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.

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.

We have introduced a new Monte Carlo method in the CI framework, CI Monte Carlo (CIMC), that uses a guiding wave function in Fock space to circumvent the sign problem and find an approximate solution to the ground state (PRA 2013). We have used the method to calculate the ground-state energy and energy-staggering pairing gap as a function of the number of particles for the trapped unitary gas.

We have applied the auxiliary-field quantum Monte Carlo (AFMC) method developed for nuclei to study the properties of a finite-size trapped cold atomic Fermi gas in the unitary limit of infinite scattering length (PRA 2013). Our calculations included 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 homogenous two-component unitary Fermi gas has been studied extensively both theoretically and experimentally, and has connections to many areas of physics. A major topic of interest and debate is the existence of a so-called pseudogap regime above the critical temperature for superfluidity. Previous quantum Monte Carlo simulations claimed to demonstrate a pronounced pseudogap effect. We have applied finite-temperature AFMC to study the thermodynamics of the homogenous Fermi gas on a spatial lattice (arxiv 2018). Our calculations differ from previous AFMC calculations in that we do not use a spherical cutoff in momentum space and carry out the calculations in the canonical ensemble of fixed particle number. We have calculated the heat capacity, condensate fraction, a model-independent pairing gap, and spin susceptibility. In contrast to previous AFMC simulations, our calculations do not show clear signatures of a pseudogap and will likely motivate further experiments.