In this paper we consider a bosonic Josephson junction described by a two-mode Bose-Hubbard model, and we thoroughly analyze a quantum phase transition occurring in the system in the limit of infinite bosonic population. We discuss the relation betwe
en this quantum phase transition and the dynamical bifurcation occurring in the spectrum of the Discrete Self Trapping equations describing the system at the semiclassical level. In particular, we identify five regimes depending on the strength of the effective interaction among bosons, and study the finite-size effects arising from the finiteness of the bosonic population. We devote a special attention to the critical regime which reduces to the dynamical bifurcation point in the thermodynamic limit of infinite bosonic population. Specifically, we highlight an anomalous scaling in the population imbalance between the two wells of the trapping potential, as well as in two quantities borrowed from Quantum Information Theory, i.e. the entropy of entanglement and the ground-state fidelity. Our analysis is not limited to the zero temperature case, but considers thermal effects as well.
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 n
onlinear 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.
We consider strongly interacting boson-boson mixtures on one-dimensional lattices and, by adopting a qualitative mean-field approach, investigate their quantum phases as the interspecies repulsion is increased. In particular, we analyze the low-energ
y quantum emulsion metastable states occurring at large values of the interspecies interaction, which are expected to prevent the system from reaching its true ground state. We argue a significant decrease in the visibility of the time-of-flight images in the case of these spontaneously disordered states.
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.
We use the fidelity approach to quantum critical points to study the zero temperature phase diagram of the one-dimensional Hubbard model. Using a variety of analytical and numerical techniques, we analyze the fidelity metric in various regions of the
phase diagram, with particular care to the critical points. Specifically we show that close to the Mott transition, taking place at on-site repulsion U=0 and electron density n=1, the fidelity metric satisfies an hyper-scaling form which we calculate. This implies that in general, as one approaches the critical point U=0, n=1, the fidelity metric tends to a limit which depends on the path of approach. At half filling, the fidelity metric is expected to diverge as U^{-4} when U is sent to zero.
The mean-field pictures based on the standard time-dependent variational approach have widely been used in the study of nonlinear many-boson systems such as the Bose-Hubbard model. The mean-field schemes relevant to Gutzwiller-like trial states $|F>$
, number-preserving states $|xi >$ and Glauber-like trial states $|Z>$ are compared to evidence the specific properties of such schemes. After deriving the Hamiltonian picture relevant to $|Z>$ from that based on $|F>$, the latter is shown to exhibit a Poisson algebra equipped with a Weyl-Heisenberg subalgebra which preludes to the $|Z>$-based picture. Then states $|Z>$ are shown to be a superposition of $cal N$-boson states $|xi>$ and the similarities/differences of the $|Z>$-based and $|xi>$-based pictures are discussed. Finally, after proving that the simple, symmetric state $|xi>$ indeed corresponds to a SU(M) coherent state, a dual version of states $|Z>$ and $|xi>$ in terms of momentum-mode operators is discussed together with some applications.
We investigate the properties of strongly interacting heteronuclear boson-boson mixtures loaded in realistic optical lattices, with particular emphasis on the physics of interfaces. In particular, we numerically reproduce the recent experimental obse
rvation that the addition of a small fraction of K induces a significant loss of coherence in Rb, providing a simple explanation. We then investigate the robustness against the inhomogeneity typical of realistic experimental realizations of the glassy quantum emulsions recently predicted to occur in strongly interacting boson-boson mixtures on ideal homogeneous lattices.
In the present paper we describe the properties induced by disorder on an ultracold gas of Bosonic atoms loaded into a two-dimensional optical lattice with global confinement ensured by a parabolic potential. Our analysis is centered on the spatial d
istribution of the various phases, focusing particularly on the superfluid properties of the system as a function of external parameters and disorder amplitude. In particular, it is shown how disorder can suppress superfluidity, while partially preserving the system coherence.
