies scattering lengths are equal and negative, our calculations suggest that both three- and four-component Fermi gases become unstable for a certain critical set of parameters. The relevant length scale associated with the collapse is set by the interspecies scattering length and we argue that the collapse is, similar to the collapse of an attractive trapped Bose gas, a many-body phenomenon. Furthermore, we consider a three-component Fermi gas in which two interspecies scattering lengths are negative while the other interspecies scattering length is zero. In this case, the stability of the Fermi system is predicted to depend appreciably on the range of the underlying two-body potential. We find parameter combinations for which the system appears to become unstable for a finite negative scattering length and parameter combinations for which the system appears to be made up of weakly-bound trimers that consist of one fermion of each species.