1,616 research outputs found
Resonant Geometric Phases for Soliton Equations
The goal of the present paper is to introduce a multidimensional generalization of asymptotic reduction given in a paper by Alber and Marsden [1992], to use this to obtain a new class of solutions that we call resonant solitons, and to study the corresponding geometric phases. The term "resonant solitons" is used because those solutions correspond to a spectrum with multiple points, and they also represent a dividing solution between two different types of solitons. In this sense, these new solutions are degenerate and, as such, will be considered as singular points in the moduli space of solitons
On Soliton-type Solutions of Equations Associated with N-component Systems
The algebraic geometric approach to -component systems of nonlinear
integrable PDE's is used to obtain and analyze explicit solutions of the
coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to
anti-kink transitions and multi-peaked soliton solutions is carried out.
Transformations are used to connect these solutions to several other equations
that model physical phenomena in fluid dynamics and nonlinear optics.Comment: 43 pages, 16 figure
Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians
The algebraic-geometric approach is extended to study solutions of
N-component systems associated with the energy dependent Schrodinger operators
having potentials with poles in the spectral parameter, in connection with
Hamiltonian flows on nonlinear subvariaties of Jacobi varieties. The systems
under study include the shallow water equation and Dym type equation. The
classes of solutions are described in terms of theta-functions and their
singular limits by using new parameterizations. A qualitative description of
real valued solutions is provided
Antisymmetric multi-partite quantum states and their applications
Entanglement is a powerful resource for processing quantum information. In
this context pure, maximally entangled states have received considerable
attention. In the case of bipartite qubit-systems the four orthonormal
Bell-states are of this type. One of these Bell states, the singlet Bell-state,
has the additional property of being antisymmetric with respect to particle
exchange. In this contribution we discuss possible generalizations of this
antisymmetric Bell-state to cases with more than two particles and with
single-particle Hilbert spaces involving more than two dimensions. We review
basic properties of these totally antisymmetric states. Among possible
applications of this class of states we analyze a new quantum key sharing
protocol and methods for comparing quantum states
Geometric analysis of optical frequency conversion and its control in quadratic nonlinear media
We analyze frequency conversion and its control among three light waves using a geometric approach that enables the dynamics of the waves to be visualized on a closed surface in three dimensions. It extends the analysis based on the undepleted-pump linearization and provides a simple way to understand the fully nonlinear dynamics. The Poincaré sphere has been used in the same way to visualize polarization dynamics. A geometric understanding of control strategies that enhance energy transfer among interacting waves is introduced, and the quasi-phase-matching strategy that uses microstructured quadratic materials is illustrated in this setting for both type I and II second-harmonic generation and for parametric three-wave interactions
Error tolerance of two-basis quantum key-distribution protocols using qudits and two-way classical communication
We investigate the error tolerance of quantum cryptographic protocols using
-level systems. In particular, we focus on prepare-and-measure schemes that
use two mutually unbiased bases and a key-distillation procedure with two-way
classical communication. For arbitrary quantum channels, we obtain a sufficient
condition for secret-key distillation which, in the case of isotropic quantum
channels, yields an analytic expression for the maximally tolerable error rate
of the cryptographic protocols under consideration. The difference between the
tolerable error rate and its theoretical upper bound tends slowly to zero for
sufficiently large dimensions of the information carriers.Comment: 10 pages, 1 figur
Controlling quantum systems by embedded dynamical decoupling schemes
A dynamical decoupling method is presented which is based on embedding a
deterministic decoupling scheme into a stochastic one. This way it is possible
to combine the advantages of both methods and to increase the suppression of
undesired perturbations of quantum systems significantly even for long
interaction times. As a first application the stabilization of a quantum memory
is discussed which is perturbed by one-and two-qubit interactions
Photon-assisted entanglement creation by minimum-error generalized quantum measurements in the strong coupling regime
We explore possibilities of entangling two distant material qubits with the
help of an optical radiation field in the regime of strong quantum
electrodynamical coupling with almost resonant interaction. For this purpose
the optimum generalized field measurements are determined which are capable of
preparing a two-qubit Bell state by postselection with minimum error. It is
demonstrated that in the strong-coupling regime some of the recently found
limitations of the non-resonant weak-coupling regime can be circumvented
successfully due to characteristic quantum electrodynamical quantum
interference effects. In particular, in the absence of photon loss it is
possible to postselect two-qubit Bell states with fidelities close to unity by
a proper choice of the relevant interaction time. Even in the presence of
photon loss this strong-coupling regime offers interesting perspectives for
creating spatially well-separated Bell pairs with high fidelities, high success
probabilities, and high repetition rates which are relevant for future
realizations of quantum repeaters.Comment: 14 pages, 12 figure
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