arXiv subjects

Andrea Trombettoni

Publications and source records attributed to Andrea Trombettoni.

At least 109 records · Page 6Linked to original sources

arXiv2017

Characteristic features of the Shannon information entropy of dipolar Bose-Einstein condensates

Calculation of the Shannon information entropy (S) and its connection with the order-disorder transition, and with inter-particle interaction provide a challenging research area in the field of quantum information. Experimental progress with cold trapped atoms has corroborated this interest. In the present work, S is calculated for the Bose-Einstein condensate (BEC) with dominant dipolar interaction for different dipole strengths, trap aspect ratio and number of particles (N). Trapped dipolar bosons in an anisotropic trap provide an example of system where the effective interaction is strongly determined by the trap geometry. The main conlcusion of the present calculation is that the anisotropic trap reduces the number of degrees of freedom, resulting in more ordered configurations. The Landsberg's order parameter exhibits quick saturation with the increase in scattering length in both prolate and oblate traps. We also define the threshold scattering length which makes the system completely disordered. Unlike non-dipolar BEC in a spherical trap, we do not find a universal linear relation between S and ln N, and we, therefore, introduce a general quintic polynomial fit rather well working for a wide range of particle number.

cond-mat.quant-gas↗

arXiv2017

Abelian gauge potentials on cubic lattices

The study of the properties of quantum particles in a periodic potential subject to a magnetic field is an active area of research both in physics and mathematics; it has been and it is still deeply investigated. In this review we discuss how to implement and describe tunable Abelian magnetic fields in a system of ultracold atoms in optical lattices. After discussing two of the main experimental schemes for the physical realization of synthetic gauge potentials in ultracold set-ups, we study cubic lattice tight-binding models with commensurate flux. We finally examine applications of gauge potentials in one-dimensional rings.

cond-mat.quant-gas↗

arXiv2017

Collapse in ultracold Bose Josephson junctions

We investigate how ultracold atoms in double well potentials can be used to study and put bounds on models describing wave function collapse. We refer in particular to the continuous spontaneous localization (CSL) model, which is the most well studied among dynamical reduction models. It modifies the Schrodinger equation in order to include the collapse of the wave function in its dynamics. We consider Bose Josephson junctions, where ultracold bosons are trapped in a double well potential,since they can be experimentally controlled with high accuracy and are suited and used to study macroscopic quantum phenomena on scale of microns with a number of particles typically ranging from $\sim 10^2-10^3$ to $\sim 10^5-10^6$. We study the CSL dynamics of three atomic states showing macroscopic quantum coherence: the atomic coherent state, the superposition of two atomic coherent states, and the NOON state. We show that for the last two states the suppression of quantum coherence induced by CSL model increases exponentially with the number of atoms. We observe that, in the case of optically trapped atoms, the spontaneous photon emission of the atoms induce a dynamics similar to the CSL one and we conclude that magnetically trapped atoms may be more convenient to experimentally test the CSL model. We finally discuss decoherence effects in order to provide reasonable estimates on the bounds that it is (or it will) possible to obtain for the parameters of the CSL model in such class of experiments: as an example, we show that a NOON state with $N \sim 10^3$ with a coherence time of $\sim 1$ s can constrain the CSL parameters in a region where the other systems presently cannot.

quant-ph↗

arXiv2016

Quantum state transfer with ultracold atoms in optical lattices

Ultracold atoms can be used to perform quantum simulations of a variety of condensed matter systems, including spin systems. These progresses point to the implementation of the manipulation of quantum states and to observe and exploit the effect of quantum correlations. A natural direction along this line is provided by the possibility to perform quantum state transfer (QST). After presenting a brief discussion of the simulation of quantum spin chains with ultracold gases and reminding the basic facts of QST, we discuss how to potentially use the tools of present-day ultracold technology to implement the QST between two regions of the atomic system (the sender and the receiver). The fidelity and the typical timescale of the QST are discussed, together with possible limitations and applications of the presented results.

quant-ph↗

arXiv2016

Effective Theory and Breakdown of Conformal Symmetry in a Long-Range Quantum Chain

