We analyze the quantum phase transition in Bose-Hubbard model borrowing two tools from quantum-information theory, i.e., ground-state fidelity and entanglement measures. consider systems at unitary filling comprising up to 50 sites show for first time that a finite-size scaling analysis of these quantities provides excellent estimates critical point. conclude is particularly suited revealing pinning down point thereof, while success measures depends on mechanisms governing transition.

We present an analytic description of the finite-temperature phase diagram Bose-Hubbard model, successfully describing physics cold bosonic atoms trapped in optical lattices and superlattices. Based on a standard statistical mechanics approach, we provide exact expression for boundary between superfluid normal fluid by solving self-consistency equations involved mean-field approximation to model. The zero-temperature limit such result supplies Mott lobes superlattices, characterized critical...

We use the fidelity approach to quantum critical points study zero-temperature phase diagram of one-dimensional Hubbard model. Using a variety analytical and numerical techniques, we analyze metric in various regions with particular care points. Specifically show that close Mott transition, taking place at on-site repulsion $U=0$ electron density $n=1$, satisfies an hyperscaling form which calculate. This implies general, as one approaches point $U=0$, tends limit depends on path approach....

We investigate the properties of strongly interacting heteronuclear boson-boson mixtures loaded in realistic optical lattices, with particular emphasis on physics interfaces. In particular, we numerically reproduce recent experimental observation that addition a small fraction 41K induces significant loss coherence 87Rb, providing simple explanation. then robustness against inhomogeneity typical realizations glassy quantum emulsions recently predicted to occur ideal homogeneous lattices.

In this paper we consider a bosonic Josephson junction described by two-mode Bose-Hubbard model, and thoroughly analyze quantum phase transition occurring in the system limit of infinite population. We discuss relation between dynamical bifurcation spectrum Discrete Self Trapping equations describing at semiclassical level. particular, identify five regimes depending on strength effective interaction among bosons, study finite-size effects arising from finiteness devote special attention to...

The zero-temperature phase diagram of a Bose-Einstein condensate confined in realistic one-dimensional $\mathit{\ensuremath{\ell}}$-periodic optical superlattices is investigated. system interacting bosons modeled terms Bose-Hubbard Hamiltonian whose site-dependent local potentials and hopping amplitudes reflect the periodicity lattice partition $\mathit{\ensuremath{\ell}}$-site cells. Relying on exact mapping between hardcore limit boson model spinless noninteracting fermions,...

We address the phase diagram of disordered Bose-Hubbard model that has been realized in several recent experiments terms optically trapped ultracold bosons. show a systematic description all expected quantum phases can be obtained at both zero and finite temperature via site-dependent decoupling mean-field approach. Also, we relate boundaries Mott-insulating to an off-diagonal noninteracting Anderson whose spectral features provide avenue for determining debated nature surrounding Mott...

We analyze thoroughly the mean-field dynamics of a linear chain three coupled Bose-Einstein condensates, where both tunneling and central-well relative depth are adjustable parameters. Owing to its nonintegrability, entailing complex with chaos occurrence, this system is paradigm for longer arrays whose simplicity still allows thorough analytical study.We identify set fixed points, along associated proper modes, establish their stability character depending on significant As an example...

We study the ground-state properties of Bose-Hubbard model with attractive interactions on an $M$-site one-dimensional periodic---necklacelike---lattice, whose experimental realization in terms ultracold atoms is promised by a recently proposed optical trapping scheme, as well control over atomic and tunneling amplitudes granted well-established techniques. compare quantum to semiclassical picture based number-conserving $\mathrm{su}(M)$ coherent state, which results set modified discrete...

The notion of negative absolute temperature emerges naturally from Boltzmann's definition ``surface'' microcanonical entropy in isolated systems with a bounded energy density. Recently, the well-posedness such construct has been challenged, on account that only Gibbs ``volume'' entropy---and strictly positive thereof---would give rise to consistent thermodynamics. Here we present analytical and numerical evidence Boltzmann provides thermometry for both signs temperature. In particular, show...

In this paper we derive an analytic approximation to the density of states for atoms in a combined optical lattice and harmonic trap potential as used current experiments with quantum degenerate gases. We compare numerical solutions demonstrate its validity regime. Our work explicitly considers role higher bands when they are important quantitative analysis system. Applying our Fermi gas, consider how adiabatic loading from into harmonic-lattice affects degeneracy temperature. results...

