Slave particle approach to the finite temperature properties of ultracold Bose gases in optical lattices

Exact diagonalization techniques are a powerful method for studying many-body problems. Here, we apply this method to systems of few bosons in an optical lattice, and use it to demonstrate the emergence of interesting quantum phenomena like fragmentation and coherence. Starting with a standard Bose-Hubbard Hamiltonian, we first revise the characterization of the superfluid to Mott insulator transitions. We then consider an inhomogeneous lattice, where one potential minimum is...

A new formulation for the study of interacting bosons on a lattice is introduced. This approach is used to give analytical expressions for the Mott insulating lobes in the phase diagram and to calculate the density-density correlation function. It is also shown that, at mean-field level, this newly introduced slave boson theory coincides with mean-field theory of a suitably introduced order parameter.

The objective of this paper is the theoretical description of the Mott-insulator to superfluid quantum phase transition of a Bose gas in an optical lattice. In former works the Rayleigh-Schr\"odinger perturbation theory was used within a mean-field approach, which yields partially non-physical results since the degeneracy between two adjacent Mott lobes is not taken into account. In order to correct such non-physical results we apply the Brillouin-Wigner perturbation theory t...

We analyze various quantum phases of ultracold bosonic atoms in a periodic one dimensional optical superlattice. Our studies have been performed using the finite size density matrix renormalization group (FS-DMRG) method in the framework of the Bose-Hubbard model. Calculations have been carried out for a wide range of densities and the energy shifts due to the superlattice potential. At commensurate fillings, we find the Mott insulator and the superfluid phases as well as Mot...

We consider the effects of temperature upon the superfluid phase of ultracold, weakly interacting bosons in a one dimensional optical lattice. We use a finite temperature treatment of the Bose-Hubbard model based upon the Hartree-Fock-Bogoliubov formalism, considering both a translationally invariant lattice and one with additional harmonic confinement. In both cases we observe an upward shift in the critical temperature for Bose condensation. For the case with additional har...

Bosonic atoms confined in optical lattices can exist in two different phases, Mott-insulator and superfluid, depending on the strength of the system parameters, such as the on-site interaction between particles and the hopping parameter. This work is motivated by the fact that non-degenerate perturbation theory applied to the mean-field approximation of the Bose-Hubbard Hamiltonian at zero and finite temperature fails to give consistent results in the vicinity of the Mott-ins...

We study quantum phases of ultracold bosonic atoms in a two-dimensional optical superlattice. The extended Bose-Hubbard model derived from the system of ultracold bosonic atoms in an optical superlattice is solved numerically with Gutzwiller approach. We find that the modulated superfluid(MS), Mott-insulator (MI) and density-wave(DW) phases appear in some regimes of parameters. The experimental detection of the first order correlations and the second order correlations of dif...

A practical finite temperature theory is developed for the superfluid regime of a weakly interacting Bose gas in an optical lattice with additional harmonic confinement. We derive an extended Bose-Hubbard model that is valid for shallow lattices and when excited bands are occupied. Using the Hartree-Fock-Bogoliubov-Popov mean-field approach, and applying local density and coarse-grained envelope approximations, we arrive at a theory that can be numerically implemented accurat...

We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive Hubbard-Stratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about ...

In this paper, we investigate systematically the Mott-insulator-Superfluid quantum phase transitions for ultracold scalar bosons in triangular, hexagonal, as well as Kagom\'e optical lattices. With the help of field-theoretical effective potential, by treating the hopping term in Bose-Hubbard model as perturbation, we calculate the phase boundaries analytically for different integer filling factors. Our analytical results are in good agreement with recent numerical results.