Effective Field Theory for Two-Species Bosons in an Optical Lattice: Multiple Order, the Nambu--Goldstone Bosons, the Higgs Mode, and Vortex Lattice

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In the previous papers, we studied the bosonic t--J mode and derived an effective field theory, which is a kind of quantum XY model. The bosonic t--J model is expected to be realized by experiments of two-component cold atoms in an optical lattice. In this paper, we consider a similar XY model that describes phase diagram of the t--J model with a mass difference. Phase diagram and critical behavior of the quantum XY model are clarified by means of the Monte-Carlo simulations. Effective field theory that describes the phase structure and low-energy excitations of the quantum XY model is derived. Nambu--Goldstone bosons and the Higgs mode are studied by using the effective field theory and interesting findings are obtained for the system with multiple order, i.e., Bose--Einstein condensations and pseudo-spin symmetry. We also investigate physical properties of the quantum XY model in an effective magnetic field that is realized by rotating the optical lattice, etc. We show that low-energy states of the system strongly depend on the strength of the ``magnetic field''. For some specific strength of the magnetic field, vortex lattice forms and the correlation function of the bosons exhibits solid like behavior, which is a kind of Bose--Einstein condensation.
2013-12-15