Universal Fermi Gas with Two- and Three-Body Resonances

We consider a Fermi gas with two components of different masses, with the $s$-wave two-body interaction tuned to unitarity. In the range of mass ratio $8.62<M/m<13.6$, it is possible for a short-range interaction between heavy fermions to produce a resonance in a three-body channel. The resulting system is scale invariant and has universal properties, and is very strongly interacting. When $M/m$ is slightly above the lower limit 8.62, the ground state energy of a $2:1$ mixture of heavy and light fermions is less than 2% of the energy of a noninteracting gas with the same number densities. We derive exact relationships between the pressures of the unitary Fermi gases with and without three-body resonance when the mass ratio is close to the critical values of 8.62 and 13.6.

Figure 1

The variational bound on $\xi$ as a function of the abundance of light fermions $x$ at $M/m=8.62+ϵ$.