arXiv subjects

Vittorio Penna

Publications and source records attributed to Vittorio Penna.

At least 37 records · Page 2Linked to original sources

arXiv2017

Two-species boson mixture on a ring: A group theoretic approach to the quantum dynamics of low-energy excitations

We investigate the weak excitations of a system made up of two condensates trapped in a Bose-Hubbard ring and coupled by an interspecies repulsive interaction. Our approach, based on the Bogoliubov approximation scheme, shows that one can reduce the problem Hamiltonian to the sum of sub-Hamiltonians $\hat{H}_k$, each one associated to momentum modes $\pm k$. Each $\hat{H}_k$ is then recognized to be an element of a dynamical algebra. This uncommon and remarkable property allows us to present a straightforward diagonalization scheme, to find constants of motion, to highlight the significant microscopic processes, and to compute their time evolution. The proposed solution scheme is applied to a simple but still very interesting closed circuit, the trimer. The dynamics of low-energy excitations, corresponding to weakly-populated vortices, is investigated considering different choices of the initial conditions, and the angular-momentum transfer between the two condensates is evidenced. Finally, the condition for which the spectral collapse and dynamical instability are observed is derived analytically.

cond-mat.quant-gas↗

arXiv2017

Quantum dynamics of bosons in a two-ring ladder: dynamical algebra, vortex-like excitations and currents

We study the quantum dynamics of the Bose-Hubbard model on a ladder formed by two rings coupled by tunneling effect. By implementing the Bogoliubov approximation scheme, we prove that, despite the presence of the inter-ring coupling term, the Hamiltonian decouples in many independent sub-Hamiltonians $\hat{H}_k$ associated to momentum-mode pairs $\pm k$. Each sub-Hamiltonian $\hat{H}_k$ is then shown to be part of a specific dynamical algebra. The properties of the latter allow us to perform the diagonalization process, to find energy spectrum, the conserved quantities of the model, and to derive the time evolution of important physical observables. We then apply this solution scheme to the simplest possible closed ladder, the double trimer. After observing that the excitations of the system are weakly-populated vortices, we explore the corresponding dynamics by varying the initial conditions and the model parameters. Finally, we show that the inter-ring tunneling determines a spectral collapse when approaching the border of the dynamical-stability region.

cond-mat.quant-gas↗

arXiv2016

Quasi-molecular bosonic complexes -- a pathway to atomic analog of SQUID with controlled sensitivity

Recent experimental advances in realizing degenerate quantum dipolar gases in optical lattices and the flexibility of experimental setups in attaining various geometries offer the opportunity to explore exotic quantum many-body phases stabilized by anisotropic, long-range dipolar interaction. Moreover, the unprecedented control over the various physical properties of these systems, ranging from the quantum statistics of the particles, to the inter-particle interactions, allow one to engineer novel devices. In this paper, we consider dipolar bosons trapped in a stack of one-dimensional optical lattice layers, previously studied in [1]. Building on our prior results, we provide a description of the quantum phases stabilized in this system which include composite superfluids, solids, and supercounterfluids, most of which are found to be threshold- less with respect to the dipolar interaction strength. We also demonstrate the effect of enhanced sensitivity to rotations of a SQUID-type device made of two composite superfluids trapped in a ring-shaped optical lattice layer with weak links.

cond-mat.quant-gas↗

arXiv2015

Inter-species entanglement of Bose-Bose mixtures trapped in optical lattices

In the present work we discuss inter-species entanglement in Bose-Bose mixtures trapped in optical lattices. This work is motivated by the observation that, in the presence of a second component, the Mott-insulator lobe shifts {\em{differently}} on the hole- and particle-side with respect to the Mott lobe of the single species system (Phys. Rev. A 82, 021601, Laser Phys. 21, 1443). We use perturbation theory, formulated in a Hilbert space decomposed by means of lattice symmetries, in order to show that the nonuniform shift of the Mott lobe is a consequence of an inter-species entanglement which differs in the lowest excited states to remove and add a particle. Our results indicate that inter-species entanglement in mixtures can provide a new perspective in understanding quantum phase transitions. To validate our approach, we compare our results from perturbation theory with quantum Monte Carlo simulations.

cond-mat.quant-gas↗

arXiv2014

Localization-delocalization transition of dipolar bosons in a four-well potential

