Studying Disorder and Correlation Effects on the Phase Diagram of Bosons via Mean Field Theory

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The thesis investigates the ground state phase diagram of interacting bosons using mean field theory on a Bose Hubbard model (BHM). A number of different relevant issues have been addressed here. They include the effects of the periodic environment of the (optical) lattice on a Bose Einstein condensate. The work nicely portrays the interplay of the condensate properties and symmetry of the underlying lattice vis a vis its coordination number. A work on random disorder with a uniform distribution in a BHM follows. The Bose glass phase is seen to occur as the sites with integer fillings form a percolating cluster in a two dimensional square lattice, with the threshold being very similar to that of a random site percolation model that is well studied in statistical mechanics. The Bose glass phase seems to prolong the superfluid phase and occurs intervening to the superfluid and the insulating phases. Dipolar interactions are hence discussed to include long range (nearest neighbour density exchange) interactions in a BHM. In presence of such extended interactions, a variety of density ordered and supersolid phases are seen to emerge. The thesis has particularly focused on the prototype of a kagome lattice, a classic example of a non-bipartite lattice. As extension of the above study is made to include the harmonic trapping effects which are indispensable in the study of cold atomic gases in optical lattices. The trap renders the system inhomogeneous and a variety of phases, such as the superfluid, Mott insulating, density ordered, supersolid etc. are seen to coexist. The thesis finally concludes with a study of a three component bosonic mixture which shows exotic mixed phases, where one component may exhibit superfluid character while the other two may possess insulating properties. Thus correlation effects which go beyond incorporating interatomic interactions to include the effects of symmetry of underlying lattice, along with disorder effects on a system of interacting bosons form the central focus of the thesis.
Supervisor: Saurabh Basu