Superfluid transition in the unitary Fermi gas

A particularly interesting example of a strongly interacting fermionic system is the Fermi gas at unitarity — a system of two-component fermions interacting with divergent scattering length. In this case the density sets the only relevant length scale and the system exhibits universal behavior. Remarkably, the critical temperature of the transition to the superfluid phase (in units of the Fermi temperature) is much higher than in any other known fermionic system. If we scale it to the density of electrons in a metal, this transition would occur far above room temperature! Thus the unitary Fermi gas promises valuable insights into the mechanisms behind high-temperature superfluidity.

Regimes of a Fermi gas as function of inverse interaction strength: the weakly interacting BCS limit (weakly bound Cooper pairs), the BEC limit of strongly bound (bosonic) molecules, and the unitary Fermi gas that exhibits maximally strong interactions between fermionic particles. The critical temperature is exponentially small in the BCS limit, while at unitarity it is remarkably high for a fermionic system (value shown is our numerical prediction)

Starting with my Ph.D. work with Matthew Wingate, I studied the unitary Fermi gas using the Determinant Diagrammatic Monte Carlo algorithm. We established the currently most accurate theoretical estimate for the critical temperature of the balanced gas, which significantly improved on previous calculations and is in excellent agreement with experiments. We also generalized the algorithm to the spin imbalanced case (unequal number of fermions in the two spin components), which was previously inaccessible with this method due to the sign problem. We calculated various other thermodynamic quantities at the critical point and studied the equation of state.