We present an extensive study of Mott insulator (MI) and superfluid (SF) shells in Bose-Hubbard (BH) models for bosons in optical lattices with harmonic traps. For this we apply the inhomogeneous mean-field theory developed by Sheshadri et al. [Phys. Rev. Lett. 75, 4075 (1995)]. Our results for the BH model with one type of spinless bosons agree quantitatively with quantum Monte Carlo simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculations on experimentally realistic, large three-dimensional systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also extend our inhomogeneous mean-field theory to study BH models with harmonic traps and (a) two species of bosons or (b) spin-1 bosons. With two species of bosons, we obtain rich phase diagrams with a variety of SF and MI phases and associated shells when we include a quadratic confining potential. For the spin-1 BH model, we show, in a representative case, that the system can display alternating shells of polar SF and MI phases, and we make interesting predictions for experiments in such systems.
We present an extensive study of Mott insulator (MI) and superfluid (SF) shells in Bose-Hubbard (BH) models for bosons in optical lattices with harmonic traps. For this we apply the inhomogeneous mean-field theory developed by Sheshadri et al. [Phys. Rev. Lett. 75, 4075 (1995)]. Our results for the BH model with one type of spinless bosons agree quantitatively with quantum Monte Carlo simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculations on experimentally realistic, large three-dimensional systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also extend our inhomogeneous mean-field theory to study BH models with harmonic traps and (a) two species of bosons or (b) spin-1 bosons. With two species of bosons, we obtain rich phase diagrams with a variety of SF and MI phases and associated shells when we include a quadratic confining potential. For the spin-1 BH model, we show, in a representative case, that the system can display alternating shells of polar SF and MI phases, and we make interesting predictions for experiments in such systems.
Abstract We develop an inhomogeneous mean‐field theory for the extended Bose‐Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean‐field theory yields the phase diagram of the homogeneous extended Bose‐Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott‐insulator (MI), density‐wave (DW), and supersolid (SS) phases in the plane of the chemical potential µ and on‐site repulsion U; we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest‐neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density‐wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold‐atom dipolar condensates in optical lattices in a confining potential.
We use quantum Monte Carlo (QMC) simulations to study the combined effects of harmonic confinement and temperature for bosons in a two-dimensional(2D) optical lattice. The scale-invariant, finite temperature state diagram is presented for the Bose-Hubbard model in terms of experimental parameters -- the particle number, confining potential and interaction strength. To distinguish the nature of the spatially separated superfluid, Mott insulator, and normal Bose liquid phases, we examine the local density, compressibility, superfluid density, and Green's function. In the annular superfluid rings, as the width of the ring decreases, the long-range superfluid correlations start to deviate from an equivalent homogeneous 2D system. At zero temperature, the correlation decay is intermediate between one-dimension and two-dimensions, while at a finite temperature, the decay is similar to that in one-dimension at a much lower temperature. The calculations reveal shortcomings of the local density approximation in describing superfluid properties of trapped bosons. We also present the finite-temperature phase diagram for the homogeneous two dimensional Bose-Hubbard model. We compare our state diagram with the results of a recent experiment at NIST on a harmonically trapped 2D lattice [Phys. Rev. Lett. 105, 110401 (2010)], and identify a finite-temperature effect in the experiment.
We generalize the mean-field theory for the spinless Bose-Hubbard model to account for the different types of superfluid phases that can arise in the spin-1 case. In particular, our mean-field theory can distinguish polar and ferromagnetic superfluids, Mott insulator, that arise at integer fillings at zero temperature, and normal Bose liquids into which the Mott insulators evolve at finite temperatures. We find, in contrast to the spinless case, that several of the superfluid-Mott insulator transitions are of first order at finite temperatures. Our systematic study yields rich phase diagrams that include first-order and second-order transitions and a variety of tricritical points. We discuss the possibility of realizing such phase diagrams in experimental systems.
We present a cluster mean-field study for ground-state phase diagram and many-body dynamics of spin-1 bosons confined in a two-chain Bose–Hubbard ladder (BHL). For unbiased BHL, we find superfluid (SF) phase and integer filling Mott insulator (IntMI) phase. For biased BHL, in addition to the SF and IntMI phases, there appears half-integer filling Mott insulator (HIntMI) phase. The phase transition between the SF and IntMI phases can be first order at a part of phase boundaries, while the phase transition between the SF and HIntMI phases is always second order. By tuning the bias energy, we report on the change of the nature of SF–MI phase transitions. Furthermore, we study the effect of the spin-dependent interaction on the many-body population dynamics. The spin-dependent interaction can lead to rich dynamical behaviors, but does not influence the particle transfer efficiency. Our results indicate a way to tune the nature of the SF–MI phase transition and open a new avenue to study the many-body dynamics of spinor bosons in optical lattices.
The Bose-Hubbard model describes the physics of a system of bosonic ultracold atoms in an optical lattice, in which a phase transition is present between a superfluid phase and a Mott insulator one. \nThe exact solution of this Hamiltonian is only feasible to find the ground-state of small systems, while other techniques (as mean-field schemes or quantum Monte Carlo) are necessary to study systems of larger size. \n \nAs a first application, we study the trapped model - relevant for the comparison with current experiments - through an inhomogeneous mean-field scheme. We describe some signatures of the phase crossover between superfluid and Mott insulator. In particular, the visibility of the quasimomentum distribution shows some kinks as a function of the lattice depth; we describe these features and we link them with the ones observed in other works in the literature. \n \nAs a second application, we use quantum Monte Carlo techniques to study the one-dimensional Bose-Hubbard model with long-range interactions and we focus on the appearance of the Haldane insulating phase, distinguishable from the Mott one through the presence of non-local hidden order. \nNon-local correlation functions are also used to describe the difference between the superfluid phase and the Mott insulator one.
Motivated by the experimental realization of synthetic spin-orbit coupling for ultracold atoms, we investigate the phase diagram of the Bose-Hubbard model in a non-Abelian gauge field in two dimensions. Using a strong coupling expansion in the combined presence of spin-orbit coupling and tunable interactions, we find a variety of interesting magnetic Hamiltonians in the Mott insulator (MI), which support magnetic textures such as spin spirals and vortex and Skyrmion crystals. An inhomogeneous mean-field treatment shows that the superfluid (SF) phases inherit these exotic magnetic orders from the MI and display, in addition, unusual modulated current patterns. We present a slave-boson theory which gives insight into such intertwined spin-charge orders in the SF, and discuss signatures of these orders in Bragg scattering, in situ microscopy, and dynamic quench experiments.