Analytical mean-field approach to the phase-diagram of ultracold bosons in optical superlattices

We report a multiple-site mean-field analysis of the zero-temperature phase diagram for ultracold bosons in realistic optical superlattices. The system of interacting bosons is described by a Bose-Hubbard model whose site-dependent parameters reflect the nontrivial periodicity of the optical superlattice. An analytic approach is formulated based on the analysis of the stability of a fixed-point of the map defined by the self-consistency condition inherent in the mean-field approximation. The experimentally relevant case of the period-2 one-dimensional superlattice is briefly discussed. In particular, it is shown that, for a special choice of the superlattice parameters, the half-filling insulator domain features an unusual loophole shape that the single-site mean-field approach fails to capture.Comment: 7 pages, 1 figur

Strong-coupling expansions for the topologically inhomogeneous Bose-Hubbard model

We consider a Bose-Hubbard model with an arbitrary hopping term and provide the boundary of the insulating phase thereof in terms of third-order strong coupling perturbative expansions for the ground state energy. In the general case two previously unreported terms occur, arising from triangular loops and hopping inhomogeneities, respectively. Quite interestingly the latter involves the entire spectrum of the hopping matrix rather than its maximal eigenpair, like the remaining perturbative terms. We also show that hopping inhomogeneities produce a first order correction in the local density of bosons. Our results apply to ultracold bosons trapped in confining potentials with arbitrary topology, including the realistic case of optical superlattices with uneven hopping amplitudes. Significant examples are provided. Furthermore, our results can be extented to magnetically tuned transitions in Josephson junction arrays.Comment: 5 pages, 2 figures,final versio

Quantum signatures of self-trapping transition in attractive lattice bosons

We consider the Bose-Hubbard model describing attractive bosonic particles hopping across the sites of a translation-invariant lattice, and compare the relevant ground-state properties with those of the corresponding symmetry-breaking semiclassical nonlinear theory. The introduction of a suitable measure allows us to highlight many correspondences between the nonlinear theory and the inherently linear quantum theory, characterized by the well-known self-trapping phenomenon. In particular we demonstrate that the localization properties and bifurcation pattern of the semiclassical ground-state can be clearly recognized at the quantum level. Our analysis highlights a finite-number effect.Comment: 9 pages, 8 figure

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, Bose-glass- are characterized in terms of condensate fraction and superfluid fraction. Furthermore, the boundary of the Mott lobes are related to an off-diagonal Anderson model featuring the same disorder distribution as the original BH Hamiltonian.Comment: 7 pages, 6 figures. Submitted to Laser Physic

Gutzwiller approach to the Bose-Hubbard model with random local impurities

Recently it has been suggested that fermions whose hopping amplitude is quenched to extremely low values provide a convenient source of local disorder for lattice bosonic systems realized in current experiment on ultracold atoms. Here we investigate the phase diagram of such systems, which provide the experimental realization of a Bose-Hubbard model whose local potentials are randomly extracted from a binary distribution. Adopting a site-dependent Gutzwiller description of the state of the system, we address one- and two-dimensional lattices and obtain results agreeing with previous findings, as far as the compressibility of the system is concerned. We discuss the expected peaks in the experimental excitation spectrum of the system, related to the incompressible phases, and the superfluid character of the {\it partially compressible phases} characterizing the phase diagram of systems with binary disorder. In our investigation we make use of several analytical results whose derivation is described in the appendices, and whose validity is not limited to the system under concern.Comment: 12 pages, 5 figures. Some adjustments made to the manuscript and to figures. A few relevant observations added throughout the manuscript. Bibliography made more compact (collapsed some items

Topology-induced confined superfluidity in inhomogeneous arrays

We report the first study of the zero-temperature phase diagram of the Bose-Hubbard model on topologically inhomogeneous arrays. We show that the usual Mott-insulator and superfluid domains, in the paradigmatic case of the comb lattice, are separated by regions where the superfluid behaviour of the bosonic system is confined along the comb backbone. The existence of such {\it confined superfluidity}, arising from topological inhomogeneity, is proved by different analytical and numerical techniques which we extend to the case of inhomogeneous arrays. We also discuss the relevance of our results to real system exhibiting macroscopic phase coherence, such as coupled Bose condensates and Josephson arrays.Comment: 6 pages, 4 figures, final versio

Attractive ultracold bosons in a necklace optical potential

We study the ground state properties of the Bose-Hubbard model with attractive interactions on a M-site one-dimensional periodic -- necklace-like -- lattice, whose experimental realization in terms of ultracold atoms is promised by a recently proposed optical trapping scheme, as well as by the control over the atomic interactions and tunneling amplitudes granted by well-established optical techniques. We compare the properties of the quantum model to a semiclassical picture based on a number-conserving su(M) coherent state, which results into a set of modified discrete nonlinear Schroedinger equations. We show that, owing to the presence of a correction factor ensuing from number conservation, the ground-state solution to these equations provides a remarkably satisfactory description of its quantum counterpart not only -- as expected -- in the weak-interaction, superfluid regime, but even in the deeply quantum regime of large interactions and possibly small populations. In particular, we show that in this regime, the delocalized, Schroedinger-cat-like quantum ground state can be seen as a coherent quantum superposition of the localized, symmetry-breaking ground-state of the variational approach. We also show that, depending on the hopping to interaction ratio, three regimes can be recognized both in the semiclassical and quantum picture of the system.Comment: 11 pages, 7 figures; typos corrected and references added; to appear in Phys. Rev.

Ground-state Properties of Small-Size Nonlinear Dynamical Lattices

We investigate the ground state of a system of interacting particles in small nonlinear lattices with M > 2 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the contexts of nonlinear optics of waveguide arrays, and Bose-Einstein condensates in optical lattices. We find that, in the presence of attractive interactions, the dynamical scenario relevant to the ground state and the lowest-energy modes of such few-site nonlinear lattices reveals a variety of nontrivial features that are absent in the large/infinite lattice limits: the single-pulse solution and the uniform solution are found to coexist in a finite range of the lattice intersite coupling where, depending on the latter, one of them represents the ground state; in addition, the single-pulse mode does not even exist beyond a critical parametric threshold. Finally, the onset of the ground state (modulational) instability appears to be intimately connected with a non-standard (``double transcritical'') type of bifurcation that, to the best of our knowledge, has not been reported previously in other physical systems.Comment: 7 pages, 4 figures; submitted to PR

Microscopic energy flows in disordered Ising spin systems

An efficient microcanonical dynamics has been recently introduced for Ising spin models embedded in a generic connected graph even in the presence of disorder i.e. with the spin couplings chosen from a random distribution. Such a dynamics allows a coherent definition of local temperatures also when open boundaries are coupled to thermostats, imposing an energy flow. Within this framework, here we introduce a consistent definition for local energy currents and we study their dependence on the disorder. In the linear response regime, when the global gradient between thermostats is small, we also define local conductivities following a Fourier dicretized picture. Then, we work out a linearized "mean-field approximation", where local conductivities are supposed to depend on local couplings and temperatures only. We compare the approximated currents with the exact results of the nonlinear system, showing the reliability range of the mean-field approach, which proves very good at high temperatures and not so efficient in the critical region. In the numerical studies we focus on the disordered cylinder but our results could be extended to an arbitrary, disordered spin model on a generic discrete structures.Comment: 12 pages, 6 figure