Decoherence in a quantum harmonic oscillator monitored by a Bose-Einstein condensate

We investigate the dynamics of a quantum oscillator, whose evolution is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double well potential. It is demonstrated that the oscillator may experience various degrees of decoherence depending on the variable being measured and the state in which the BEC is prepared. These range from a `coherent' regime in which only the variances of the oscillator position and momentum are affected by measurement, to a slow (power law) or rapid (Gaussian) decoherence of the mean values themselves.Comment: 4 pages, 3 figures, lette

Stochastic exclusion processes versus coherent transport

Stochastic exclusion processes play an integral role in the physics of non-equilibrium statistical mechanics. These models are Markovian processes, described by a classical master equation. In this paper a quantum mechanical version of a stochastic hopping process in one dimension is formulated in terms of a quantum master equation. This allows the investigation of coherent and stochastic evolution in the same formal framework. The focus lies on the non-equilibrium steady state. Two stochastic model systems are considered, the totally asymmetric exclusion process and the fully symmetric exclusion process. The steady state transport properties of these models is compared to the case with additional coherent evolution, generated by the $XX$-Hamiltonian

Entanglement as a signature of quantum chaos

We explore the dynamics of entanglement in classically chaotic systems by considering a multiqubit system that behaves collectively as a spin system obeying the dynamics of the quantum kicked top. In the classical limit, the kicked top exhibits both regular and chaotic dynamics depending on the strength of the chaoticity parameter $\kappa$ in the Hamiltonian. We show that the entanglement of the multiqubit system, considered for both bipartite and pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite entanglement is enhanced in the chaotic region, pairwise entanglement is suppressed. Furthermore, we define a time-averaged entangling power and show that this entangling power changes markedly as $\kappa$ moves the system from being predominantly regular to being predominantly chaotic, thus sharply identifying the edge of chaos. When this entangling power is averaged over initial states, it yields a signature of global chaos. The qualitative behavior of this global entangling power is similar to that of the classical Lyapunov exponent.Comment: 8 pages, 8 figure

Many-body symbolic dynamics of a classical oscillator chain

We study a certain type of the celebrated Fermi-Pasta-Ulam particle chain, namely the inverted FPU model, where the inter-particle potential has a form of a quartic double well. Numerical evidence is given in support of a simple symbolic description of dynamics (in the regime of sufficiently high potential barrier between the wells) in terms of an (approximate) Markov process. The corresponding transition matrix is formally identical to a ferromagnetic Heisenberg quantum spin-1/2 chain with long range coupling, whose diagonalization yields accurate estimates for a class of time correlation functions of the model.Comment: 22 pages in LaTeX with 14 figures; submitted to Nonlinearity ; corrected page offset proble

Stability of quantum motion and correlation decay

We derive a simple and general relation between the fidelity of quantum motion, characterizing the stability of quantum dynamics with respect to arbitrary static perturbation of the unitary evolution propagator, and the integrated time auto-correlation function of the generator of perturbation. Surprisingly, this relation predicts the slower decay of fidelity the faster decay of correlations is. In particular, for non-ergodic and non-mixing dynamics, where asymptotic decay of correlations is absent, a qualitatively different and faster decay of fidelity is predicted on a time scale 1/delta as opposed to mixing dynamics where the fidelity is found to decay exponentially on a time-scale 1/delta^2, where delta is a strength of perturbation. A detailed discussion of a semi-classical regime of small effective values of Planck constant is given where classical correlation functions can be used to predict quantum fidelity decay. Note that the correct and intuitively expected classical stability behavior is recovered in the classical limit hbar->0, as the two limits delta->0 and hbar->0 do not commute. In addition we also discuss non-trivial dependence on the number of degrees of freedom. All the theoretical results are clearly demonstrated numerically on a celebrated example of a quantized kicked top.Comment: 32 pages, 10 EPS figures and 2 color PS figures. Higher resolution color figures can be obtained from authors; minor changes, to appear in J.Phys.A (March 2002

