Characteristics of Bose Glass in a Disordered Optical Lattice
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When bosonic atoms are trapped in optical lattices, they exhibit one of the two phases: superfluid (SF), where atoms move coherently without any collisions, or Mott insulator (MI), where atoms are localized. These quantum phases on clean bosonic lattices have been thoroughly studied ^7,8,13. When the optical lattices are disturbed by a source of disorder, a third exotic phase, Bose glass, has been predicted to appear ^1,3. In this thesis, we utilize a mean field theory coupled within the Bose Hubbard model ^1 to investigate the phases of two-dimensional disordered bosonic optical lattices. We study the phase of the systems as a function of chemical potential and hopping-parameter by using the SF density, compressibility, and number density of the system as characterizing order parameters. We have discovered that, even with the presence of disorder, the phase at each optical lattice site is either MI or SF. Real-space analyses show that the disordered systems contain separated MI and SF phases at different sites, rather than a new global phase. We have also discovered that the local phase at each lattice site is weakly correlated with the phase of neighboring sites; the phase at each site strongly depends on the strength of the local disorder potential.