42 research outputs found
Quantum jumps on Anderson attractors
In a closed single-particle quantum system, spatial disorder induces Anderson
localization of eigenstates and halts wave propagation. The phenomenon is
vulnerable to interaction with environment and decoherence, that is believed to
restore normal diffusion. We demonstrate that for a class of experimentally
feasible non-Hermitian dissipators, which admit signatures of localization in
asymptotic states, quantum particle opts between diffusive and ballistic
regimes, depending on the phase parameter of dissipators, with sticking about
localization centers. In diffusive regime, statistics of quantum jumps is
non-Poissonian and has a power-law interval, a footprint of intermittent
locking in Anderson modes. Ballistic propagation reflects dispersion of an
ordered lattice and introduces a new timescale for jumps with non-monotonous
probability distribution. Hermitian dephasing dissipation makes localization
features vanish, and Poissonian jump statistics along with normal diffusion are
recovered.Comment: 6 pages, 5 figure
Subdiffusion of nonlinear waves in quasiperiodic potentials
We study the spatio-temporal evolution of wave packets in one-dimensional
quasiperiodic lattices which localize linear waves. Nonlinearity (related to
two-body interactions) has destructive effect on localization, as recently
observed for interacting atomic condensates [Phys. Rev. Lett. 106, 230403
(2011)]. We extend the analysis of the characteristics of the subdiffusive
dynamics to large temporal and spatial scales. Our results for the second
moment consistently reveal an asymptotic and
intermediate laws. At variance to purely random systems
[Europhys. Lett. 91, 30001 (2010)] the fractal gap structure of the linear wave
spectrum strongly favors intermediate self-trapping events. Our findings give a
new dimension to the theory of wave packet spreading in localizing
environments
Anderson localization or nonlinear waves? A matter of probability
In linear disordered systems Anderson localization makes any wave packet stay
localized for all times. Its fate in nonlinear disordered systems is under
intense theoretical debate and experimental study. We resolve this dispute
showing that at any small but finite nonlinearity (energy) value there is a
finite probability for Anderson localization to break up and propagating
nonlinear waves to take over. It increases with nonlinearity (energy) and
reaches unity at a certain threshold, determined by the initial wave packet
size. Moreover, the spreading probability stays finite also in the limit of
infinite packet size at fixed total energy. These results are generalized to
higher dimensions as well.Comment: 4 pages, 3 figure
Control of a single-particle localization in open quantum systems
We investigate the possibility to control localization properties of the
asymptotic state of an open quantum system with a tunable synthetic
dissipation. The control mechanism relies on the matching between properties of
dissipative operators, acting on neighboring sites and specified by a single
control parameter, and the spatial phase structure of eigenstates of the system
Hamiltonian. As a result, the latter coincide (or near coincide) with the dark
states of the operators. In a disorder-free Hamiltonian with a flat band, one
can either obtain a localized asymptotic state or populate whole flat and/or
dispersive bands, depending on the value of the control parameter. In a
disordered Anderson system, the asymptotic state can be localized anywhere in
the spectrum of the Hamiltonian. The dissipative control is robust with respect
to an additional local dephasing.Comment: 6 pages, 5 figure
Localization in periodically modulated speckle potentials
Disorder in a 1D quantum lattice induces Anderson localization of the
eigenstates and drastically alters transport properties of the lattice. In the
original Anderson model, the addition of a periodic driving increases, in a
certain range of the driving's frequency and amplitude, localization length of
the appearing Floquet eigenstates. We go beyond the uncorrelated disorder case
and address the experimentally relevant situation when spatial correlations are
present in the lattice potential. Their presence induces the creation of an
effective mobility edge in the energy spectrum of the system. We find that a
slow driving leads to resonant hybridization of the Floquet states, by
increasing both the participation numbers and effective widths of the states in
the strongly localized band and decreasing values of these characteristics for
the states in the quasi-extended band. Strong driving homogenizes the bands, so
that the Floquet states loose compactness and tend to be spatially smeared. In
the basis of the stationary Hamiltonian, these states retain localization in
terms of participation number but become de-localized and spectrum-wide in term
of their effective widths. Signatures of thermalization are also observed.Comment: 6 pages, 3 figure
Localization in open quantum systems
In an isolated single-particle quantum system a spatial disorder can induce
Anderson localization. Being a result of interference, this phenomenon is
expected to be fragile in the face of dissipation. Here we show that
dissipation can drive a disordered system into a steady state with tunable
localization properties. This can be achieved with a set of identical
dissipative operators, each one acting non-trivially only on a pair of
neighboring sites. Operators are parametrized by a uniform phase, which
controls selection of Anderson modes contributing to the state. On the
microscopic level, quantum trajectories of a system in a localized steady
regime exhibit intermittent dynamics consisting of long-time sticking events
near selected modes interrupted by jumps between them.Comment: 5 pages, 5 figure
The crossover from strong to weak chaos for nonlinear waves in disordered systems
We observe a crossover from strong to weak chaos in the spatiotemporal
evolution of multiple site excitations within disordered chains with cubic
nonlinearity. Recent studies have shown that Anderson localization is
destroyed, and the wave packet spreading is characterized by an asymptotic
divergence of the second moment in time (as ), due to weak
chaos. In the present paper, we observe the existence of a qualitatively new
dynamical regime of strong chaos, in which the second moment spreads even
faster (as ), with a crossover to the asymptotic law of weak chaos at
larger times. We analyze the pecularities of these spreading regimes and
perform extensive numerical simulations over large times with ensemble
averaging. A technique of local derivatives on logarithmic scales is developed
in order to quantitatively visualize the slow crossover processes.Comment: 5 pages, 3 figures. Submitted Europhysics Letter