Quantum Monte Carlo Studies of the BCS-BEC crossover

Abstract

This dissertation focuses on the physics of dilute Fermi gases in the so-called BCS-BEC crossover, with short-range attractive interactions and large scattering lengths. It introduces a new statistical ensemble, the particle asymmetry constrained ensemble, and uses it for calculations along with more conventional ensembles like the grand canonical ensemble and the canonical ensemble. The dissertation presents results for the energy, condensate fraction, superfluid critical temperature, spin susceptibility, even-odd energy pairing gap, and Tan contact and argues for the existence, or at least non-exclusion, of the pseudogap in the unitary regime with infinite scattering length. Finally, it uses the same quantum Monte Carlo techniques, this time in a zero-temperature setting, to determine the quasiparticle properties of infinite neutron matter, namely the effective mass, self-energy, and pairing gap.