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.     

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.     

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.     

Quench dynamics and nonequilibrium phase diagram of the bose-hubbard model

We investigate the time evolution of correlations in the Bose-Hubbard model following a quench from the superfluid to the Mott insulator. For large values of the final interaction strength the system approaches a distinctly nonequilibrium steady state that bears strong memory of the initial conditions. In contrast, when the final interaction strength is comparable to the hopping, the correlations are rather well approximated by those at thermal equilibrium. The existence of two distinct nonequilibrium regimes is surprising given the nonintegrability of the Bose-Hubbard model. We relate this phenomenon to the role of quasiparticle interactions in the Mott insulator.     

Quantum fluctuations, temperature, and detuning effects in solid-light systems

The superfluid to Mott insulator transition in cavity polariton arrays is analyzed using the variational cluster approach, taking into account quantum fluctuations exactly on finite length scales. Phase diagrams in one and two dimensions exhibit important non-mean-field features. Single-particle excitation spectra in the Mott phase are dominated by particle and hole bands separated by a Mott gap. In contrast to Bose-Hubbard models, detuning allows for changing the nature of the bosonic particles from quasilocalized excitons to polaritons to weakly interacting photons. The Mott state with density one exists up to temperatures T/g > or = 0.03, implying experimentally accessible temperatures for realistic cavity couplings g.     

Superfluidity-insulator phase transition in ensemble of Fermi atoms in optical lattice

An ultracold Fermi gas in an optical lattice with a parabolic potential is modeled by the quantum Monte Carlo method. The gas density profile is calculated in the Hubbard model; it is shown that a domain with a density of one atom per site is formed in the trap that corresponds to the Mott insulator state. The insulator phase is surrounded by a superfluid region occupying the center of the trap, as well as its periphery.     

Zoo of quantum phases and excitations of cold bosonic atoms in optical lattices

Quantum phases and phase transitions of weakly to strongly interacting bosonic atoms in deep to shallow optical lattices are described by a single multiorbital mean-field approach in real space. For weakly interacting bosons in one dimension, the critical value of the superfluid to Mott insulator (MI) transition found is in excellent agreement with many-body treatments of the Bose-Hubbard model. For strongly interacting bosons, (i) additional MI phases appear, for which two (or more) atoms residing in each site undergo a Tonks-Girardeau-like transition and localize, and (ii) on-site excitation becomes the excitation lowest in energy. Experimental implications are discussed.     

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.     

Superfluid-Mott-Insulator Phase Transition of Bosons in an Optical Lattice

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 Mort phase. We propose a mean-field theory based on a constraint SU（3） pseudo-boson representation on the effective model to study the properties of the superfluid-Mott-insulator phase transition. By calculating the elementary excitation spectra and the average particle number tluctuation in the Brillouin zone center, we lind that the energy gaps vanish continuously around （JXY/Jz）c≈ 0.175 and （JxY/Jz）c ≈ 0.094 for 2D and 3D cubic lattices respectively, where the superfluid order parameters come up from zero and the Mort insulator state changes into a superfluid state.     

Strong coupling expansion for the Bose-Hubbard and Jaynes-Cummings lattice models

A strong coupling expansion based on the Kato-Bloch perturbation theory, which has recently been proposed by Eckardt et?al (2009 Phys. Rev. B 79 195131) and Teichmann et?al (2009 Phys. Rev. B 79 224515), is implemented in order to study various aspects of the Bose-Hubbard and Jaynes-Cummings lattice models. The approach, which allows us to generate numerically all diagrams up to a desired order in the interaction strength, is generalized for disordered systems and for the Jaynes-Cummings lattice model. Results for the Bose-Hubbard and Jaynes-Cummings lattice models will be presented and compared with results from the variational cluster approach and density matrix renormalization group. Our focus will be on the Mott insulator to superfluid transition.     

Scaling property of the critical hopping parameters for the Bose-Hubbard model

Recently precise results for the boundary between the Mott insulator phase and the superfluid phase of the homogeneous Bose-Hubbard model have become available for arbitrary integer filling factor g and any lattice dimension d ≥ 2. We use these data for demonstrating that the critical hopping parameters obey a scaling relationship which allows one to map results for different g onto each other. Unexpectedly, the mean-field result captures the dependence of the exact critical parameters on the filling factor almost fully. We also present an approximation formula which describes the critical parameters for d ≥ 2 and any g with high accuracy.     

Sweeping from the superfluid to the Mott phase in the Bose-Hubbard model

We study the sweep through the quantum phase transition from the superfluid to the Mott state for the Bose-Hubbard model with a time-dependent tunneling rate J(t). In the experimentally relevant case of exponential decay J(t) proportional variant e -gamma t, an adapted mean-field expansion for large fillings n yields a scaling solution for the fluctuations. This enables us to analytically calculate the evolution of the number and phase variations (on-site) and correlations (off-site) for slow (gammamu) sweeps, where mu is the chemical potential. Finally, we derive the dynamical decay of the off-diagonal long-range order as well as the temporal shrinkage of the superfluid fraction in a persistent ring-current setup.     