We deal with the problem of studying the effective theories and the symmetries of long-range models around critical points. We focus in particular on the Kitaev chain with long-range pairings decaying with distance as power-law with exponent $α$. This is a quadratic solvable model, yet displaying non-trivial quantum phase transitions. By renormalization group approach we derive first the effective theory close to the critical line at positive chemical potential. This is the sum of two terms: a Dirac action $S_D$, found in the short-range Ising universality class, and a CS breaking term $S_{AN}$. While $S_D$ originates from low-energy excitations, $S_{AN}$ derives from the higher energy modes where singularities develop, due to the long-range nature of the model. At criticality $S_{AN}$ flows to zero if $α> 2$, while if $α< 2$ it dominates and determines the breakdown of the CS. Out of criticality $S_{AN}$ breaks, in the considered approximation, the effective Lorentz invariance (ELI) for every finite $α$. As $α$ increases, such ELI breakdown becomes less and less pronounced and in the short-range limit $α\to \infty$ the ELI is restored. To test the validity of the effective theory, we compared the two-fermion static correlations and the von Neumann entropy obtained from them with the ones calculated on the lattice, finding agreement. From the effective theory one can also see that new phases emerge for $α< 1$. Finally we show that at every finite $α$ the critical exponents are the same as for the short-range ($α\to \infty$) model. At variance, for the critical line with negative chemical potential, only $S_{AN}$ ($S_D$) is present for $1 < α< 2$ (for $α> 2$). Close to this line, where the minimum of the spectrum coincides with the momentum where singularities develop, the critical exponents change exactly where CS is broken.

cond-mat.str-el↗

arXiv2016

Hydrodynamics of local excitations after an interaction quench in 1D cold atomic gases

We discuss the hydrodynamic approach to the study of the time evolution -induced by a quench- of local excitations in one dimension. We focus on interaction quenches: the considered protocol consists in creating a stable localized excitation propagating through the system, and then operating a sudden change of the interaction between the particles. To highlight the effect of the quench, we take the initial excitation to be a soliton. The quench splits the excitation into two packets moving in opposite directions, whose characteristics can be expressed in a universal way. Our treatment allows to describe the internal dynamics of these two packets in terms of the different velocities of their components. We confirm our analytical predictions through numerical simulations performed with the Gross-Pitaevskii equation and with the Calogero model (as an example of long range interactions and solvable with a parabolic confinement). Through the Calogero model we also discuss the effect of an external trapping on the protocol. The hydrodynamic approach shows that there is a difference between the bulk velocities of the propagating packets and the velocities of their peaks: it is possible to discriminate the two quantities, as we show through the comparison between numerical simulations and analytical estimates. In the realizations of the discussed quench protocol in a cold atom experiment, these different velocities are accessible through different measurement procedures.

cond-mat.quant-gas↗

arXiv2016

From four- to two-channel Kondo effect in junctions of XY spin chains

We consider the Kondo effect in Y-junctions of anisotropic XY models in an applied magnetic field along the critical lines characterized by a gapless excitation spectrum. We find that, while the boundary interaction Hamiltonian describing the junction can be recasted in the form of a four-channel, spin-1/2 antiferromagnetic Kondo Hamiltonian, the number of channels effectively participating in the Kondo effect depends on the chain parameters, as well as on the boundary couplings at the junction. The system evolves from an effective four-channel topological Kondo effect for a junction of XX-chains with symmetric boundary couplings into a two-channel one at a junction of three quantum critical Ising chains. The effective number of Kondo channels depends on the properties of the boundary and of the bulk. The XX-line is a "critical" line, where a four-channel topological Kondo effect can be recovered by fine-tuning the boundary parameter, while along the line in parameter space connecting the extreme regimes, XX-line and the critical Ising point the junction is effectively equivalent to a two-channel topological Kondo Hamiltonian. Using a renormalization group approach, we determine the flow of the boundary couplings, which allows us to define and estimate the critical couplings and Kondo temperatures of the different Kondo (pair) channels. Finally, we study the local transverse magnetization in the center of the Y-junction, eventually arguing that it provides an effective tool to monitor the onset of the two-channel Kondo effect.

