13 research outputs found
Quantum interference in nanofractals and its optical manifestation
We consider quantum interferences of ballistic electrons propagating inside
fractal structures with nanometric size of their arms. We use a scaling
argument to calculate the density of states of free electrons confined in a
simple model fractal. We show how the fractal dimension governs the density of
states and optical properties of fractal structures in the RF-IR region. We
discuss the effect of disorder on the density of states along with the
possibility of experimental observation.Comment: 19 pages, 6 figure
Effects of nonlinear sweep in the Landau-Zener-Stueckelberg effect
We study the Landau-Zener-Stueckelberg (LZS) effect for a two-level system
with a time-dependent nonlinear bias field (the sweep function) W(t). Our main
concern is to investigate the influence of the nonlinearity of W(t) on the
probability P to remain in the initial state. The dimensionless quantity
epsilon = pi Delta ^2/(2 hbar v) depends on the coupling Delta of both levels
and on the sweep rate v. For fast sweep rates, i.e., epsilon << l and
monotonic, analytic sweep functions linearizable in the vicinity of the
resonance we find the transition probability 1-P ~= epsilon (1+a), where a>0 is
the correction to the LSZ result due to the nonlinearity of the sweep. Further
increase of the sweep rate with nonlinearity fixed brings the system into the
nonlinear-sweep regime characterized by 1-P ~= epsilon ^gamma with gamma neq 1
depending on the type of sweep function. In case of slow sweep rates, i.e.,
epsilon >>1 an interesting interference phenomenon occurs. For analytic W(t)
the probability P=P_0 e^-eta is determined by the singularities of sqrt{Delta
^2+W^2(t)} in the upper complex plane of t. If W(t) is close to linear, there
is only one singularity, that leads to the LZS result P=e^-epsilon with
important corrections to the exponent due to nonlinearity. However, for, e.g.,
W(t) ~ t^3 there is a pair of singularities in the upper complex plane.
Interference of their contributions leads to oscillations of the prefactor P_0
that depends on the sweep rate through epsilon and turns to zero at some
epsilon. Measurements of the oscillation period and of the exponential factor
would allow to determine Delta, independently.Comment: 11 PR pages, 12 figures. To be published in PR
Localization and fluctuations of local spectral density on tree-like structures with large connectivity: Application to the quasiparticle line shape in quantum dots
We study fluctuations of the local density of states (LDOS) on a tree-like
lattice with large branching number . The average form of the local spectral
function (at given value of the random potential in the observation point)
shows a crossover from the Lorentzian to semicircular form at ,
where , is the typical value of the hopping matrix
element, and is the width of the distribution of random site energies. For
the LDOS fluctuations (with respect to this average form) are
weak. In the opposite case, , the fluctuations get strong and the
average LDOS ceases to be representative, which is related to the existence of
the Anderson transition at . On the localized side
of the transition the spectrum is discrete, and LDOS is given by a set of
-like peaks. The effective number of components in this regime is given
by , with being the inverse participation ratio. It is shown that
has in the transition point a limiting value close to unity, , so that the system undergoes a transition directly from the deeply
localized to extended phase. On the side of delocalized states, the peaks in
LDOS get broadened, with a width being exponentially small near the
transition point. We discuss application of our results to the problem of the
quasiparticle line shape in a finite Fermi system, as suggested recently by
Altshuler, Gefen, Kamenev, and Levitov.Comment: 12 pages, 1 figure. Misprints in eqs.(21) and (28) corrected, section
VII added. Accepted for publication in Phys. Rev.
Josephson dynamics for coupled polariton modes under the atom-field interaction in the cavity
We consider a new approach to the problem of Bose-Einstein condensation (BEC)
of polaritons for atom-field interaction under the strong coupling regime in
the cavity. We investigate the dynamics of two macroscopically populated
polariton modes corresponding to the upper and lower branch energy states
coupled via Kerr-like nonlinearity of atomic medium. We found out the
dispersion relations for new type of collective excitations in the system under
consideration. Various temporal regimes like linear (nonlinear) Josephson
transition and/or Rabi oscillations, macroscopic quantum self-trapping (MQST)
dynamics for population imbalance of polariton modes are predicted. We also
examine the switching properties for time-averaged population imbalance
depending on initial conditions, effective nonlinear parameter of atomic medium
and kinetic energy of low-branch polaritons.Comment: 10 pages, 6 postscript figures, uses svjour.cl
Linear optics substituting scheme for multi-mode operations
We propose a scheme allowing a conditional implementation of suitably
truncated general single- or multi-mode operators acting on states of traveling
optical signal modes. The scheme solely relies on single-photon and coherent
states and applies beam splitters and zero- and single-photon detections. The
signal flow of the setup resembles that of a multi-mode quantum teleportation
scheme thus allowing the individual signal modes to be spatially separated from
each other. Some examples such as the realization of cross-Kerr nonlinearities,
multi-mode mirrors, and the preparation of multi-photon entangled states are
considered.Comment: 11 pages, 4 eps-figures, using revtex
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Non-holonomic Quantum Devices
NoWe analyze the possibility and efficiency of nonholonomic control over quantum devices with exponentially large number of Hilbert space dimensions. We show that completely controllable devices of this type can be assembled from elementary units of arbitrary physical nature, and can be employed efficiently for universal quantum computations and simulation of quantum-field dynamics. As an example we describe a toy device that can perform Toffoli-gate transformations and discrete Fourier transform on 9 qubits
Fractal growth in the presence of a surface force field
We numerically simulate the dynamics of atomic clusters aggregation deposited on a
surface interacting with the growing island. We make use of the well-known DLA model but
replace the underlying diffusion equation by the Smoluchowski equation which results in a
drifted DLA model and anisotropic jump probabilities. The shape of the structures
resulting from their aggregation-limited random walk is affected by the presence of a
Laplacian potential due to, for instance, the surface stress field. We characterize the
morphologies we obtain by their Hausdorff fractal dimension as well as the so-called
external fractal dimension. We compare our results to previously published experimental
results for antimony and silver clusters deposited onto graphite surface
NATO Advanced Research Workshop on Decoherence, Entanglement and Information Protection in Complex Quantum Systems
This book is a collection of articles on the contemporary status of quantum mechanics, dedicated to the fundamental issues of entanglement, decoherence, irreversibility, information processing, and control of quantum evolution, with a view of possible applications. It has multidisciplinary character and is addressed at a broad readership in physics, computer science, chemistry, and electrical engineering. It is written by the world-leading experts in pertinent fields such as quantum computing, atomic, molecular and optical physics, condensed matter physics, and statistical physics
Coherence protection by the quantum Zeno effect and nonholonomic control in a Rydberg rubidium isotope.
NoThe protection of the coherence of open quantum systems against the influence of their environment is a very topical issue. A scheme is proposed here which protects a general quantum system from the action of a set of arbitrary uncontrolled unitary evolutions. This method draws its inspiration from ideas of standard error-correction (ancilla adding, coding and decoding) and the Quantum Zeno Effect. A pedagogical demonstration of our method on a simple atomic system, namely a Rubidium isotope, is proposed