Slow dynamics in translation-invariant quantum lattice models

Many-body quantum systems typically display fast dynamics and ballistic spreading of information. Here we address the open problem of how slow the dynamics can be after a generic breaking of integrability by local interactions. We develop a method based on degenerate perturbation theory that reveals slow dynamical regimes and delocalization processes in general translation invariant models, along with accurate estimates of their delocalization time scales. Our results shed light on the fundamental questions of the robustness of quantum integrable systems and the possibility of many-body localization without disorder. As an example, we construct a large class of one-dimensional lattice models where, despite the absence of asymptotic localization, the transient dynamics is exceptionally slow, i.e., the dynamics is indistinguishable from that of many-body localized systems for the system sizes and time scales accessible in experiments and numerical simulations

Entangled random pure states with orthogonal symmetry: exact results

We compute analytically the density $\varrho_{N,M}(\lambda)$ of Schmidt eigenvalues, distributed according to a fixed-trace Wishart-Laguerre measure, and the average R\'enyi entropy $\langle\mathcal{S}_q\rangle$ for reduced density matrices of entangled random pure states with orthogonal symmetry $(\beta=1)$. The results are valid for arbitrary dimensions $N=2k,M$ of the corresponding Hilbert space partitions, and are in excellent agreement with numerical simulations.Comment: 15 pages, 5 figure

Quantum state transfer in a XX chain with impurities

One spin excitation states are involved in the transmission of quantum states and entanglement through a quantum spin chain, the localization properties of these states are crucial to achieve the transfer of information from one extreme of the chain to the other. We investigate the bipartite entanglement and localization of the one excitation states in a quantum $XX$ chain with one impurity. The bipartite entanglement is obtained using the Concurrence and the localization is analyzed using the inverse participation ratio. Changing the strength of the exchange coupling of the impurity allows us to control the number of localized or extended states. The analysis of the inverse participation ratio allows us to identify scenarios where the transmission of quantum states or entanglement can be achieved with a high degree of fidelity. In particular we identify a regime where the transmission of quantum states between the extremes of the chain is executed in a short transmission time $\sim N/2$, where $N$ is the number of spins in the chain, and with a large fidelity

Hypersensitivity and chaos signatures in the quantum baker's maps

Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has lead to a number of proposals for perturbation-based characterizations of quantum chaos, including linear growth of entropy, exponential decay of fidelity, and hypersensitivity to perturbation. All of these accurately predict chaos in the classical limit, but it is not clear that they behave the same far from the classical realm. We investigate the dynamics of a family of quantizations of the baker's map, which range from a highly entangling unitary transformation to an essentially trivial shift map. Linear entropy growth and fidelity decay are exhibited by this entire family of maps, but hypersensitivity distinguishes between the simple dynamics of the trivial shift map and the more complicated dynamics of the other quantizations. This conclusion is supported by an analytical argument for short times and numerical evidence at later times.Comment: 32 pages, 6 figure

Compact smallest eigenvalue expressions in Wishart-Laguerre ensembles with or without fixed-trace

The degree of entanglement of random pure states in bipartite quantum systems can be estimated from the distribution of the extreme Schmidt eigenvalues. For a bipartition of size M\geq N, these are distributed according to a Wishart-Laguerre ensemble (WL) of random matrices of size N x M, with a fixed-trace constraint. We first compute the distribution and moments of the smallest eigenvalue in the fixed trace orthogonal WL ensemble for arbitrary M\geq N. Our method is based on a Laplace inversion of the recursive results for the corresponding orthogonal WL ensemble by Edelman. Explicit examples are given for fixed N and M, generalizing and simplifying earlier results. In the microscopic large-N limit with M-N fixed, the orthogonal and unitary WL distributions exhibit universality after a suitable rescaling and are therefore independent of the constraint. We prove that very recent results given in terms of hypergeometric functions of matrix argument are equivalent to more explicit expressions in terms of a Pfaffian or determinant of Bessel functions. While the latter were mostly known from the random matrix literature on the QCD Dirac operator spectrum, we also derive some new results in the orthogonal symmetry class.Comment: 25 pag., 4 fig - minor changes, typos fixed. To appear in JSTA