301 research outputs found
Vibration Induced Non-adiabatic Geometric Phase and Energy Uncertainty of Fermions in Graphene
We investigate geometric phase of fermion states under relative vibrations of
two sublattices in graphene by solving time-dependent Sch\"{o}dinger equation
using Floquet scheme. In a period of vibration the fermions acquire different
geometric phases depending on their momenta. There are two regions in the
momentum space: the adiabatic region where the geometric phase can be
approximated by the Berry phase and the chaotic region where the geometric
phase drastically fluctuates in changing parameters. The energy of fermions due
to vibrations shows spikes in the chaotic region. The results suggest a
possible dephasing mechanism which may cause classical-like transport
properties in graphene.Comment: 9 pages, 5 figure
Localization of quantum wave packets
We study the semiclassical propagation of squeezed Gau{\ss}ian states. We do
so by considering the propagation theorem introduced by Combescure and Robert
\cite{CR97} approximating the evolution generated by the Weyl-quantization of
symbols . We examine the particular case when the Hessian
evaluated at the corresponding solution of
Hamilton's equations of motion is periodic in time. Under this assumption, we
show that the width of the wave packet can remain small up to the Ehrenfest
time. We also determine conditions for ``classical revivals'' in that case.
More generally, we may define recurrences of the initial width. Some of these
results include the case of unbounded classical motion. In the classically
unstable case we recover an exponential spreading of the wave packet as in
\cite{CR97}
Rigorous derivation of coherent resonant tunneling time and velocity in finite periodic systems
The velocity of resonant tunneling electrons in finite periodic
structures is analytically calculated in two ways. The first method is based on
the fact that a transmission of unity leads to a coincidence of all still
competing tunneling time definitions. Thus, having an indisputable resonant
tunneling time we apply the natural definition
to calculate the velocity. For the second method we
combine Bloch's theorem with the transfer matrix approach to decompose the wave
function into two Bloch waves. Then the expectation value of the velocity is
calculated. Both different approaches lead to the same result, showing their
physical equivalence. The obtained resonant tunneling velocity is
smaller or equal to the group velocity times the magnitude of the complex
transmission amplitude of the unit cell. Only at energies where the unit cell
of the periodic structure has a transmission of unity equals the
group velocity. Numerical calculations for a GaAs/AlGaAs superlattice are
performed. For typical parameters the resonant velocity is below one third of
the group velocity.Comment: 12 pages, 3 figures, LaTe
Light propagation through closed-loop atomic media beyond the multiphoton resonance condition
The light propagation of a probe field pulse in a four-level double-lambda
type system driven by laser fields that form a closed interaction loop is
studied. Due to the finite frequency width of the probe pulse, a
time-independent analysis relying on the multiphoton resonance assumption is
insufficient. Thus we apply a Floquet decomposition of the equations of motion
to solve the time-dependent problem beyond the multiphoton resonance condition.
We find that the various Floquet components can be interpreted in terms of
different scattering processes, and that the medium response oscillating in
phase with the probe field in general is not phase-dependent. The phase
dependence arises from a scattering of the coupling fields into the probe field
mode at a frequency which in general differs from the probe field frequency. We
thus conclude that in particular for short pulses with a large frequency width,
inducing a closed loop interaction contour may not be advantageous, since
otherwise the phase-dependent medium response may lead to a distortion of the
pulse shape. Finally, using our time-dependent analysis, we demonstrate that
both the closed-loop and the non-closed loop configuration allow for sub- and
superluminal light propagation with small absorption or even gain. Further, we
identify one of the coupling field Rabi frequencies as a control parameter that
allows to conveniently switch between sub- and superluminal light propagation.Comment: 10 pages, 8 figure
Non-Abelian Geometric Phase, Floquet Theory, and Periodic Dynamical Invariants
For a periodic Hamiltonian, periodic dynamical invariants may be used to
obtain non-degenerate cyclic states. This observation is generalized to the
degenerate cyclic states, and the relation between the periodic dynamical
invariants and the Floquet decompositions of the time-evolution operator is
elucidated. In particular, a necessary condition for the occurrence of cyclic
non-adiabatic non-Abelian geometrical phase is derived. Degenerate cyclic
states are obtained for a magnetic dipole interacting with a precessing
magnetic field.Comment: Plain LaTeX, 13 pages, accepted for publication in J. Phys. A: Math.
