Quantum glass phases in the disordered Bose-Hubbard model

The phase diagram of the Bose-Hubbard model in the presence of off-diagonal disorder is determined using quantum Monte Carlo simulations. A sequence of quantum glass phases intervene at the interface between the Mott insulating and the superfluid phases of the clean system. In addition to the standard Bose glass phase, the coexistence of gapless and gapped regions close to the Mott insulating phase leads to a novel Mott glass regime which is incompressible yet gapless. Numerical evidence for the properties of these phases is given in terms of global (compressibility, superfluid stiffness) and local (compressibility, momentum distribution) observables.     

Staggered-vortex superfluid of ultracold bosons in an optical lattice

We show that the dynamics of cold bosonic atoms in a two-dimensional square optical lattice produced by a bichromatic light-shift potential is described by a Bose-Hubbard model with an additional effective staggered magnetic field. In addition to the known uniform superfluid and Mott insulating phases, the zero-temperature phase diagram exhibits a novel kind of finite-momentum superfluid phase, characterized by a quantized staggered rotational flux. An extension for fermionic atoms leads to an anisotropic Dirac spectrum, which is relevant to graphene and high-T(c) superconductors.     

Quantum phase analysis of 1D superconducting quantum dot lattice using extended Bose-Hubbard model

We have obtained the quantum phase diagram of a one-dimensional superconducting quantum dot lattice using the extended Bose-Hubbard model for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from the Mott insulating phase to the superconducting phase for integer band fillings of Cooper pairs. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, besides the charge density wave and superconducting phases for half-integer band fillings. We also predict that extended range interactions are necessary to obtain the correct phase boundary of a one-dimensional interacting Cooper system. We have used the density matrix renormalization group method and Abelian bosonization to study our system.     

Dipolar molecules in optical lattices

We study the extended Bose-Hubbard model describing an ultracold gas of dipolar molecules in an optical lattice, taking into account all on-site and nearest-neighbor interactions, including occupation-dependent tunneling and pair tunneling terms. Using exact diagonalization and the multiscale entanglement renormalization ansatz, we show that these terms can destroy insulating phases and lead to novel quantum phases. These considerable changes of the phase diagram have to be taken into account in upcoming experiments with dipolar molecules.     

Off-site trimer superfluid on a one-dimensional optical lattice

The Bose-Hubbard model with an effective off-site three-body tunneling,characterized by jumps towards one another,between one atom on a site and a pair atoms on the neighborhood site,is studied systematically on a one-dimensional(1D) lattice,by using the density matrix renormalization group method.The off-site trimer superfluid,condensing at momentum k = 0,emerges in the softcore Bose-Hubbard model but it disappears in the hardcore Bose-Hubbard model.Our results numerically verify that the off-site trimer superfluid phase derived in the momentum space from[Phys.Rev.A81,011601(R)(2010)]is stable in the thermodynamic limit.The off-site trimer superfluid phase,the partially off-site trimer superfluid phase and the Mott insulator phase are found,as well as interesting phase transitions,such as the continuous or first-order phase transition from the trimer superfluid phase to the Mott insulator phase.Our results are helpful in realizing this novel off-site trimer superfluid phase by cold atom experiments.     

Artificial gauge fields for the Bose-Hubbard model on a checkerboard superlattice and extended Bose-Hubbard model

We study the effects of an artificial gauge field on the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and alternating Mott insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid-alternating-Mott insulator phase transition boundaries. Finally, since the phase diagram of the Bose-Hubbard model on a checkerboard superlattice is in many ways similar to that of the extended Bose-Hubbard model, we comment on the effects of magnetic field on the latter model, and derive an analytical mean-field expression for the superfluid-insulator phase transition boundaries as well.     

Effective Bose-Hubbard interaction with enhanced nonlinearity in an array of coupled cavities

An array of coupled cavities,each of which contains an N four-level atom,is investigated.When cavity fields dispersively interact with the atoms,an effective Bose-Hubbard model can be achieved.By numerically comparing the full Hamiltonian with the effective one,we find that within the parameters region,the effective Hamiltonian can completely account for the Mott-insulator as well as the phase transition from the similar Mott-insulator to superfluid.Through jointly adjusting the classical Rabi frequency and the detuning,the nonlinearity can be improved.     

Classical behaviour of various variables in an open Bose-Hubbard system

Quantum dispersions of various sets of dynamical variables of an open Bose-Hubbard system in a classical limit are studied. To this end, an open system is described in terms of stochastic evolution of its quantum pure states. It is shown that the class of variables that display classical behaviour crucially depends on the type of noise. This is relevant in the mean-field approximation of open Bose-Hubbard dynamics.     

Classical behaviour of various variables in an open Bose-Hubbard system

Quantum dispersions of various sets of dynamical variables of an open Bose-Hubbard system in a classical limit are studied. To this end, an open system is described in terms of stochastic evolution of its quantum pure states. It is shown that the class of variables that display classical behaviour crucially depends on the type of noise. This is relevant in the mean-field approximation of open Bose-Hubbard dynamics.     

On the pressure-temperature phase diagram of intermediate valence compounds

The pressure-temperature (P, T) phase diagram of intermediate valence compounds has been calculated on the basis of the periodic Anderson model which was extended to include the interaction of 4f electrons with longitudinal optical phonons. It is shown that the positive slope (dP/dT>0) of the phase boundary between the insulating and the mixed valence phase as observed experimentally in Sm S and many other systems is determined by the behaviour of the electronic density of states of the interacting system as function ofP. Moreover, the observed anomalous thermal contraction in the insulating phase near the phase boundary and the anomalously large thermal expansion in the metallic phase are well described by numerical results for the extended periodic Anderson model.     

