Complexity in parametric Bose-Hubbard Hamiltonians and structural analysis of eigenstates

We consider a family of chaotic Bose-Hubbard Hamiltonians (BHH) parameterized by the coupling strength $k$ between neighboring sites. As $k$ increases the eigenstates undergo changes, reflected in the structure of the Local Density of States. We analyze these changes, both numerically and analytically, using perturbative and semiclassical methods. Although our focus is on the quantum trimer, the presented methodology is applicable for the analysis of longer lattices as well.Comment: 4 pages, 4 figure

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

Catching homologies by geometric entropy

A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability to single out topological features of networks proceeding in a bottom-up manner: first we consider small size networks by analytical methods and then large size networks by numerical techniques. Two different classes of networks, the random graphs and the scale--free networks, are investigated computing their Betti numbers and then showing the capability of geometric entropy of detecting homologies.Comment: 12 pages, 2 Figure

Self-trapping mechanisms in the dynamics of three coupled Bose-Einstein condensates

We formulate the dynamics of three coupled Bose-Einstein condensates within a semiclassical scenario based on the standard boson coherent states. We compare such a picture with that of Ref. 1 and show how our approach entails a simple formulation of the dimeric regime therein studied. This allows to recognize the parameters that govern the bifurcation mechanism causing self-trapping, and paves the way to the construction of analytic solutions. We present the results of a numerical simulation showing how the three-well dynamics has, in general, a cahotic behavior.Comment: 4 pages, 5 figure

Negative Temperature States in the Discrete Nonlinear Schroedinger Equation

We explore the statistical behavior of the discrete nonlinear Schroedinger equation. We find a parameter region where the system evolves towards a state characterized by a finite density of breathers and a negative temperature. Such a state is metastable but the convergence to equilibrium occurs on astronomical time scales and becomes increasingly slower as a result of a coarsening processes. Stationary negative-temperature states can be experimentally generated via boundary dissipation or from free expansions of wave packets initially at positive temperature equilibrium.Comment: 4 pages, 5 figure

Dynamics of atoms in a time-orbiting-potential trap: Consequences of the classical description

The classical model that describes the motion of an atom in a magnetic trap is solved in order to investigate the relationship between the failure of the usual adiabatic approximation assumption and the physical parameters of the trap. This allows us to evaluate the effect that reversing of the bias field rotation produces on the vertical position of the atomic orbit, a displacement that is closely related to the adiabatic character of the trap motion. The present investigation has been motivated by a similar experimental test previously carried out in the actual magnetic time-orbiting-potential trap. We find that the non-adiabatic effects provided by the classical model are extremely small. Thus, we conclude that the theoretical explanation of the experimental measures requires a quantum description of the dynamics in magnetic traps

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

Phase transitions at high energy vindicate negative microcanonical temperature

The notion of negative absolute temperature emerges naturally from Boltzmann’s definition of “surface” microcanonical entropy in isolated systems with a bounded energy density. Recently, the well-posedness of such construct has been challenged, on account that only the Gibbs “volume” entropy—and the strictly positive temperature thereof—would give rise to a consistent thermodynamics. Here we present analytical and numerical evidence that Boltzmann microcanonical entropy provides a consistent thermometry for both signs of the temperature. In particular, we show that Boltzmann (negative) temperature allows the description of phase transitions occurring at high energy densities, at variance with Gibbs temperature. Our results apply to nonlinear lattice models standardly employed to describe the propagation of light in arrays of coupled wave guides and the dynamics of ultracold gases trapped in optical lattices. Optically induced photonic lattices, characterized by saturable nonlinearity, are particularly appealing because they offer the possibility of observing states and phase transitions at both signs of the temperature. ©2017 American Physical Societ

Dynamical Instability in a Trimeric Chain of Interacting Bose-Einstein Condensates

We analyze thoroughly the mean-field dynamics of a linear chain of three coupled Bose-Einstein condensates, where both the tunneling and the central-well relative depth are adjustable parameters. Owing to its nonintegrability, entailing a complex dynamics with chaos occurrence, this system is a paradigm for longer arrays whose simplicity still allows a thorough analytical study.We identify the set of dynamics fixed points, along with the associated proper modes, and establish their stability character depending on the significant parameters. As an example of the remarkable operational value of our analysis, we point out some macroscopic effects that seem viable to experiments.Comment: 5 pages, 3 figure

Quantum information processing in bosonic lattices

We consider a class of models of self-interacting bosons hopping on a lattice. We show that properly tailored space-temporal coherent control of the single-body coupling parameters allows for universal quantum computation in a given sector of the global Fock space. This general strategy for encoded universality in bosonic systems has in principle several candidates for physical implementation.Comment: 4 pages, 2 figs, RevTeX 4; updated to the published versio