Magnetic phase transition in coherently coupled Bose gases in optical lattices

We describe the ground state of a gas of bosonic atoms with two coherently coupled internal levels in a deep optical lattice in a one dimensional geometry. In the single-band approximation this system is described by a Bose-Hubbard Hamiltonian. The system has a superfluid and a Mott insulating phase which can be either paramagnetic or ferromagnetic. We characterize the quantum phase transitions at unit filling by means of a density matrix renormalization group technique and compare it with a mean-field approach. The presence of the ferromagnetic Ising-like transition modifies the Mott lobes. In the Mott insulating region the system maps to the ferromagnetic spin-1/2 XXZ model in a transverse field and the numerical results compare very well with the analytical results obtained from the spin model. In the superfluid regime quantum fluctuations strongly modify the phase transition with respect to the well established mean-field three dimensional classical bifurcation.Comment: 6 pages, 3 figure

Non-Local Order Parameters as a Probe for Phase Transitions in the Extended Fermi-Hubbard Model

The Extended Fermi-Hubbard model is a rather studied Hamiltonian due to both its many applications and a rich phase diagram. Here we prove that all the phase transitions encoded in its one dimensional version are detectable via non-local operators related to charge and spin fluctuations. The main advantage in using them is that, in contrast to usual local operators, their asymptotic average value is finite only in the appropriate gapped phases. This makes them powerful and accurate probes to detect quantum phase transitions. Our results indeed confirm that they are able to properly capture both the nature and the location of the transitions. Relevantly, this happens also for conducting phases with a spin gap, thus providing an order parameter for the identification of superconducting and paired superfluid phasesComment: 7 pages, 3 figures; Submitted to EPJ Special Topics, Quantum Gases and Quantum Coherenc

Localized-Interaction-Induced Quantum Reflection and Filtering of Bosonic Matter in a One-Dimensional Lattice Guide

We study the dynamics of quantum bosonic waves confined in a one-dimensional tilted optical lattice. The bosons are under the action of an effective spatially localized nonlinear two-body potential barrier set in the central part of the lattice. This version of the Bose-Hubbard model can be realized in atomic Bose-Einstein condensates, by means of localized Feshbach resonance, and in quantum optics, using an arrayed waveguide with selectively doped guiding cores. Our numerical analysis demonstrates that the central barrier induces anomalous quantum reflection of incident wave packets acting solely on bosonic components with multiple onsite occupancies. From the other side single-occupancy components can pass the barrier thus allowing one to distill them in the central interacting zone. As a consequence, in this region one finds a state in which the multiple occupancy is forbidden, i.e., a Tonks-Girardeau gas. Our results demonstrate that this regime can be obtained dynamically, using relatively weak interactions, irrespective of their sign.Comment: 10 pages, 7 figures. Accepted for publication in NJP (Focus issue on "Strongly interacting quantum gases in one dimension"

Quantum bright solitons in the Bose-Hubbard model with site-dependent repulsive interactions

We introduce a one-dimensional (1D) spatially inhomogeneous Bose-Hubbard model (BHM) with the strength of the onsite repulsive interactions growing, with the discrete coordinate $z_{j}$, as $|z_{j}|^{\alpha }$ with $\alpha >0$. Recently, the analysis of the mean-field (MF) counterpart of this system has demonstrated self-trapping of robust unstaggered discrete solitons, under condition $\alpha >1$. Using the numerically implemented method of the density matrix renormalization group (DMRG), we demonstrate that, in a certain range of interaction, the BHM also self-traps, in the ground state, into a soliton-like configuration, at $\alpha >1$, and remains weakly localized at $\alpha <1$. An essential quantum feature is a residual density in the background surrounding the soliton-like peak in the BHM ground state, while in the MF limit the finite-density background is absent. Very strong onsite repulsion eventually destroys soliton-like states, and, for integer densities, the system enters the Mott phase with a spatially uniform densityComment: Phys. Rev. A, in pres

Out-of-equilibrium states and quasi-many-body localization in polar lattice gases

The absence of energy dissipation leads to an intriguing out-of-equilibrium dynamics for ultracold polar gases in optical lattices, characterized by the formation of dynamically-bound on-site and inter-site clusters of two or more particles, and by an effective blockade repulsion. These effects combined with the controlled preparation of initial states available in cold gases experiments can be employed to create interesting out-of-equilibrium states. These include quasi-equilibrated effectively repulsive 1D gases for attractive dipolar interactions and dynamically-bound crystals. Furthermore, non-equilibrium polar lattice gases can offer a promising scenario for the study of many-body localization in the absence of quenched disorder. This fascinating out-of-equilibrium dynamics for ultra-cold polar gases in optical lattices may be accessible in on-going experiments.Comment: 5+1 pages, 4+1 figure