cond-mat.str-el↗

arXiv2016

Anisotropic Long-Range Spin Systems

We consider anisotropic long-range interacting spin systems in $d$ dimensions. The interaction between the spins decays with the distance as a power law with different exponents in different directions: we consider an exponent $d_{1}+σ_1$ in $d_1$ directions and another exponent $d_{2}+σ_2$ in the remaining $d_2\equiv d-d_1$ ones. We introduce a low energy effective action with non analytic power of the momenta. As a function of the two exponents $σ_1$ and $σ_2$ we show the system to have three different regimes, two where it is actually anisotropic and one where the isotropy is finally restored. We determine the phase diagram and provide estimates of the critical exponents as a function of the parameters of the system, in particular considering the case of one of the two $σ$'s fixed and the other varying. A discussion of the physical relevance of our results is also presented.

cond-mat.stat-mech↗

arXiv2016

Universal dynamics of a soliton after an interaction quench

We propose a new type of experimentally feasible quantum quench protocol in which a quantum system is prepared in a coherent, localized excited state of a Hamiltonian. During the evolution of this solitonic excitation, the microscopic interaction is suddenly changed. We study the dynamics of solitons after this interaction quench for a wide class of systems using a hydrodynamic approach. We find that the post-quench dynamics is universal at short times, i.e. it does not depend on the microscopic details of the physical system. Numerical support for these results is presented using generalized non-linear Schroedinger equation, relevant for the implementation of the proposed protocol with ultracold bosons, as well as for the integrable Calogero model in harmonic potential. Finally, it is shown that the effects of integrability breaking by a parabolic potential and by a power-law non-linearity do not change the universality of the short-time dynamics.

cond-mat.quant-gas↗

arXiv2016

Boltzmann equation with double-well potentials

We study the dynamics of an interacting classical gas trapped in a double-well potential at finite temperature. Two model potentials are considered: a cubic box with a square barrier in the middle, and a harmonic trap with a gaussian barrier along one direction. The study is performed using the Boltzmann equation, solved numerically via the test-particle method. We introduce and discuss a simple analytical model that allows to provide estimates of the relaxation time, which are compared with numerical results. Finally, we use our findings to make numerical and analytical predictions for the case of a fermionic mixture in the normal-fluid phase in a realistic double-well potential relevant for experiments with cold atoms.

cond-mat.quant-gas↗

arXiv2015

Quantum simulation of conductivity plateaux and fractional quantum Hall effect using ultracold atoms

We analyze the role of impurities in the fractional quantum Hall effect using a highly controllable system of ultracold atoms. We investigate the mechanism responsible for the formation of plateaux in the resistivity/conductivity as a function of the applied magnetic field in the lowest Landau level regime. To this aim, we consider an impurity immersed in a small cloud of an ultracold quantum Bose gas subjected to an artificial magnetic field. We consider scenarios corresponding to experimentally realistic systems with gauge fields induced either by rotation or by appropriately designed laser fields. Systems of this kind are adequate to simulate quantum Hall effects in ultracold atom setups. We use exact diagonalization for few atoms and, to emulate transport equations, we analyze the time evolution of the system under a periodic perturbation. We provide a theoretical proposal to detect the up-to-now elusive presence of strongly correlated states related to fractional filling factors in the context of ultracold atoms. We analyze the conditions under which these strongly correlated states are associated with the presence of the resistivity/conductivity plateaux. Our main result is the presence of a plateau in a region, where the transfer between localized and non-localized particles takes place, as a necessary condition to maintain a constant value of the resistivity/conductivity as the magnetic field increases.

