155 research outputs found
Can quantum fractal fluctuations be observed in an atom-optics kicked rotor experiment?
We investigate the parametric fluctuations in the quantum survival
probability of an open version of the delta-kicked rotor model in the deep
quantum regime. Spectral arguments [Guarneri I and Terraneo M 2001 Phys. Rev. E
vol. 65 015203(R)] predict the existence of parametric fractal fluctuations
owing to the strong dynamical localisation of the eigenstates of the kicked
rotor. We discuss the possibility of observing such dynamically-induced
fractality in the quantum survival probability as a function of the kicking
period for the atom-optics realisation of the kicked rotor. The influence of
the atoms' initial momentum distribution is studied as well as the dependence
of the expected fractal dimension on finite-size effects of the experiment,
such as finite detection windows and short measurement times. Our results show
that clear signatures of fractality could be observed in experiments with cold
atoms subjected to periodically flashed optical lattices, which offer an
excellent control on interaction times and the initial atomic ensemble.Comment: 18 pp, 7 figs., 1 tabl
Driven Macroscopic Quantum Tunneling of Ultracold Atoms in Engineered Optical Lattices
Coherent macroscopic tunneling of a Bose-Einstein condensate between two
parts of an optical lattice separated by an energy barrier is theoretically
investigated. We show that by a pulsewise change of the barrier height, it is
possible to switch between tunneling regime and a self-trapped state of the
condensate. This property of the system is explained by effectively reducing
the dynamics to the nonlinear problem of a particle moving in a double square
well potential. The analysis is made for both attractive and repulsive
interatomic forces, and it highlights the experimental relevance of our
findings
Resonant tunneling of Bose-Einstein condensates in optical lattices
In this article, we present theoretical as well as experimental results on
resonantly enhanced tunneling of Bose-Einstein condensates in optical lattices
both in the linear case and for small nonlinearities. Our results demonstrate
the usefulness of condensates in optical lattices for simulating Hamiltonians
originally used for describing solid state phenomena.Comment: New J. Phys., in pres
Resonant forcing of select degrees of freedom of multidimensional chaotic map dynamics
We study resonances of multidimensional chaotic map dynamics. We use the
calculus of variations to determine the additive forcing function that induces
the largest response, that is, the greatest deviation from the unperturbed
dynamics. We include the additional constraint that only select degrees of
freedom be forced, corresponding to a very general class of problems in which
not all of the degrees of freedom in an experimental system are accessible to
forcing. We find that certain Lagrange multipliers take on a fundamental
physical role as the efficiency of the forcing function and the effective
forcing experienced by the degrees of freedom which are not forced directly.
Furthermore, we find that the product of the displacement of nearby
trajectories and the effective total forcing function is a conserved quantity.
We demonstrate the efficacy of this methodology with several examples.Comment: 11 pages, 3 figure
Microscopic modeling of photoluminescence of strongly disordered semiconductors
A microscopic theory for the luminescence of ordered semiconductors is
modified to describe photoluminescence of strongly disordered semiconductors.
The approach includes both diagonal disorder and the many-body Coulomb
interaction. As a case study, the light emission of a correlated plasma is
investigated numerically for a one-dimensional two-band tight-binding model.
The band structure of the underlying ordered system is assumed to correspond to
either a direct or an indirect semiconductor. In particular, luminescence and
absorption spectra are computed for various levels of disorder and sample
temperature to determine thermodynamic relations, the Stokes shift, and the
radiative lifetime distribution.Comment: 35 pages, 14 figure
Nonlinear Dynamics in Double Square Well Potential
Considering the coherent nonlinear dynamics in double square well potential
we find the example of coexistence of Josephson oscillations with a
self-trapping regime. This macroscopic bistability is explained by proving
analytically the simultaneous existence of symmetric, antisymmetric and
asymmetric stationary solutions of the associated Gross-Pitaevskii equation.
The effect is illustrated and confirmed by numerical simulations. This property
allows to make suggestions on possible experiments using Bose-Einstein
condensates in engineered optical lattices or weakly coupled optical waveguide
arrays
A two-band Bose-Hubbard model for many-body resonant tunneling in the Wannier-Stark system
We study an experimentally realizable paradigm of complex many-body quantum
systems, a two-band Wannier-Stark model, for which diffusion in Hilbert space
as well as many-body Landau-Zener processes can be engineered. A cross-over
between regular to quantum chaotic spectra is found within the many-body
avoided crossings at resonant tunneling conditions. The spectral properties are
shown to determine the evolution of states across a cascade of Landau-Zener
events. We apply the obtained spectral information to study the non-equilibrium
dynamics of our many-body system in different parameter regimes.Comment: much extended and improved version (13 pages, 10 figures); comments
are very welcome
Effective spin model for interband transport in a Wannier-Stark lattice system
We show that the interband dynamics in a tilted two-band Bose-Hubbard model
can be reduced to an analytically accessible spin model in the case of resonant
interband oscillations. This allows us to predict the revival time of these
oscillations which decay and revive due to inter-particle interactions. The
presented mapping onto the spin model and the so achieved reduction of
complexity has interesting perspectives for future studies of many-body
systems.Comment: 7 pages, 4 figure
Tunnelling rates for the nonlinear Wannier-Stark problem
We present a method to numerically compute accurate tunnelling rates for a
Bose-Einstein condensate which is described by the nonlinear Gross-Pitaevskii
equation. Our method is based on a sophisticated real-time integration of the
complex-scaled Gross-Pitaevskii equation, and it is capable of finding the
stationary eigenvalues for the Wannier-Stark problem. We show that even weak
nonlinearities have significant effects in the vicinity of very sensitive
resonant tunnelling peaks, which occur in the rates as a function of the Stark
field amplitude. The mean-field interaction induces a broadening and a shift of
the peaks, and the latter is explained by analytic perturbation theory
Structure, Time Propagation and Dissipative Terms for Resonances
For odd anharmonic oscillators, it is well known that complex scaling can be
used to determine resonance energy eigenvalues and the corresponding
eigenvectors in complex rotated space. We briefly review and discuss various
methods for the numerical determination of such eigenvalues, and also discuss
the connection to the case of purely imaginary coupling, which is PT-symmetric.
Moreover, we show that a suitable generalization of the complex scaling method
leads to an algorithm for the time propagation of wave packets in potentials
which give rise to unstable resonances. This leads to a certain unification of
the structure and the dynamics. Our time propagation results agree with known
quantum dynamics solvers and allow for a natural incorporation of structural
perturbations (e.g., due to dissipative processes) into the quantum dynamics.Comment: 14 pages; LaTeX; minor change
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