We study the nonequilibrium dynamics of the Quantum Ising Model following an abrupt quench of the transverse field. We focus on the onsite autocorrelation function of the order parameter, and extract the phase coherence time τ ϕ Q from its asymptotic behavior. We show that the initial state determines τ ϕ Q only through an effective temperature set by its energy and the final Hamiltonian. Moreover, we observe that the dependence of τ ϕ Q on the effective temperature fairly agrees with that obtained in thermal equilibrium as a function of the equilibrium temperature.PACS numbers: 75.40. Gb, 75.10.Pq, 73.43.Nq, 03.65.Sq A recent series of beautiful experiments with cold atomic gases [1,2,3] have triggered a great deal of interest in some fundamental aspects of the non-equilibrium dynamics of correlated quantum systems. The peculiarity of the dynamics of cold atoms is its phase coherence on long time scales. This was clearly demonstrated by the cycles of collapse and revival of the order parameter observed in Ref. [2]. The interplay between phase coherence, strong interactions, and low dimensionality may result in surprising effects: an example is the lack of thermalization recently observed in quasi-one dimensional condensates [3]. The attribution of this phenomenon to the closeness of these systems to integrability spurred an intense discussion on the general relation between quantum integrability and thermalization in the long-time dynamics of strongly correlated quantum systems [4,5,6,7,8,9,10,11,12,13,14,15].The simplest nonequilibrium process to be considered in order to study the long-time dynamics of a quantum system is the quantum quench: an abrupt change in time of one of the system parameters or of its boundary conditions. Recent studies of strongly correlated models [4,5,6,7,8,9,10,11,12,13,14,15] have demonstrated that the behavior of integrable and nonintegrable systems can be quite different. Thermalization can be observed, under specific circumstances, in nonintegrable systems [8,9,10]: asymptotic values of significant observables, such as the momentum distribution function, do not depend on the details of the initial state, but only on its energy [8]. On the other hand, for integrable systems thermalization does not occur [5,6,7,11,12,13,14,15]: a larger amount of information on the initial state seems necessary to predict the asymptotic state. It has been conjectured that this information consists of the expectation value of a set of constants of motion fixing in the Lagrange multipliers of a generalized Gibbs ensemble [7]. For a special quench in a 1D Bose-Hubbard model [11] and for integrable systems with free quasiparticles [12], the local reduced density matrix was indeed proven to asymptotically tend to such generalized ensemble. Moreover, the generalized Gibbs ensemble was shown to correctly predict the asymptotic momentum distribution functions for a variety of models and quenches [6,7,13,14]. However, it should be pointed out that neglection of correlations of the occupation of differen...

By means of analytical and numerical methods we analyze the phase diagram of polaritons in one-dimensional coupled cavities. We locate the phase boundary, discuss the behavior of the polariton compressibility and visibility fringes across the critical point, and find a nontrivial scaling of the phase boundary as a function of the number of atoms inside each cavity. We also predict the emergence of a polaritonic glassy phase when the number of atoms fluctuates from cavity to cavity.

We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, XY , or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the XY models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent Density Matrix Renormalization Group.

We introduce and study the properties of an array of QED cavities coupled by nonlinear elements, in the presence of photon leakage and driven by a coherent source. The nonlinear couplings lead to photon hopping and to nearest-neighbor Kerr terms. By tuning the system parameters, the steady state of the array can exhibit a photon crystal associated with a periodic modulation of the photon blockade. In some cases, the crystalline ordering may coexist with phase synchronization. The class of cavity arrays we consider can be built with superconducting circuits of existing technology.

We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of dynamical origin, and is established only at very long times, whereas in thermodynamic equilibrium it arises from the properties of the (free) energy. To this end, by combining the cluster methods extensively used in equilibrium phase transitions to quantum trajectories and tensor-network techniques, we extend them to nonequilibrium phase transitions in dissipative many-body systems. We analyze in detail a model of spin-1=2 on a lattice interacting through an XYZ Hamiltonian, each of them coupled to an independent environment that induces incoherent spin flips. In the steady-state phase diagram derived from our cluster approach, the location of the phase boundaries and even its topology radically change, introducing reentrance of the paramagnetic phase as compared to the single-site mean field where correlations are neglected. Furthermore, a stability analysis of the cluster mean field indicates a susceptibility towards a possible incommensurate ordering, not present if short-range correlations are ignored.