cond-mat.quant-gas↗

arXiv2015

Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices

We show how the area law for the entanglement entropy may be violated by free fermions on a lattice and look for conditions leading to the emergence of a volume law. We give an explicit construction of the states with maximal entanglement entropy based on the fact that, once a bipartition of the lattice in two complementary sets $A$ and $\bar{A}$ is given, the states with maximal entanglement entropy (volume law) may be factored into Bell-pairs (BP) formed by two states with support on $A$ and $\bar{A}$. We then exhibit, for translational invariant fermionic systems on a lattice, an Hamiltonian whose ground state is such to yield an exact volume law. As expected, the corresponding Fermi surface has a fractal topology. We also provide some examples of fermionic models for which the ground state may have an entanglement entropy $S_A$ between the area and the volume law, building an explicit example of a one-dimensional free fermion model where $S_A (L) \propto L^β$ with $β$ being intermediate between $β= 0$ (area law) and $β= 1$ (BP-state inducing volume law). For this model, the dispersion relation has a "zig-zag" structure leading to a fractal Fermi surface whose counting box dimension equals, for large lattices, $β$. Our analysis clearly relates the violation of the area law for the entanglement entropy of the ground state to the emergence of a non-trivial topology of the Fermi surface.

cond-mat.stat-mech↗

arXiv2015

Thermodynamics of the Topological Kondo Model

Using the thermodynamic Bethe ansatz, we investigate the topological Kondo model, which describes a set of one-dimensional external wires, pertinently coupled to a central region hosting a set of Majorana bound states. After a short review of the Bethe ansatz solution, we study the system at finite temperature and derive its free energy for arbitrary (even and odd) number of external wires. We then analyse the ground state energy as a function of the number of external wires and of their couplings to the Majorana bound states. Then, we compute, both for small and large temperatures, the entropy of the Majorana degrees of freedom localized within the central region and connected to the external wires. Our exact computation of the impurity entropy provides evidence of the importance of fermion parity symmetry in the realization of the topological Kondo model. Finally, we also obtain the low-temperature behaviour of the specific heat of the Majorana bound states, which provides a signature of the non-Fermi-liquid nature of the strongly coupled fixed point.

cond-mat.str-el↗

arXiv2014

Fixed Points Structure & Effective Fractional Dimension for O(N) Models with Long-Range Interactions

We study O(N) models with power-law interactions by using functional renormalization group methods: we show that both in Local Potential Approximation (LPA) and in LPA' their critical exponents can be computed from the ones of the corresponding short-range O(N) models at an effective fractional dimension. In LPA such effective dimension is given by $D_{eff}=2d/σ$, where d is the spatial dimension and $d+σ$ is the exponent of the power-law decay of the interactions. In LPA' the prediction by Sak [Phys. Rev. B 8, 1 (1973)] for the critical exponent $η$ is retrieved and an effective fractional dimension $D_{eff}'$ is obtained. Using these results we determine the existence of multicritical universality classes of long-range O(N) models and we present analytical predictions for the critical exponent $ν$ as a function of $σ$ and N: explicit results in 2 and 3 dimensions are given. Finally, we propose an improved LPA" approximation to describe the full theory space of the models where both short-range and long-range interactions are present and competing: a long-range fixed point is found to branch from the short-range fixed point at the critical value $σ_* = 2-η_{SR}$ (where $η_{SR}$ is the anomalous dimension of the short-range model), and to subsequently control the critical behavior of the system for $σ< σ_*$.

cond-mat.stat-mech↗

arXiv2014

Simulation of two-flavors symmetry-locking phases in ultracold fermionic mixtures

We describe an ultracold fermionic set-up where it is possible to synthesize a superfluid phase with symmetry obtained by locking independent invariance groups of the normal state. In this phase, named two-flavors symmetry-locking phase (TFSL), non-Abelian fractional vortices with semi-integer flux and gapless non-Abelian Goldstone modes localized on them appear. Considerations on the possible experimental realization of the TFSL are also provided.

