Physics of ultra-cold atomic gas in unconventional optical lattice

Abstract

In the past decades, there has been extraordinary experimental progresses in realizing various optical lattices in different dimensions. Apart from the regular lattices like square, triangular or honeycomb, quasi-periodic lattices have been realized. As a result, it is timely to investigate physics of bosons and fermions in unconventional lattice systems. In this thesis, we will study three topics related to cold atoms in optical potential. The primary focus of our studies is the properties of the ground state and its elementary excitations. Wherever possible, conclusions from our studies will be compared with available experiments.

In the first topic, we study the Josephson effect of spin-1 Bose Einstein Condensates in a double well potential, including its ground state properties and elementary excitations. We derived the spinor Josephson Hamilton and the dynamic equations for number and phases for each spin component. In the second topic, we perform the first Quantum Monte Carlo calculation of Bose-Hubbard model in a Penrose tilling lattice at finite temperature. We compute the phase diagram and investigate the behaviour of phase transitions by looking at several observables including entropy, heat capacity, momentum distribution, distributions of condensate fraction and density. In the third topic, we study a double-layer two-component Fermi gas system at zero temperature. At half-filling, we find that there is an insulator-superfluid transition and uncover a particular excitonic mode in the system. We investigate in detail the properties of the excitonic excitations, including its gap and effective mass.