Quasiadiabatic dynamics of ultracold bosonic atoms in a one-dimensional optical superlattice

We study the quasiadiabatic dynamics of a one-dimensional system of ultracold bosonic atoms loaded in an optical superlattice. Focusing on a slow linear variation in time of the superlattice potential, the system is driven from a conventional Mott insulator phase to a superlattice-induced Mott insulator, crossing in between a gapless critical superfluid region. Due to the presence of a gapless region, a number of defects depending on the velocity of the quench appear. Our findings suggest a power-law dependence similar to the Kibble-Zurek mechanism for intermediate values of the quench rate. For the temporal ranges of the quench dynamics that we considered, the scaling of defects depends nontrivially on the width of the superfluid region.Comment: 6 Pages, 4 Figure

Diagnosing order by disorder in quantum spin systems

In this paper we study the frustrated J1-J2 quantum Heisenberg model on the square lattice for J2 > 2J1, in a magnetic field. In this regime the classical system is known to have a degenerate manifold of lowest energy configurations, where standard thermal order by disorder occurs. In order to study its quantum version we use a path integral formulation in terms of coherent states. We show that the classical degeneracy in the plane transverse to the magnetic field is lifted by quantum fluctuations. Collinear states are then selected, in a similar pattern to that set by thermal order by disorder, leaving a Z2 degeneracy. A careful analysis reveals a purely quantum mechanical effect given by the tunneling between the two minima selected by fluctuations. The effective description contains two planar (XY -like) fields conjugate to the total magnetization and the difference of the two sublattice magnetizations. Disorder in either or both of these fields produces the locking of their conjugate observables. Furthermore, within this scenario we argue that the quantum state is close to a product state.Comment: 8 pages, 3 figure

On the Path Integral Representation for Spin Systems

We propose a classical constrained Hamiltonian theory for the spin. After the Dirac treatment we show that due to the existence of second class constraints the Dirac brackets of the proposed theory represent the commutation relations for the spin. We show that the corresponding partition function, obtained via the Fadeev-Senjanovic procedure, coincides with the one obtained using coherent states. We also evaluate this partition function for the case of a single spin in a magnetic field.Comment: To be published in J.Phys. A: Math. and Gen. Latex file, 12 page

Effective thermal dynamics following a quantum quench in a spin chain

We study the nonequilibrium dynamics of the Quantum Ising Model following an abrupt quench of the transverse field. We focus on the on-site autocorrelation function of the order parameter, and extract the phase coherence time $\tau^{\phi}_Q$ from its asymptotic behavior. We show that the initial state determines $\tau^{\phi}_Q$ only through an effective temperature set by its energy and the final Hamiltonian. Moreover, we observe that the dependence of $\tau^{\phi}_Q$ on the effective temperature fairly agrees with that obtained in thermal equilibrium as a function of the equilibrium temperature.Comment: 4 pages, 4 figures. Published versio

Quantum Breathing of an Impurity in a One-dimensional Bath of Interacting Bosons

By means of time-dependent density-matrix renormalization-group (TDMRG) we are able to follow the real-time dynamics of a single impurity embedded in a one-dimensional bath of interacting bosons. We focus on the impurity breathing mode, which is found to be well-described by a single oscillation frequency and a damping rate. If the impurity is very weakly coupled to the bath, a Luttinger-liquid description is valid and the impurity suffers an Abraham-Lorentz radiation-reaction friction. For a large portion of the explored parameter space, the TDMRG results fall well beyond the Luttinger-liquid paradigm.Comment: 10 pages, 7 figures, main text and supplementary material merged in a single PRB style documen

Decoherence induced by interacting quantum spin baths

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.Comment: 18 pages, 20 figure

Quantum Critical Dynamics of A Qubit Coupled to An Isotropic Lipkin-Meshkov-Glick Bath

We explore a dynamic signature of quantum phase transition (QPT) in an isotropic Lipkin-Meshkov-Glick (LMG) model by studying the time evolution of a central qubit coupled to it. We evaluate exactly the time-dependent purity, which can be used to measure quantum coherence, of the central qubit. It is found that distinctly different behaviors of the purity as a function of the parameter reveal clearly the QPT point in the system. It is also clarified that the present model is equivalent to an anti Jaynes-Cummings model under certain conditions.Comment: 8 pages, 4 figure