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arXiv:cond-mat/0308235 · Physical Review A

Two-component Bose gas in an optical lattice at single-particle filling

K. Ziegler

Published Nov 3, 2003• 26 citations
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Abstract

The Bose-Hubbard model of a twofold degenerate Bose gas is studied in an optical lattice with one particle per site and virtual tunneling to empty and doubly occupied sites. An effective Hamiltonian for this system is derived within a continued-fraction approach. The ground state of the effective model is studied in mean-field approximation for a modulated optical lattice. A dimerized mean-field state gives a Mott insulator whereas the lattice without modulations develops long-range correlated phase fluctuations due to a Goldstone mode. This result is discussed in comparison with the superfluid and the Mott-insulating state of a single-component hard-core Bose gas.

DOI
10.1103/physreva.68.053602

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The Bose-Hubbard model of a twofold degenerate Bose gas is studied in an optical lattice with one particle per site and virtual tunneling to empty and doubly occupied sites. An effective Hamiltonian for this system is derived within a continued-fraction approach. The ground state of the effective model is studied in mean-field approximation for a modulated optical lattice. A dimerized mean-field state gives a Mott insulator whereas the lattice without modulations develops long-range correlated phase fluctuations due to a Goldstone mode. This result is discussed in comparison with the superfluid and the Mott-insulating state of a single-component hard-core Bose gas.
We discuss the superfluid to Mott insulator transition of an atomic Bose gas in an optical lattice with high filling factors. We show that in this multiband situation, the long-wavelength physics is described by a single-band Bose-Hubbard model. We determine the many-body renormalization of the tunneling and interaction parameters in the effective Bose-Hubbard Hamiltonian, and consider the resulting model at nonzero temperatures. We show that, in particular, for a one- or two-dimensional optical lattice, the Mott-insulator phase is more difficult to realize than anticipated previously.
We investigate properties of an ultracold, two-component bosonic gas in a square optical lattice at unit filling. In addition to density-density interactions, the atoms are subject to coherent light-matter interactions that couple different internal states. We examine the influence of this coherent coupling on the system and its quantum phases by using Gutzwiller mean-field theory as well as bosonic dynamical mean-field theory. We find that the interplay of strong interspecies repulsion and coherent coupling affects the Mott insulator to superfluid transition and shifts the tip of the Mott lobe toward higher values of the tunneling amplitude. In the strongly interacting Mott regime, the resulting Bose-Hubbard model can be mapped onto an effective spin Hamiltonian that offers additional insights into the observed phenomena.
We describe the ground state of a gas of bosonic atoms with two coherently coupled internal levels in a deep optical lattice in a one-dimensional geometry. In the single-band approximation this system is described by a Bose-Hubbard Hamiltonian. The system has a superfluid and a Mott insulating phase that can be either paramagnetic or ferromagnetic. We characterize the quantum phase transitions at unit filling by means of a density-matrix renormalization-group technique and compare the results with a mean-field approach and an effective spin Hamiltonian. The presence of the ferromagnetic Ising-like transition modifies the Mott lobes. In the Mott insulating region the system maps to the ferromagnetic spin-1/2 XXZXXZXXZ model in a transverse field and the numerical results compare very well with the analytical results obtained from the spin model. In the superfluid regime quantum fluctuations strongly modify the phase transition with respect to the well-established mean-field three-dimensional classical bifurcation.
The Bose Hubbard model describing interacting bosons in an optical lattice is reduced to a simple spin-1 XY model with single-ion anisotropy in the vicinity of the Mott phase. In the strong coupling Mott insulating regime, we propose a mean field theory based on a constraint SU (3) pseudo-boson representation on the effective model and discuss the excitation spectra and the phase transition to the superfluid state. Further to the superfluid phase, we use the coherent-state approach to derive the collective excitation modes. It is found that the Mott phase has two degenerate gapped quadratic excitation spectra which graduate into two degenerate gapless linear ones at the transition point, and one gapless linear mode with one gapped quadratic mode in the superfluid phase.
Two-component coupled Bose gas in a 1D optical lattice is examined. In addition to the postulated Mott insulator and Superfluid phases, multiple bosonic components manifest spin degrees of freedom. Coupling of the components in the Bose gas within same site and neighboring sites leads to substantial change in the previously observed spin phases revealing fascinating remarkable spin correlations. In the presence of strong interactions it gives rise to unconventional effective ordering of the spins leading to unprecedented spin phases: site-dependent z-xz\textsf{-}xz-x spin configuration with tunable (by hopping parameter) proclivity of spin alignment along zzz. Exact analysis and Variational Monte Carlo (VMC) along with stochastic minimization on Entangled Plaquette State (EPS) bestow a unique and enhanced perspective into the system beyond the scope of mean-field treatment. The physics of complex intra-component tunneling and inter-component coupling and filling factor greater than unity are discussed.
Abstract We study cold bosonic atoms on a two-dimensional inhomogeneous optical lattice with site-dependent atomic interactions. With the tight-binding approximation, we derive the extended Bose–Hubbard model. Base on the mean-field approximation, the ground states are solved by the exact diagonalization method. We calculate the mean-field order parameter and particle number density for the ground states. We find the coexistence of superfluid phase and Mott-insulator phase on the two-dimensional inhomogeneous optical lattice in appropriate parameter ranges.