We study interacting dipolar atomic bosons in a four-well potential within a ring geometry and outline how a four-site Bose-Hubbard (BH) model including next-nearest-neighbor interaction terms can be derived for the above four-well system. We analyze the ground state of dipolar bosons by varying the strength of the interaction between particles in next-nearest-neighbor wells. We perform this analysis both numerically and analytically by reformulating the dipolar-boson model within the continuous variable picture applied in [Phys. Rev. A {\bf 84}, 061601(R) (2011)]. By using this approach we obtain an effective description of the transition mechanism and show that when the next-nearest-neighbor interaction crosses a precise value of the on-site interaction, the ground state exhibits a change from the uniform state (delocalization regime) to a macroscopic two-pulse state, with strongly localized bosons (localization regime). These predictions are confirmed by the results obtained by diagonalizing numerically the four-site BH Hamiltonian.

cond-mat.quant-gas↗

arXiv2014

Analysis and resolution of the ground-state degeneracy of the two-component Bose-Hubbard model

We study the degeneracy of the ground-state energy $E$ of the two-component Bose-Hubbard model and of the perturbative correction $E_1$. We show that the degeneracy properties of $E$ and $E_1$ are closely related to the connectivity properties of the lattice. We determine general conditions under which $E$ is nondegenerate. This analysis is then extended to investigate the degeneracy of $E_1$. In this case, in addition to the lattice structure, the degeneracy also depends on the number of particles present in the system. After identifying the cases in which $E_1$ is degenerate and observing that the standard (degenerate) perturbation theory is not applicable, we develop a method to determine the zeroth-order correction to the ground state by exploiting the symmetry properties of the lattice. This method is used to implement the perturbative approach to the two-component Bose-Hubbard model in the case of degenerate $E_1$ and is expected to be a valid tool to perturbatively study the asymmetric character of the Mott-insulator to superfluid transition between the particle and hole side.

cond-mat.quant-gas↗

arXiv2014

Spectral properties of attractive bosons in a ring lattice including a single-site potential

The ground-state properties of attractive bosons trapped in a ring lattice including a single attractive potential well with an adjustable depth are investigated. The energy spectrum is reconstructed both in the strong-interaction limit and in the superfluid regime within the Bogoliubov picture. The analytical results thus obtained are compared with those found numerically from the exact Hamiltonian, in order to identify the regions in the parameter space where this picture is effective. The single potential introduced is the simplest way to break the translational symmetry and to observe, through a completely analytical approach, how the absence of symmetry affects the properties of the low-excited eigenstates of the system. This model gives a first insight into the properties of systems including more complex potentials.

quant-ph↗

arXiv2014

Perturbative approach to the dynamics of a trapped ion interacting with a light field

We present a second-order perturbative analysis of the model describing a two-level trapped ion interacting with a traveling laser field, in the Lamb-Dicke regime. Unlike the customary approach, based on the interaction picture and the rotating wave approximation, we reduce the original Hamiltonian to a time-independent model, unitarily equivalent to a spin-boson model, which features a form well suited to apply the perturbation theory. We determine the first and second-order corrections of eigenstates and eigenvalues. By varying the interaction parameters we identify four regimes characterized by different eigenvalue distributions (possibly including level doublets) and suggest the presence of an intermediate regime where the spectrum undergoes macroscopic changes. In this regime, where the perturbation approach does not hold, our reduced Hamiltonian is shown to reproduce the Jaynes-Cummings model.

quant-ph↗

arXiv2014

Dynamics of the central-depleted-well regime in the open Bose-Hubbard trimer

We study the quantum dynamics of the central-depleted-well (CDW) regime in a three-mode Bose Hubbard model subject to a confining parabolic potential. By introducing a suitable set of momentum-like modes we identify the microscopic variables involved in the quantization process and the dynamical algebra of the model. We describe the diagonalization procedure showing that the model reduces to a double oscillator. Interestingly, we find that the parameter-space domain where this scheme entails a discrete spectrum well reproduces the two regions where the classical trimer excludes unstable oscillations. Spectral properties are examined in different limiting cases together with various delocalization effects. These are shown to characterize quantum states of the CDW regime in the proximity of the borderline with classically-unstable domains.

cond-mat.quant-gas↗

arXiv2011

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.

cond-mat.stat-mech↗

arXiv2011

Ising antiferromagnet with ultracold bosonic mixtures confined in a harmonic trap