A bivariate geometric distribution allowing for positive or negative correlation

In this paper, we propose a new bivariate geometric model, derived by linking two univariate geometric distributions through a specific copula function, allowing for positive and negative correlations. Some properties of this joint distribution are presented and discussed, with particular reference to attainable correlations, conditional distributions, reliability concepts, and parameter estimation.AMonteCarlo simulation study empirically evaluates and compares the performance of the proposed estimators in terms of bias and standard error. Finally, in order to demonstrate its usefulness, the model is applied to a real data set

A bivariate count model with discrete Weibull margins

Multivariate discrete data arise in many fields (statistical quality control, epidemiology, failure and reliability analysis, etc.) and modelling such data is a relevant task. Here we consider the construction of a bivariate model with discrete Weibull margins, based on Farlie-Gumbel-Morgenstern copula, analyse its properties especially in terms of attainable correlation, and propose several methods for the point estimation of its parameters. Two of them are the standard one-step and two-step maximum likelihood procedures; the other two are based on an approximate method of moments and on the method of proportion, which represent intuitive alternatives for estimating the dependence parameter. A Monte Carlo simulation study is presented, comprising more than one hundred artificial settings, which empirically assesses the performance of the different estimation techniques in terms of statistical properties and computational cost. For illustrative purposes, the model and related inferential procedures are fitted and applied to two datasets taken from the literature, concerning failure data, presenting either positive or negative correlation between the two observed variables. The applications show that the proposed bivariate discrete Weibull distribution can model correlated counts even better than existing and well-established joint distributions

Approximation of Continuous Random Variables for the Evaluation of the Reliability Parameter of Complex Stress-Strength Models

A stress-strength model consists of an item, a component, or a system with an intrinsic random strength that is subject to a random stress during its functioning, so that it works until the strength is greater than the stress. The probability of this event occurring is called the reliability parameter. Since stress and strength are often functions of elementary stochastic factors and the form of these functions is usually very complex, it descends that finding their exact statistical distribution, and then the value of the reliability parameter, is at least cumbersome if not actually impossible. It is standard practice to carry out Monte Carlo simulations in order to find this value numerically. A convenient alternative solution to this impasse comprises discretization, i.e., substituting the probability density functions of the continuous random variables with the probability mass functions of properly chosen approximating discrete random variables. Thus, an approximate value of the reliability parameter can be recovered by enumeration. Many discretization methods have been proposed in the literature so far, which may differ from one another in their ultimate scope and range of applicability [1, 2, 3]. In this work, we will revise and further rene these techniques and apply them to the context of complex stress-strength models. A comparative study will empirically investigate the performance of these methods by considering several well-known engineering problems and give some practical advice on their mindful use

Inducing a Target Association between Ordinal Variables by Using a Parametric Copula Family

The need for building and generating statistically dependent random variables arises in various fields of study where simulation has proven to be a useful tool. In this work, we present an approach for constructing ordinal variables with arbitrarily assigned marginal distributions and value of association or correlation, expressed in terms of either Goodman and Kruskal's gamma or Pearson's linear correlation. The approach first constructs a class of bivariate copula-based distributions matching the assigned margins, and then, within this class, identifies the distribution matching the assigned association or correlation, by calibrating the copula parameter. A numerical example and a possible application are illustrated

Disorderless quasi-localization of polar gases in one-dimensional lattices

One-dimensional polar gases in deep optical lattices present a severely constrained dynamics due to the interplay between dipolar interactions, energy conservation, and finite bandwidth. The appearance of dynamically-bound nearest-neighbor dimers enhances the role of the $1/r^3$ dipolar tail, resulting, in the absence of external disorder, in quasi-localization via dimer clustering for very low densities and moderate dipole strengths. Furthermore, even weak dipoles allow for the formation of self-bound superfluid lattice droplets with a finite doping of mobile, but confined, holons. Our results, which can be extrapolated to other power-law interactions, are directly relevant for current and future lattice experiments with magnetic atoms and polar molecules.Comment: 5 + 2 Page