Superfluid-insulator transition in a periodically driven optical lattice

We demonstrate that the transition from a superfluid to a Mott insulator in the Bose-Hubbard model can be induced by an oscillating force through an effective renormalization of the tunneling matrix element. The mechanism involves adiabatic following of Floquet states, and can be tested experimentally with Bose-Einstein condensates in periodically driven optical lattices. Its extension from small to very large systems yields nontrivial information on the condensate dynamics.     

Migration of Bosonic particles across a Mott insulator to a superfluid phase interface

We consider a boundary between a Mott insulator and a superfluid region of a Bose-Hubbard model at unit filling. Initially both regions are decoupled and cooled to their respective ground states. We show that, after switching on a small tunneling rate between both regions, all particles of the Mott region migrate to the superfluid area. This migration takes place whenever the difference between the chemical potentials of both regions is less than the maximal energy of any eigenmode of the superfluid. We verify our results numerically with density matrix renormalization group simulations and explain them analytically with a master equation approximation, finding good agreement between both approaches. Finally we carry out a feasibility study for the observation of the effect in coupled arrays of microcavities and optical lattices.     

Creation of a dipolar superfluid in optical lattices

We show that, by loading a Bose-Einstein condensate of two different atomic species into an optical lattice, it is possible to achieve a Mott-insulator phase with exactly one atom of each species per lattice site. A subsequent photoassociation leads to the formation of one heteronuclear molecule with a large electric dipole moment, at each lattice site. The melting of such a dipolar Mott insulator creates a dipolar superfluid, and eventually a dipolar molecular condensate.     

A review of Monte Carlo simulations for the Bose–Hubbard model with diagonal disorder

We review the physics of the Bose–Hubbard model with disorder in the chemical potential focusing on recently published analytical arguments in combination with quantum Monte Carlo simulations. Apart from the superfluid and Mott insulator phases that can occur in this system without disorder, disorder allows for an additional phase, called the Bose glass phase. The topology of the phase diagram is subject to strong theorems proving that the Bose Glass phase must intervene between the superfluid and the Mott insulator and implying a Griffiths transition between the Mott insulator and the Bose glass. The full phase diagrams in 3d and 2d are discussed, and we zoom in on the insensitivity of the transition line between the superfluid and the Bose glass in the close vicinity of the tip of the Mott insulator lobe. We briefly comment on the established and remaining questions in the 1d case, and give a short overview of numerical work on related models.     

Superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice

The accessibility of the critical parameters for the superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice is investigated. We determine the hopping matrix element J, the on-site interaction U, and hence the ratio J/U, in the harmonic oscillator wave function approximation. We show that for a range of realistic parameters the critical values of J/U, predicted by different methods for the Bose-Hubbard model in 2D, such as mean field theory and Monte Carlo simulations, are accessible in a 2D permanent magnetic lattice. The calculations are performed for a 2D permanent magnetic lattice created by two crossed arrays of parallel rectangular magnets plus a bias magnetic field.     

Superfluid to Mott‐insulator transition in an anisotropic two‐dimensional optical lattice

We study the superfluid to Mott‐insulator transition of bosons in an optical anisotropic lattice by employing the Bose‐Hubbard model living on a two‐dimensional lattice with anisotropy parameter κ. The compressible superfluid state and incompressible Mott‐insulator (MI) lobes are efficiently described analytically, using the quantum U(1) rotor approach. The ground state phase diagram showing the evolution of the MI lobes is quantified for arbitrary values of κ, corresponding to various kind of lattices: from square, through rectangular to almost one‐dimensional.     

Tuning the Mott transition in a Bose-Einstein condensate by multiple photon absorption

We study the time-dependent dynamics of a Bose-Einstein condensate trapped in an optical lattice. Modeling the system as a Bose-Hubbard model, we show how applying a periodic driving field can induce coherent destruction of tunneling. In the low-frequency regime, we obtain the novel result that the destruction of tunneling displays extremely sharp peaks when the driving frequency is resonant with the depth of the trapping potential ("multi-photon resonances"), which allows the quantum phase transition between the Mott insulator and the superfluid state to be controlled with high precision. We further show how the waveform of the field can be chosen to maximize this effect.     

Phase diagram for a Bose-Einstein condensate moving in an optical lattice

The stability of superfluid currents in a system of ultracold bosons was studied using a moving optical lattice. Superfluid currents in a very weak lattice become unstable when their momentum exceeds 0.5 recoil momentum. Superfluidity vanishes already for zero momentum as the lattice deep reaches the Mott insulator (MI) phase transition. We study the phase diagram for the disappearance of superfluidity as a function of momentum and lattice depth between these two limits. Our phase boundary extrapolates to the critical lattice depth for the superfluid-to-MI transition with 2% precision. When a one-dimensional gas was loaded into a moving optical lattice a sudden broadening of the transition between stable and unstable phases was observed.