By means of the density matrix renormalization group technique, we accurately determine the zero-temperature phase diagram of the one-dimensional extended Bose-Hubbard model with on-site and nearest-neighbor interactions. We analyze the scaling of the charge and of the neutral ground-state energy gaps, as well as of various order parameters. In this way we come to an accurate location of the boundaries between the superfluid and the insulating phases. In this last region, we are able to distinguish between the conventional Mott insulating and density-wave phases and the Haldane insulator phase displaying long-range string ordering, as originally predicted by Dalla Torre et al (2006 Phys. Rev. Lett. 97 260401). 10 Acknowledgment 11 References 11 IntroductionOver the last decade, ultracold atomic gases loaded in optical lattices were successfully established as an excellent setup to probe the equilibrium, as well as the out-of-equilibrium physics of strongly correlated quantum systems. The great advantages of these experimental setups are essentially related to two aspects. On the one hand, they have a very high degree of flexibility: in addition to the ability to address different geometries, and to deal with bosonic and with fermionic species, they also admit the possibility of manipulating the underlying Hamiltonian system parameters to a large extent. Moreover, the remarkably high degree of isolation from any environmental source of decoherence opened up entirely new scenarios in the observation of genuinely many-body quantum phenomena [1].The paradigm model to describe cold bosonic atoms trapped in an optical lattice is obtained by combining the kinetic energy in the lowest band with the on-site repulsion arising for sufficiently deep lattices. This leads to the celebrated Bose-Hubbard model (BHM) [2]. The rich physics of the BHM stems from the competition between the kinetic energy J , which is gained by delocalizing particles across the lattice in an extended Bloch state, and the repulsive on-site interaction U , which disfavors having more than one particle per site. When the kinetic energy term dominates, the system is in a coherent superfluid (SF) phase; on the other hand, repulsive interactions tend to favor a Mott insulating (MI) phase [3].The recent advances in manipulating magnetic atoms and molecules with a large dipole momentum make it possible to achieve longer-range interactions, which can be accurately tuned as well, thus permitting us to probe the interplay between strong correlations and chargeordering effects [4]. Dipolar bosons confined in optical lattices are typically described by an extended version of the BHM, the so-called extended Bose-Hubbard model (EBHM), which includes a two-body non-local repulsive term typically decaying as r −3 with distance r .Interestingly, the presence of long-range interactions noticeably enriches the phase diagram of the BHM, for example leading to a stabilization of a peculiar insulating phase, named the bosonic Haldane insulator (HI). This gapped phase pre...

We conjecture that thermalization following a quantum quench in a strongly correlated quantum system is closely connected to many-body delocalization in the space of quasi-particles. This scenario is tested in the anisotropic Heisenberg spin chain with different types of integrability-breaking terms. We first quantify the deviations from integrability by analyzing the level spacing statistics and the inverse participation ratio of the system's eigenstates. We then focus on thermalization, by studying the dynamics after a sudden quench of the anisotropy parameter. Our numerical simulations clearly support the conjecture, as long as the integrability-breaking term acts homogeneously on the quasiparticle space, in such a way as to induce ergodicity over all the relevant Hilbert space. © 2011 American Physical Society

We study the charge conductivity in one-dimensional prototype models of interacting particles, such as the Hubbard and the t-V spinless fermion models, when coupled to some external baths injecting and extracting particles at the boundaries. We show that, if these systems are driven far from equilibrium, a negative differential conductivity regime can arise. The above electronic models can be mapped into Heisenberg-like spin ladders coupled to two magnetic baths, so that charge transport mechanisms are explained in terms of quantum spin transport. The negative differential conductivity is due to oppositely polarized ferromagnetic domains that arise at the edges of the chain and therefore inhibit spin transport: we propose a qualitative understanding of the phenomenon by analyzing the localization of one-magnon excitations created at the borders of a ferromagnetic region. We also show that negative differential conductivity is stable against breaking of integrability. Numerical simulations of nonequilibrium time evolution have been performed by employing a Monte Carlo wave function approach and a matrix product operator formalism. © 2009 The American Physical Society