Abstract
Bose-Hubbard Model on Penrose Tilling Lattices
The standard Bose-Hubbard model has provided a paradigmatic example to explore the quantum phases in a strongly interacting boson system. However, studies so far have considered lattice models with the conventional lattice symmetry (square, triangular, honeycomb etc. in two dimensions), and very few studies have addressed the case of a quasi-crystal. Experimentally, quasi-crystaline optical lattices have been realized in the experiments and this provides a very timely opportunity to investigate the possible quantum states of a Bose-Hubbard model in a quasi-crystal. In our work, we performed the first Quantum Monte Carlo of Bose-Hubbard model on a Penrose tilling lattice at finite temperature. We compute the phase diagram and investigate the behavior of phase transitions by looking at several observables, including entropy, heat capacity, momentum distribution, distribution of condensate fraction and density distributions. Our work can be checked in future experiments.
Josephson Effect of Spinor BECs
The Josephson Effect is an important quantum phenomena in coherent quantum matters such as superconductors and superfluid. The Josephson effect in Bose condensed gas, however, was realized recently in 2005. Unlike the usual superfluid, the Bose condensate in atomic gas can have multiple internal degrees of freedom (the so-called spinor condensate). It thus becomes very interesting to study the Josephson effects in a spinor condensate. We compute the spinor Josephson Hamiltonian and study the Josephson oscillation in the linear regime.
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