Bistability in sine-Gordon: the ideal switch

The sine-Gordon equation, used as the representative nonlinear wave equation, presents a bistable behavior resulting from nonlinearity and generating hysteresis properties. We show that the process can be understood in a comprehensive analytical formulation and that it is a generic property of nonlinear systems possessing a natural band gap. The approach allows to discover that sine-Gordon can work as an it ideal switch by reaching a transmissive regime with vanishing driving amplitude.Comment: Phys. Rev. E, (to be published, May 2005

Bistable light detectors with nonlinear waveguide arrays

Bistability induced by nonlinear Kerr effect in arrays of coupled waveguides is studied and shown to be a means to conceive light detectors that switch under excitation by a weak signal. The detector is obtained by coupling two single 1D waveguide to an array of coupled waveguides with adjusted indices and coupling. The process is understood by analytical description in the conservative and continuous case and illustrated by numerical simulations of the model with attenuation.Comment: Phys. Rev. Lett., v.94, (2005, to be published

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

Topological structures of adiabatic phase for multi-level quantum systems

The topological properties of adiabatic gauge fields for multi-level (three-level in particular) quantum systems are studied in detail. Similar to the result that the adiabatic gauge field for SU(2) systems (e.g. two-level quantum system or angular momentum systems, etc) have a monopole structure, the curvature two-forms of the adiabatic holonomies for SU(3) three-level and SU(3) eight-level quantum systems are shown to have monopole-like (for all levels) or instanton-like (for the degenerate levels) structures.Comment: 15 pages, no figures. Accepted by J.Phys.

Another Leigh-Strassler deformation through the Matrix model

In here the matrix model approach, by Dijkgraaf and Vafa, is used in order to obtain the effective superpotential for a certain deformation of N=4 SYM discovered by Leigh and Strassler. An exact solution to the matrix model Lagrangian is found and is expressed in terms of elliptic functions.Comment: 15 pages,2 figure

Finite-level systems, Hermitian operators, isometries, and a novel parameterization of Stiefel and Grassmann manifolds

In this paper we obtain a description of the Hermitian operators acting on the Hilbert space \C^n, description which gives a complete solution to the over parameterization problem. More precisely we provide an explicit parameterization of arbitrary $n$-dimensional operators, operators that may be considered either as Hamiltonians, or density matrices for finite-level quantum systems. It is shown that the spectral multiplicities are encoded in a flag unitary matrix obtained as an ordered product of special unitary matrices, each one generated by a complex $n-k$-dimensional unit vector, $k=0,1,...,n-2$. As a byproduct, an alternative and simple parameterization of Stiefel and Grassmann manifolds is obtained.Comment: 21 page

Unification of Dynamical Decoupling and the Quantum Zeno Effect

We unify the quantum Zeno effect (QZE) and the "bang-bang" (BB) decoupling method for suppressing decoherence in open quantum systems: in both cases strong coupling to an external system or apparatus induces a dynamical superselection rule that partitions the open system's Hilbert space into quantum Zeno subspaces. Our unification makes use of von Neumann's ergodic theorem and avoids making any of the symmetry assumptions usually made in discussions of BB. Thus we are able to generalize BB to arbitrary fast and strong pulse sequences, requiring no symmetry, and to show the existence of two alternatives to pulsed BB: continuous decoupling, and pulsed measurements. Our unified treatment enables us to derive limits on the efficacy of the BB method: we explicitly show that the inverse QZE implies that BB can in some cases accelerate, rather than inhibit, decoherence.Comment: 6 pages. To appear in Phys. Rev.

Polynomial-Time Simulation of Pairing Models on a Quantum Computer

We propose a polynomial-time algorithm for simulation of the class of pairing Hamiltonians, e.g., the BCS Hamiltonian, on an NMR quantum computer. The algorithm adiabatically finds the low-lying spectrum in the vicinity of the gap between ground and first excited states, and provides a test of the applicability of the BCS Hamiltonian to mesoscopic superconducting systems, such as ultra-small metallic grains.Comment: 5 pages, RevTeX, Latest, modified version to appear in Phys. Rev. Let

Soliton surfaces associated with symmetries of ODEs written in Lax representation

The main aim of this paper is to discuss recent results on the adaptation of the Fokas-Gel'fand procedure for constructing soliton surfaces in Lie algebras, which was originally derived for PDEs [Grundland, Post 2011], to the case of integrable ODEs admitting Lax representations. We give explicit forms of the \g-valued immersion functions based on conformal symmetries involving the spectral parameter, a gauge transformation of the wave function and generalized symmetries of the linear spectral problem. The procedure is applied to a symmetry reduction of the static $\phi^4$-field equations leading to the Jacobian elliptic equation. As examples, we obtain diverse types of surfaces for different choices of Jacobian elliptic functions for a range of values of parameters.Comment: 14 Pages, 2 figures Conference Proceedings for QST7 Pragu