We present accurate results based on Quantum Monte Carlo simulations of two-component bosonic systems on a square lattice and in the presence of an external harmonic confinement. Starting from hopping parameters and interaction strengths which stabilize the Ising antiferromagnetic phase in the homogeneous case and at half integer filling factor, we study how the presence of the harmonic confinement challenge the realization of such phase. We consider realistic trapping frequencies and number of particles, and establish under which conditions, i.e. total number of particles and population imbalance, the antiferromagnetic phase can be observed in the trap.

cond-mat.quant-gas↗

arXiv2007

Mean-field description of ultracold Bosons on disordered two-dimensional optical 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 distribution 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.

cond-mat.dis-nn↗

arXiv2005

Attractive ultracold bosons in a necklace optical potential

We study the ground state properties of the Bose-Hubbard model with attractive interactions on a M-site one-dimensional periodic -- necklace-like -- 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 su(M) coherent state, which results into a set of modified discrete nonlinear Schroedinger 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, Schroedinger-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.

cond-mat.stat-mech↗

arXiv2005

Hubbard-like Hamiltonian for ultracold atoms in a 1D optical lattice

Based on the standard many-fermion field theory, the authors construct models describing ultracold fermions in a 1D optical lattices by implementing a mode expansion of the fermionic field operator where modes, in addition to space localization, take into account the quantum numbers inherent in local fermion interactions. The resulting models are generalized Hubbard Hamiltonians whose interaction parameters are derived by a fully-analytical calculation. The special interest for this derivation resides in its model-generating capability and in the flexibility of the trapping techniques that allow the tuning of the Hamiltonian interaction parameters over a wide range of values. While the Hubbard Hamiltonian is recovered in a very low-density regime for a fermionic system, in general, far more complicated Hamiltonians characterise high-density regimes, revealing a rich scenario for both the phenomenology of interacting trapped fermions and the experimental realization of devices for quantum information processing. As a first example of the different situations that may arise beyond the models well known in the literature (the unpolarized-spin fermion model and the noninteracting spin-polarized fermion model), we derive a Rotational Hubbard Hamiltonian describing the local rotational activity of spin-polarized fermions. Based on a standard techniques we obtain the mean-field version of our model Hamiltonian and show how different dynamical algebras characterize the case of attractive and repulsive two-body potentials.

cond-mat.mes-hall↗

arXiv2005

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.

cond-mat.stat-mech↗

arXiv2005

Fractional-filling loophole insulator domains for ultracold bosons in optical superlattices

The zero-temperature phase diagram of a Bose-Einstein condensate confined in realistic one-dimensional $\ell$-periodic optical superlattices is investigated. The system of interacting bosons is modeled in terms of a Bose-Hubbard Hamiltonian whose site-dependent local potentials and hopping amplitudes reflect the periodicity of the lattice partition in $\ell$-site cells. Relying on the exact mapping between the hard-core limit of the boson Hamiltonian and the model of spinless noninteracting fermions, incompressible insulator domains are shown to exist for rational fillings that are predicted to be compressible in the atomic limit. The corresponding boundaries, qualitatively described in a {\it multiple-site} mean-field approach, are shown to exhibit an unusual loophole shape. A more quantitative description of the loophole domain boundaries at half filling for the special case $\ell$ = 2 is supplied in terms of analytic strong-coupling expansions and quantum Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2002

Collective modes, chaotic behavior and self-trapping in the dynamics of three coupled Bose-Einstein condensates

The dynamics of three coupled bosonic wells (trimer) containing $N$ bosons is investigated within a standard (mean-field) semiclassical picture based on the coherent-state method. Various periodic solutions (configured as $π$-like, dimerlike and vortex states) representing collective modes are obtained analitically when the fixed points of trimer dynamics are identified on the $N$=const submanifold in the phase space. Hyperbolic, maximum and minimum points are recognized in the fixed-point set by studying the Hessian signature of the trimer Hamiltonian. The system dynamics in the neighbourhood of periodic orbits (associated to fixed points) is studied via numeric integration of trimer motion equations thus revealing a diffused chaotic behavior (not excluding the presence of regular orbits), macroscopic effects of population-inversion and self-trapping. In particular, the behavior of orbits with initial conditions close to the dimerlike periodic orbits shows how the self-trapping effect of dimerlike integrable subregimes is destroyed by the presence of chaos.

cond-mat.mes-hall↗

arXiv2001

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.

cond-mat.mes-hall↗