Quantum Monte Carlo studies of the population imbalanced Fermi Gas

Abstract

In this thesis Quantum Monte Carlo (QMC) techniques are used to provide an approximation-free investigation of the phases of the one- and two-dimensional attractive Hubbard Hamiltonian in the presence of population imbalance between two species of fermions. In the first part we present the results of the studies of the one dimensional system. We show that the ¿Fulde-Ferrel-Larkin-Ovchinnikov¿ (FFLO) pairing is the mechanism governing the properties of the system at low temperature. The effects of finite temperature and mass imbalance are investigated. Polarization-temperature phase diagram is presented. Furthermore we study the case of mass imbalance between the imbalanced populations. In the second part, we investigate the population imbalanced gas in two dimensions. Contrary to claims of fragility with increased dimensionality we find that this phase is stable across wide range of values for the polarization, temperature and interaction strength. Both homogenous and harmonically trapped systems display pairing with finite center of mass momentum.