Theoretical studies of ultracold atoms in optical lattices and superlattices

Abstract

The study of ultracold atoms is one of the frontier research areas of modern physics. The ability to control precisely the interactions between the ultracold atoms in optical lattices has led to the prediction and in some cases observation of different phases of matter at ultracold temperatures. Further investigations in this area could lead to the realization of quantum computers and a better understanding of high temperature superconductivity. The applications of ultracold atoms are not restricted to the field of condensed matter physics. These systems can be used to simulate the physics of the early universe and also some astrophysical phenomena. This thesis reports on certain specific theoretical studies of ultracold atoms in optical lattices and superlattices. Ultracold atoms can exhibit different kinds of phases depending

on the strengths of various interactions, densities and geometry of the system. We inves- tigate some of these phases primarily using the mean-field theory and the density matrix

renormalization group (DMRG) method. In Chapter 1, we give a brief introduction to the field of ultracold atoms. In Chapter 2, we give a description of the theoretical tools used to obtain quantitative results for the problems studied in this thesis work. In Chapter 3, we focus on the well known superfluid to Mott-insulator phase transition of ultracold atoms in optical lattices. We obtained the transition critical points as well as the phase diagram using perturbation theory first and then mean-field theory, to compare the two methods. We then present our results for ultracold atoms in optical superlattices. Chapters 4 and 5 are based on the study of ultracold atoms in optical lattices and superlattices with the

on-site three body interaction, using mean-field and DMRG methods, respectively. In Chapter 6, we report our findings on the quantum phases of attractive bosons in two coupled one -dimensional optical lattices. In Chapter 7, we discuss our results obtained for a non-equilibrium study of ultracold atoms in optical lattices within the frame work of the extended Bose-Hubbard model. Finally, in Chapter 8 we summarize our findings for the above mentioned problems and suggest scope for future work in this field.