Recent experimental advances allow trapped dilute Fermi gases of ^{6}Li and ^{40}K to be cooled far below the quantum-degeneracy temperature. Using a Feshbach resonance, experimentalists can tune the strength of the inter-particle interaction by adjusting a magnetic field. This allows experimentalists to realize tunable, strongly interacting, nonperturbative systems that bear strong similarity to nuclei and neutron matter and that exhibit a wide range of interesting physical phenomena, including the crossover from a Bose-Einstein condensate (BEC) regime to a Bardeen-Cooper-Schrieffer (BCS) regime. Of particular interest is the unitary regime, where the interaction is strongest (i.e., infinite scattering length). A pseudogap phase, in which the pairing gap is non-zero, was proposed to exist in the unitary gas above the superfluid critical temperature.

We are studying such cold atomic Fermi gases in the framework of the CI shell model, an approach widely used in atomic, molecular and nuclear physics. We have recently applied the shell model Monte Carlo (SMMC) method developed for nuclei to study the properties of a finite-size cold atomic Fermi gas in the unitary limit (PRA 2013). Our calculations include the first ab initio determination of the heat capacity and energy-staggering pairing gap across the superfuid phase transition in any cold atomic system.

The inter-particle interaction is usually modeled by a contact interaction. This interaction requires a regularization such as a cutoff in the number of oscillator shells in relative motion. The convergence of the many-particle energies in the regularization parameter is slow. We have introduced a new, separable effective interaction in the CI approach that allows for much faster convergence of the energies in the regularization parameter (PRL 2008, PRA 2012). This fast convergence has enabled us to calculate accurately spectra of few-atom systems.