Ge
One-Dimensional Kronig-Penney Model with Positional Disorder: Theory versus Experiment
We study the effects of random positional disorder in the transmission of
waves in a 1D Kronig-Penny model. For weak disorder we derive an analytical
expression for the localization length and relate it to the transmission
coefficient for finite samples. The obtained results describe very well the
experimental frequency dependence of the transmission in a microwave
realization of the model. Our results can be applied both to photonic crystals
and semiconductor super lattices.Comment: 9 pages, 6 figure
Entanglement between photons and atoms coupled out from a Bose-Einstein-Condensate
We study the limitations to the relative number squeezing between photons and
atoms coupled out from a homogeneous Bose-Einstein-Condensate. We consider the
coupling between the translational atomic states by two photon Bragg processes,
with one of the photon modes involved in the Bragg process in a coherent state,
and the other initially unpopulated. We start with an interacting Bose-
condensate at zero temperature and compute the time evolution for the system.
We study the squeezing, i.e. the variance of the occupation number difference
between the second photon and the atomic c.m. mode. We discuss how collisions
between the atoms and photon rescattering affect the degree of squeezing which
may be reached in such experiments.Comment: 4 pages RevTeX, 3 figure
Frequency Dependence of Quantum Localization in a Periodically Driven System
We study the quantum localization phenomena for a random matrix model
belonging to the Gaussian orthogonal ensemble (GOE). An oscillating external
field is applied on the system. After the transient time evolution, energy is
saturated to various values depending on the frequencies. We investigate the
frequency dependence of the saturated energy. This dependence cannot be
explained by a naive picture of successive independent Landau-Zener transitions
at avoided level crossing points. The effect of quantum interference is
essential. We define the number of Floquet states which have large overlap with
the initial state, and calculate its frequency dependence. The number of
Floquet states shows approximately linear dependence on the frequency, when the
frequency is small. Comparing the localization length in Floquet states and
that in energy states from the viewpoint of the Anderson localization, we
conclude that the Landau-Zener picture works for the local transition processes
between levels.Comment: 12 pages and 6 figure
Single electron quantum tomography in quantum Hall edge channels
We propose a quantum tomography protocol to measure single electron coherence
in quantum Hall edge channels and therefore access for the first time the wave
function of single electron excitations propagating in ballistic quantum
conductors. Its implementation would open the way to quantitative studies of
single electron decoherence and would provide a quantitative tool for analyzing
single to few electron sources. We show how this protocol could be implemented
using ultrahigh sensitivity noise measurement schemes.Comment: Version 3: long version (7 figures): corrections performed and
references have been added. Figures reprocessed for better readabilit
Reduced Bloch mode expansion for periodic media band structure calculations
Reduced Bloch mode expansion is presented for fast periodic media band
structure calculations. The expansion employs a natural basis composed of a
selected reduced set of Bloch eigenfunctions. The reduced basis is selected
within the irreducible Brillouin zone at high symmetry points determined by the
medium's crystal structure and group theory (and possibly at additional related
points). At each of the reciprocal lattice selection points, a number of Bloch
eigenfunctions are selected up to the frequency range of interest for the band
structure calculations. Since it is common to initially discretize the periodic
unit cell and solution field using some choice of basis, reduced Bloch mode
expansion is practically a secondary expansion that uses a selected set of
Bloch eigenvectors. Such expansion therefore keeps, and builds on, any
favorable attributes a primary expansion approach might exhibit. Being in line
with the well known concept of modal analysis, the proposed approach maintains
accuracy while reducing the computation time by up to two orders of magnitudes
or more depending on the size and extent of the calculations. Results are
presented for phononic, photonic and electronic band structures.Comment: 15 pages of text, 8 figures, submitted for journal publication, minor
edits and correction of typo
- …