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

Topological Reduction of Tight-Binding Models on Complex Networks

Complex molecules and mesoscopic structures are naturally described by general networks of elementary building blocks and tight-binding is one of the simplest quantum model suitable for studying the physical properties arising from the network topology. Despite the simplicity of the model, topological complexity can make the evaluation of the spectrum of the tight-binding Hamiltonian a rather hard task, since the lack of translation invariance rules out such a powerful tool as Fourier transform. In this paper we introduce a rigorous analytical technique, based on topological methods, for the exact solution of this problem on branched structures. Besides its analytic power, this technique is also a promising engineering tool, helpful in the design of netwoks displaying the desired spectral features.Comment: 19 pages, 14 figure

Glassy features of a Bose Glass

We study a two-dimensional Bose-Hubbard model at a zero temperature with random local potentials in the presence of either uniform or binary disorder. Many low-energy metastable configurations are found with virtually the same energy as the ground state. These are characterized by the same blotchy pattern of the, in principle, complex nonzero local order parameter as the ground state. Yet, unlike the ground state, each island exhibits an overall random independent phase. The different phases in different coherent islands could provide a further explanation for the lack of coherence observed in experiments on Bose glasses.Comment: 14 pages, 4 figures

Control of unstable macroscopic oscillations in the dynamics of three coupled Bose condensates

We study the dynamical stability of the macroscopic quantum oscillations characterizing a system of three coupled Bose-Einstein condensates arranged into an open-chain geometry. The boson interaction, the hopping amplitude and the central-well relative depth are regarded as adjustable parameters. After deriving the stability diagrams of the system, we identify three mechanisms to realize the transition from an unstable to stable behavior and analyze specific configurations that, by suitably tuning the model parameters, give rise to macroscopic effects which are expected to be accessible to experimental observation. Also, we pinpoint a system regime that realizes a Josephson-junction-like effect. In this regime the system configuration do not depend on the model interaction parameters, and the population oscillation amplitude is related to the condensate-phase difference. This fact makes possible estimating the latter quantity, since the measure of the oscillating amplitudes is experimentally accessible.Comment: 25 pages, 12 figure

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

Persistence of mean-field features in the energy spectrum of small arrays of Bose-Einstein condensates

The Bose-Hubbard Hamiltonian capturing the essential physics of the arrays of interacting Bose-Einstein condensates is addressed, focusing on arrays consisting of two (dimer) and three (trimer) sites. In the former case, some results concerning the persistence of mean-field features in the energy spectrum of the symmetric dimer are extended to the asymmetric version of the system, where the two sites are characterized by different on-site energies. Based on a previous systematic study of the mean-field limit of the trimer, where the dynamics is exhaustively described in terms of its fixed points for every choice of the significant parameters, an interesting mapping between the dimer and the trimer is emphasized and used as a guide in investigating the persistence of mean-field features in the rather complex energy spectrum of the trimer. These results form the basis for the systematic investigation of the purely quantum trimer extending and completing the existing mean-field analysis. In this respect we recall that, similar to larger arrays, the trimer is characterized by a non-integrable mean-field dynamics featuring chaotic trajectories. Hence, the correspondence between mean-field fixed points and quantum energy levels emphasized in the present work may provide a key to investigate the quantum counterpart of classical instability.Comment: 12 pages, 6 figures, to appear on Journal of Physics B (Special Issue: Levico BEC workshop). Publication status update

Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model

We analyze the quantum phase transition in the Bose-Hubbard model borrowing two tools from quantum-information theory, i.e. the ground-state fidelity and entanglement measures. We consider systems at unitary filling comprising up to 50 sites and show for the first time that a finite-size scaling analysis of these quantities provides excellent estimates for the quantum critical point.We conclude that fidelity is particularly suited for revealing a quantum phase transition and pinning down the critical point thereof, while the success of entanglement measures depends on the mechanisms governing the transition.Comment: 7 pages, 5 figures (endfloats used due to problems with figures and latex. Sorry about that); final version, similar to the published on

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

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