Single component fermion near a P-wave resonance and few-body problem with correlated disorder potential

Abstract

The superfluid phase of Helium III has motivated the interest in p-wave system for a long time. In ultracold atoms, related experiments on p-wave resonance have already been conducted with the important tool called Feshbach resonance which could adjust the interactions between atoms to strongly interacting regime. The physics near Feshbach resonance has become an interesting topic because the lack of traditional perturbation parameter and hence can’t be treated with traditional perturbation theory. With a many-body trial wave function, lowest order constrained variational (LOCV) method can be used in calculating the ground state energy of a strongly interacting quantum fluid. We adopt this method to study the single component Fermi gas near a p-wave resonance and obtain the energy per particle for the ground state of single component Fermi gas near a p-wave resonance. We also calculate compressibility of the single component Fermi gas near a p-wave resonance and identify a region where the system would lose its stability near the p- wave resonance. The two p-wave contacts are also calculated and compared with the experimental results. The other topic discussed in this thesis work is the few-body problem in the presence of correlated disorder in two dimensions. Motivated by the recent experimental and theoretical progress in many-body localization, we examine the effect of correlated disorder on few-body problem with exact diagonalization (ED) method. We give the phase diagram for single particle in the presence of quasi-periodic disorder potential and also analyse the effect of strong interaction on the phase diagram in two dimensions. For the speckle disorder potential case, we examine both the effect of correlation length and disorder strength on single particle ground state energy and two-particle binding energy. The transport property is also calculated and discussed at last.