556 research outputs found
Breakdown of adiabatic transfer of light in waveguides in the presence of absorption
In atomic physics, adiabatic evolution is often used to achieve a robust and
efficient population transfer. Many adiabatic schemes have also been
implemented in optical waveguide structures. Recently there has been increasing
interests in the influence of decay and absorption, and their engineering
applications. Here it is shown that even a small decay can significantly
influence the dynamical behaviour of a system, above and beyond a mere change
of the overall norm. In particular, a small decay can lead to a breakdown of
adiabatic transfer schemes, even when both the spectrum and the eigenfunctions
are only sightly modified. This is demonstrated for the generalization of a
STIRAP scheme that has recently been implemented in optical waveguide
structures. Here the question how an additional absorption in either the
initial or the target waveguide influences the transfer property of the scheme
is addressed. It is found that the scheme breaks down for small values of the
absorption at a relatively sharp threshold, which can be estimated by simple
analytical arguments.Comment: 8 pages, 7 figures, revised and extende
Calculations of time-dependent observables in non-Hermitian quantum mechanics: The problem and a possible solution
The solutions of the time independent Schrodinger equation for non-Hermitian
(NH) Hamiltonians have been extensively studied and calculated in many
different fields of physics by using L^2 methods that originally have been
developed for the calculations of bound states. The existing non-Hermitian
formalism breaks down when dealing with wavepackets(WP). An open question is
how time dependent expectation values can be calculated when the Hamiltonian is
NH ? Using the F-product formalism, which was recently proposed, [J. Phys.
Chem., 107, 7181 (2003)] we calculate the time dependent expectation values of
different observable quantities for a simple well known study test case model
Hamiltonian. We carry out a comparison between these results with those
obtained from conventional(i.e., Hermitian) quantum mechanics (QM)
calculations. The remarkable agreement between these results emphasizes the
fact that in the NH-QM, unlike standard QM, there is no need to split the
entire space into two regions; i.e., the interaction region and its
surrounding. Our results open a door for a type of WP propagation calculations
within the NH-QM formalism that until now were impossible.Comment: 20 pages, 5 Postscript figures. To be Published in Physical Review
Infinite matrices may violate the associative law
The momentum operator for a particle in a box is represented by an infinite
order Hermitian matrix . Its square is well defined (and diagonal),
but its cube is ill defined, because . Truncating these
matrices to a finite order restores the associative law, but leads to other
curious results.Comment: final version in J. Phys. A28 (1995) 1765-177
Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime
We study the transmission through different small systems as a function of
the coupling strength to the two attached leads. The leads are identical
with only one propagating mode in each of them. Besides the
conductance , we calculate the phase rigidity of the scattering wave
function in the interior of the system. Most interesting results are
obtained in the regime of strongly overlapping resonance states where the
crossover from staying to traveling modes takes place. The crossover is
characterized by collective effects. Here, the conductance is plateau-like
enhanced in some energy regions of finite length while corridors with zero
transmission (total reflection) appear in other energy regions. This
transmission picture depends only weakly on the spectrum of the closed system.
It is caused by the alignment of some resonance states of the system with the
propagating modes in the leads. The alignment of resonance states
takes place stepwise by resonance trapping, i.e. it is accompanied by the
decoupling of other resonance states from the continuum of propagating modes.
This process is quantitatively described by the phase rigidity of the
scattering wave function. Averaged over energy in the considered energy window,
is correlated with . In the regime of strong coupling, only two
short-lived resonance states survive each aligned with one of the channel wave
functions . They may be identified with traveling modes through the
system. The remaining trapped narrow resonance states are well separated
from one another.Comment: Resonance trapping mechanism explained in the captions of Figs. 7 to
11. Recent papers added in the list of reference
Calculating resonance positions and widths using the Siegert approximation method
Here we present complex resonance states (or Siegert states), that describe
the tunneling decay of a trapped quantum particle, from an intuitive point of
view which naturally leads to the easily applicable Siegert approximation
method that can be used for analytical and numerical calculations of complex
resonances of both the linear and nonlinear Schr\"odinger equation. Our
approach thus complements other treatments of the subject that mostly focus on
methods based on continuation in the complex plane or on semiclassical
approximations.Comment: 15 pages, 1 figure, contains MATLAB source code; new version with
additional illustration
Spectral Properties and Lifetimes of Neutral Spin-1/2-Fermions in a Magnetic Guide
We investigate the resonant motion of neutral spin-1/2-fermions in a magnetic
guide. A wealth of unitary and anti-unitary symmetries is revealed in
particular giving rise to a two-fold degeneracy of the energy levels. To
compute the energies and decay widths of a large number of resonances the
complex scaling method is employed. We discuss the dependence of the lifetimes
on the angular momentum of the resonance states. In this context the existence
of so-called quasi-bound states is shown. In order to approximately calculate
the resonance energies of such states a radial Schr\"odinger equation is
derived which improves the well-known adiabatic approximation. The effects of
an additionally applied homogeneous Ioffe field on the resonance energies and
decay widths are also considered. The results are applied to the case of the
atom in the hyperfine ground state.Comment: accepted for publication in PR
Use of computers to exclude the influence of radiometer instability upon measurement results
A radiometer, practically insensitive to great fluctuations in the equipment amplification coefficient, was developed by dividing the useful signal by a reference signal and modulating the two signals at different frequencies. The signals are simultaneously separated by corresponding synchronous detectors and recorded over two channels. The operation is simplified by replacing the continuous signals by a sampling of discrete values, and using a digital computer. The four steps involved in the process are described and a block diagram is included. This technique not only directly connects the radiometer with the computer, but also records all data provided by the control and signal channels
Calculation of the Density of States Using Discrete Variable Representation and Toeplitz Matrices
A direct and exact method for calculating the density of states for systems
with localized potentials is presented. The method is based on explicit
inversion of the operator . The operator is written in the discrete
variable representation of the Hamiltonian, and the Toeplitz property of the
asymptotic part of the obtained {\it infinite} matrix is used. Thus, the
problem is reduced to the inversion of a {\it finite} matrix
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