cond-mat.quant-gas↗

arXiv2014

Energy-pressure relation for low-dimensional gases

A particularly simple relation of proportionality between internal energy and pressure holds for scale invariant thermodynamic systems, including classical and quantum Bose and Fermi ideal gases. One can quantify the deviation from such a relation by introducing the internal energy shift as the difference between the internal energy of the system and the corresponding value for scale invariant gases. We discuss general thermodynamic properties associated to the scale invariance, provide criteria for which the internal energy shift density is a bounded function of temperature. We then study the internal energy shift and deviations from the energy-pressure proportionality in low dimensional models of gases interpolating between the ideal Bose and the ideal Fermi gases, focusing on the Lieb-Liniger model in 1d and on the anyonic gas in 2d. In 1d the internal energy shift is determined from the thermodynamic Bethe ansatz integral equations and an explicit relation for it is given at high temperature. Our results show that the internal energy shift is positive, it vanishes in the two limits of zero and infinite coupling (respectively the ideal Bose and the Tonks Girardeau gas) and it has a maximum at a finite, temperature depending, value of the coupling. Remarkably, at fixed coupling the energy shift density saturates to a finite value for infinite temperature. In 2d we consider systems of Abelian anyons and non Abelian Chern-Simons particles: as it can be seen also directly from a study of the virial coefficients, in the usually considered hard-core limit the internal energy shift vanishes and the energy is just proportional to the pressure, with the proportionality constant being simply the area of the system. Soft-core boundary conditions at coincident points for the two-body wavefunction introduce a length scale, and induce a non-vanishing internal energy shift.

quant-ph↗

arXiv2014

Critical energy density of O$(n)$ models in $d=3$

A relation between O$(n)$ models and Ising models has been recently conjectured [L. Casetti, C. Nardini, and R. Nerattini, Phys. Rev. Lett. 106, 057208 (2011)]. Such a relation, inspired by an energy landscape analysis, implies that the microcanonical density of states of an O$(n)$ spin model on a lattice can be effectively approximated in terms of the density of states of an Ising model defined on the same lattice and with the same interactions. Were this relation exact, it would imply that the critical energy densities of all the O$(n)$ models (i.e., the average values per spin of the O$(n)$ Hamiltonians at their respective critical temperatures) should be equal to that of the corresponding Ising model; it is therefore worth investigating how different the critical energies are and how this difference depends on $n$. We compare the critical energy densities of O$(n)$ models in three dimensions in some specific cases: the O$(1)$ or Ising model, the O$(2)$ or $XY$ model, the O$(3)$ or Heisenberg model, the O$(4)$ model and the O$(\infty)$ or spherical model, all defined on regular cubic lattices and with ferromagnetic nearest-neighbor interactions. The values of the critical energy density in the $n=2$, $n=3$, and $n=4$ cases are derived through a finite-size scaling analysis of data produced by means of Monte Carlo simulations on lattices with up to $128^3$ sites. For $n=2$ and $n=3$ the accuracy of previously known results has been improved. We also derive an interpolation formula showing that the difference between the critical energy densities of O$(n)$ models and that of the Ising model is smaller than $1\%$ if $n<8$ and never exceeds $3\%$ for any $n$.

cond-mat.stat-mech↗

arXiv2013

Semimetal-superfluid quantum phase transitions in 2D and 3D lattices with Dirac points

We study the superfluid properties of attractively interacting fermions hopping in a family of 2D and 3D lattices in the presence of synthetic gauge fields having π-flux per plaquette. The reason for such a choice is that the π-flux cubic lattice displays Dirac points and that decreasing the hopping coefficient in a spatial direction (say, t_z) these Dirac points are unaltered: it is then possible to study the 3D-2D interpolation towards the π-flux square lattice. We also consider the lattice configuration providing the continuous interpolation between the 2D π-flux square lattice and the honeycomb geometry. We investigate by a mean field analysis the effects of interaction and dimensionality on the superfluid gap, chemical potential and critical temperature, showing that these quantities continuously vary along the patterns of interpolation. In the two-dimensional cases at zero temperature and at half filling there is a quantum phase transition occurring at a critical (negative) interaction U_c presenting a linear critical exponent for the gap as a function of |U-U_c|. We show that in three dimensions this quantum phase transition is again retrieved, pointing out that the critical exponent for the gap changes from 1 to 1/2 for each finite value of t_z.

cond-mat.str-el↗