Mott-insulator transition in a two-dimensional atomic Bose gas

Cold atoms in periodic potentials are versatile quantum systems for implementing simple models prevalent in condensed matter theory. Here we realize the 2D Bose-Hubbard model by loading a Bose-Einstein condensate into an optical lattice, and study the resulting Mott insulator. The measured momentum distributions agree quantitatively with theory (no adjustable parameters). In these systems, the Mott insulator forms in a spatially discrete shell structure which we probe by focusing on correlations in atom shot noise. These correlations show a marked dependence on the lattice depth, consistent with the changing size of the insulating shell expected from simple arguments.     

Extended Bose-Hubbard model with pair hopping on triangular lattice

We study systematically an extended Bose-Hubbard model on the triangular lattice by means of a meanfield method based on the Gutzwiller ansatz. Pair hopping terms are explicitly included and a three-body constraint is applied. The zero-temperature phase diagram and a variety of quantum phase transitions are investigated in great detail. In particular, we show the existence and the stability of the pair supersolid phase.     

Quantum phase transitions in the bosonic single-impurity Anderson model

We consider a quantum impurity model in which a bosonic impurity level is coupled to a non-interacting bosonic bath, with the bosons at the impurity site subject to a local Coulomb repulsion U. Numerical renormalization group calculations for this bosonic single-impurity Anderson model reveal a zero-temperature phase diagram where Mott phases with reduced charge fluctuations are separated from a Bose-Einstein condensed phase by lines of quantum critical points. We discuss possible realizations of this model, such as atomic quantum dots in optical lattices. Furthermore, the bosonic single-impurity Anderson model appears as an effective impurity model in a dynamical mean-field theory of the Bose-Hubbard model.     

Bose-Hubbard phase transition with two- and three-body interaction in a magnetic field

Phase boundaries of classical and quantum phase transitions of two-dimensional Bose-Hubbard model with two- and three-body on-site interactions in a magnetic field are obtained analytically in a unified theoretical frame. All results illustrate that the introduction of magnetic field enhances the stability of normal state and Mott insulator.     

Phase Dissipation of an Open Two-Mode Bose-Einstein Condensate

We study the dynamics of a two-mode Bose-Hubbard model with phase dissipation, based on the master equation.An analytical solution is presented with nonzero asymmetry and phase noise. The effects of asymmetry and phase noise play a contrasting role in the dynamics. The asymmetry makes the oscillation fast, while phase noise enlarges the period. The conditions for the cases of fast decay and oscillation are presented. As a possible application,the dynamical evolution of the population for cold atomic gases with synthetic gauge interaction, which can be understood as two-mode dynamics in momentum space, is predicted.     

Excitation Spectrum and Momentum Distribution of Bose-Hubbard Model with On-site Two-and Three-Body Interaction

An effective action for Bose-Hubbard model with two-and three-body on-site interaction in a square optical lattice is derived in the frame of a strong-coupling approach developed by Sengupta and Dupuis.From this effective action,superfluid-Mott insulator(MI) phase transition,excitation spectrum and momentum distribution for two phases are calculated by taking into account Gaussian fluctuation about the saddle-point approximation.In addition the effects of three-body interaction are also discussed.     

Mean-field phase diagram for Bose-Hubbard Hamiltonians with random hopping

The zero temperature phase diagram for ultracold bosons in a random 1D potential is obtained through a site decoupling mean-field scheme performed over a Bose-Hubbard (BH) Hamiltonian, whose hopping term is considered as a random variable. As for the model with random on-site potential, the presence of disorder leads to the appearance of a Bose glass phase. The different phases—i.e., Mott insulator, superfluid, and Bose glass—are characterized in terms of condensate fraction and superfluid fraction. Furthermore, the boundary of the Mott lobes is related to an off-diagonal Anderson model featuring the same disorder distribution as the original BH Hamiltonian.     

Possibility of a first-order superfluid-Mott-insulator transition of spinor bosons in an optical lattice

We study the superfluid-Mott-insulator transition of antiferromagnetic spin-1 bosons in an optical lattice described by a Bose-Hubbard model. Our variational study with the Gutzwiller variational wave function determines that the superfluid-Mott-insulator transition is a first-order one at a part of the phase boundary curve, contrary to the spinless case.     

Magnetic field induced metal-insulator transitions in p-SiGe

Low density modulation doped p-SiGe, where the holes lie in a strained SiGe quantum well, frequently exhibits anomalous insulating behaviour between filling factors ν=2 and 1. There is also anomalous metallic behavior with a metal-insulator transition between the two. It is shown that in these samples exchange effects are sufficiently large to induce the paramagnetic-ferromagnetic phase transition predicted by Giuliani and Quinn in 1985, also that the metallic and insulating behavior is associated with the coincidence of two Landau levels of opposite spin. A model calculation shows that while a ferromagnetic polarization may occur at integer filling factors screening suppresses it for non-integer filling factors. It is argued the Landau levels then stick-together and allow a spin-density instability to form. Because of the strong spin-orbit coupling in p-SiGe the transport properties of this state differ from those of other systems where a similar quantum Hall ferromagnet probably forms.