17 research outputs found
Fractional-filling Mott domains in two dimensional optical superlattices
Ultracold bosons in optical superlattices are expected to exhibit
fractional-filling insulating phases for sufficiently large repulsive
interactions. On strictly 1D systems, the exact mapping between hard-core
bosons and free spinless fermions shows that any periodic modulation in the
lattice parameters causes the presence of fractional-filling insulator domains.
Here, we focus on two recently proposed realistic 2D structures where such
mapping does not hold, i.e. the two-leg ladder and the trimerized kagome'
lattice. Based on a cell strong-coupling perturbation technique, we provide
quantitatively satisfactory phase diagrams for these structures, and give
estimates for the occurrence of the fractional-filling insulator domains in
terms of the inter-cell/intra-cell hopping amplitude ratio.Comment: 4 pages, 3 figure
On the dispute between Boltzmann and Gibbs entropy
Very recently, the validity of the concept of negative temperature has been
challenged by several authors since they consider Boltzmann's entropy (that
allows negative temperatures) inconsistent from a mathematical and statistical
point of view, whereas they consider Gibbs' entropy (that does not admit
negative temperatures) the correct definition for microcanonical entropy.
In the present paper we prove that for systems with equivalence of the
statistical ensembles Boltzmann entropy is the correct microcanonical entropy.
Analytical results on two systems supporting negative temperatures, confirm the
scenario we propose. In addition, we corroborate our proof by numeric
simulations on an explicit lattice system showing that negative temperature
equilibrium states are accessible and obey standard statistical mechanics
prevision.Comment: To appear in Annals of Physic
Engineering many-body quantum dynamics by disorder
Going beyond the currently investigated regimes in experiments on quantum
transport of ultracold atoms in disordered potentials, we predict a crossover
between regular and quantum-chaotic dynamics when varying the strength of
disorder. Our spectral approach is based on the Bose-Hubbard model describing
interacting atoms in deep random potentials. The predicted crossover from
localized to diffusive dynamics depends on the simultaneous presence of
interactions and disorder, and can be verified in the laboratory by monitoring
the evolution of typical experimental initial states.Comment: 4 pages, 4 figures (improved version), to be published in PR
Dynamical bifurcation as a semiclassical counterpart of a quantum phase transition
We illustrate how dynamical transitions in nonlinear semiclassical models can
be recognized as phase transitions in the corresponding -- inherently linear --
quantum model, where, in a Statistical Mechanics framework, the thermodynamic
limit is realized by letting the particle population go to infinity at fixed
size. We focus on lattice bosons described by the Bose-Hubbard (BH) model and
Discrete Self-Trapping (DST) equations at the quantum and semiclassical level,
respectively.
After showing that the gaussianity of the quantum ground states is broken at
the phase transition, we evaluate finite populations effects introducing a
suitable scaling hypothesis; we work out the exact value of the critical
exponents and we provide numerical evidences confirming our hypothesis. Our
analytical results rely on a general scheme obtained from a large-population
expansion of the eigenvalue equation of the BH model. In this approach the DST
equations resurface as solutions of the zeroth-order problem.Comment: 4 pages, 3 figures; a few changes made in the layout of equations;
improved visibility of some figures; added some references and endnote
Dipolar bosons on an optical lattice ring
We consider an ultra-small system of polarized bosons on an optical lattice
with a ring topology interacting via long range dipole-dipole interactions.
Dipoles polarized perpendicular to the plane of the ring reveal sharp
transitions between different density wave phases. As the strength of the
dipolar interactions is varied the behavior of the transitions is first-order
like. For dipoles polarized in the plane of the ring the transitions between
possible phases show pronounced sensitivity to the lattice depth. The abundance
of possible configurations may be useful for quantum information applications.Comment: decompressed version now reaching 6 page
Attractive ultracold bosons in a necklace optical lattice
We study the ground-state properties of the Bose-Hubbard model with attractive interactions on an M-site one-dimensional periodic—necklacelike—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 su͑M͒ coherent state, which results in a set of modified discrete nonlinear Schrödinger 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, Schrödinger-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