We consider the Bose-Hubbard model describing attractive bosonic particles hopping across sites of a translation-invariant lattice and compare relevant ground-state properties with those corresponding symmetry-breaking semiclassical nonlinear theory. The introduction suitable measure allows us to highlight many correspondences between theory inherently linear quantum theory, characterized by well-known self-trapping phenomenon. In particular we demonstrate that localization bifurcation...

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 such systems, which experimental realization Bose-Hubbard model potentials are randomly extracted from binary distribution. Adopting site-dependent Gutzwiller description state system, address one- and two-dimensional lattices...

We consider correlated L\'evy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution regions, featuring different diffusion properties. introduce geometric parameter $\ensuremath{\alpha}$, playing role analogous to exponent characterizing step-length in random systems. By single-long-jump approximation, we analytically determine long-time asymptotic behavior moments probability as function...

The mean-field pictures based on the standard time-dependent variational approach have widely been used in study of nonlinear many-boson systems such as Bose-Hubbard model. schemes relevant to Gutzwiller-like trial states $|F>$, number-preserving $|ξ>$ and Glauber-like $|Z>$ are compared evidence specific properties schemes. After deriving Hamiltonian picture from that latter is shown exhibit a Poisson algebra equipped with Weyl-Heisenberg subalgebra which preludes $|Z>$-based...

The phase diagram of ultracold bosons in realistic optical superlattices is addressed via second-order cell strong coupling perturbative expansions for the Bose-Hubbard model describing system. Taking advantage partition inherent complex periodic modulation a superlattice, this technique allows description unusual loophole-shaped insulator domains that may occur system, unlike standard approach. Furthermore, comparisons with quantum Monte Carlo simulations show our approach provides...

We illustrate how dynamical transitions in nonlinear semiclassical models can be recognized as phase the corresponding---inherently linear---quantum model, where, a statistical-mechanics framework, thermodynamic limit is realized by letting particle population go to infinity at fixed size. focus on lattice bosons described Bose-Hubbard (BH) model and discrete self-trapping (DST) equations quantum levels, respectively. After showing that Gaussianity of ground states broken transition, we...

We consider an ultra-small system of polarized bosons on optical lattice with a ring topology interacting via long range dipole-dipole interactions. Dipoles perpendicular to the plane reveal sharp transitions between different density wave phases. As strength dipolar interactions is varied behavior first-order like. For dipoles in possible phases show pronounced sensitivity depth. The abundance configurations may be useful for quantum information applications.

Ultracold bosons in optical superlattices are expected to exhibit fractional-filling insulating phases for sufficiently large repulsive interactions. On strictly one-dimensional systems, the exact mapping between hard-core and free spinless fermions shows that any periodic modulation lattice parameters causes presence of insulator domains. Here, we focus on two recently proposed realistic two-dimensional structures where such does not hold, i.e., two-leg ladder trimerized kagom\'e lattice....

We study the dynamical stability of macroscopic quantum oscillations characterizing a system three coupled Bose–Einstein condensates arranged into an open-chain geometry. The boson interaction, hopping amplitude and central-well relative depth are regarded as adjustable parameters. After deriving diagrams system, we identify mechanisms for realizing transition from unstable to stable behaviour analyse specific configurations that, by suitably tuning model parameters, give rise effects which...

We study the filling of states in a pure hopping boson model on comb lattice, low-dimensional discrete structure where geometrical inhomogeneity induces Bose-Einstein condensation (BEC) at finite temperature. By careful analysis thermodynamic limit combs we show that, unlike standard lattice case, BEC is characterized by macroscopic occupation number with energy belonging to small neighborhood ground state energy. Such remarkable feature gives rise an anomalous behavior large distance...

We report a multiple-site mean-field analysis of the zero-temperature phase diagram for ultracold bosons in realistic optical superlattices. The system interacting is described by Bose-Hubbard model whose site-dependent parameters reflect nontrivial periodicity superlattice. An analytic approach formulated based on stability fixed-point map defined self-consistency condition inherent approximation. experimentally relevant case period-2 one-dimensional superlattice briefly discussed. In...