Multidimensional quantum solitons with nondegenerate parametric interactions: Photonic and Bose-Einstein condensate environments

We consider the quantum theory of three fields interacting via parametric and repulsive quartic couplings. This can be applied to treat photonic chi((2)) and chi((3)) interactions, and interactions in atomic Bose-Einstein condensates or quantum Fermi gases, describing coherent molecule formation together with a-wave scattering. The simplest two-particle quantum solitons or bound-state solutions of the idealized Hamiltonian, without a momentum cutoff, are obtained exactly. They have a pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. We show that the solutions can be regularized with a momentum cutoff. The parametric quantum solitons have much more realistic length scales and binding energies than chi((3)) quantum solitons, and the resulting effects could potentially be experimentally tested in highly nonlinear optical parametric media or interacting matter-wave systems. N-particle quantum solitons and the ground state energy are analyzed using a variational approach. Applications to atomic/molecular Bose-Einstein condensates (BEC's) are given, where we predict the possibility of forming coupled BEC solitons in three space dimensions, and analyze superchemistry dynamics.

Computational chemistry on Fujitsu vector-parallel processors: Development and performance of applications software

In this and a preceding paper, we provide an introduction to the Fujitsu VPP range of vector-parallel supercomputers and to some of the computational chemistry software available for the VPP. Here, we consider the implementation and performance of seven popular chemistry application packages. The codes discussed range from classical molecular dynamics to semiempirical and ab initio quantum chemistry. All have evolved from sequential codes, and have typically been parallelised using a replicated data approach. As such they are well suited to the large-memory/fast-processor architecture of the VPP. For one code, CASTEP, a distributed-memory data-driven parallelisation scheme is presented. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

Atoms in an amplitude-modulated standing wave - dynamics and pathways to quantum chaos

Cold rubidium atoms are subjected to an amplitude-modulated far-detuned standing wave of light to form a quantum-driven pendulum. Here we discuss the dynamics of these atoms. Phase space resonances and chaotic transients of the system exhibit dynamics which can be useful in many atom optics applications as they can be utilized as means for phase space state preparation. We explain the occurrence of distinct peaks in the atomic momentum distribution, analyse them in detail and give evidence for the importance of the system for quantum chaos and decoherence studies.

Dynamics of trapped Bose-Einstein condensates: Beyond the mean-field

Since dilute Bose gas condensates were first experimentally produced, the Gross-Pitaevskii equation has been successfully used as a descriptive tool. As a mean-field equation, it cannot by definition predict anything about the many-body quantum statistics of condensate. We show here that there are a class of dynamical systems where it cannot even make successful predictions about the mean-field behavior, starting with the process of evaporative cooling by which condensates are formed. Among others are parametric processes, such as photoassociation and dissociation of atomic and molecular condensates.

Anharmonic effects on a phonon-number measurement of a quantum-mesoscopic-mechanical oscillator

We generalize a proposal for detecting single-phonon transitions in a single nanoelectromechanical system (NEMS) to include the intrinsic anharmonicity of each mechanical oscillator. In this scheme two NEMS oscillators are coupled via a term quadratic in the amplitude of oscillation for each oscillator. One NEMS oscillator is driven and strongly damped and becomes a transducer for phonon number in the other measured oscillator. We derive the conditions for this measurement scheme to be quantum limited and find a condition on the size of the anharmonicity. We also derive the relation between the phase diffusion back-action noise due to number measurement and the localization time for the measured system to enter a phonon-number eigenstate. We relate both these time scales to the strength of the measured signal, which is an induced current proportional to the position of the read-out oscillator.

Characterization of optically driven fluid stress fields with optical tweezers

We present a controlled stress microviscometer with applications to complex fluids. It generates and measures microscopic fluid velocity fields, based on dual beam optical tweezers. This allows an investigation of bulk viscous properties and local inhomogeneities at the probe particle surface. The accuracy of the method is demonstrated in water. In a complex fluid model (hyaluronic acid), we observe a strong deviation of the flow field from classical behavior. Knowledge of the deviation together with an optical torque measurement is used to determine the bulk viscosity. Furthermore, we model the observed deviation and derive microscopic parameters.

Resonance fluorescence and Autler-Townes spectra of a two-level atom driven by two fields of equal frequencies

We study the effects of driving a two-level atom by two intense field modes that have equal frequencies but are otherwise distinguishable; the intensity of one mode is also assumed to be greater than that of the other. We calculate first the dressed states of the system, and then its resonance fluorescence and Autler-Townes absorption spectra. We find that the energy spectrum of the doubly dressed atom consists of a ladder of doublet continua. These continua manifest themselves in the fluorescence spectrum, where they produce continua at the positions of the Mellow sideband frequencies omega(L)+/-2 Omega of the strong field, and in the Autler-Townes absorption spectrum, which becomes a two-continuum doublet.

Classical and quantum signatures of competing chi((2)) nonlinearities

We report the observation of the quantum effects of competing chi((2)) nonlinearities. We also report classical signatures of competition, namely, clamping of the second-harmonic power and production of nondegenerate frequencies in the visible. Theory is presented that describes the observations as resulting from competition between various chi((2)) up-conversion and down-conversion processes. We show that competition imposes hitherto unsuspected limits to both power generation and squeezing. The observed signatures are expected to be significant effects in practical systems.

Quantum signatures of chaos in the dynamics of a trapped ion

We show how a nonlinear chaotic system, the parametrically kicked nonlinear oscillator, may be realized in the dynamics of a trapped, laser-cooled ion, interacting with a sequence of standing-wave pulses. Unlike the original optical scheme [G. J. Milburn and C.A. Holmes, Phys. Rev. A 44, 4704 (1991)], the trapped ion enables strongly quantum dynamics with minimal dissipation. This should permit an experimental test of one of the quantum signatures of chaos: irregular collapse and revival dynamics of the average vibrational energy.

Simulations of thermal Bose fields in the classical limit

We demonstrate that the time-dependent projected Gross-Pitaevskii equation (GPE) derived earlier [M. J. Davis, R. J. Ballagh, and K. Burnett, J. Phys. B 34, 4487 (2001)] can represent the highly occupied modes of a homogeneous, partially-condensed Bose gas. Contrary to the often held belief that the GPE is valid only at zero temperature, we find that this equation will evolve randomized initial wave functions to a state describing thermal equilibrium. In the case of small interaction strengths or low temperatures, our numerical results can be compared to the predictions of Bogoliubov theory and its perturbative extensions. This demonstrates the validity of the GPE in these limits and allows us to assign a temperature to the simulations unambiguously. However, the GPE method is nonperturbative, and we believe it can be used to describe the thermal properties of a Bose gas even when Bogoliubov theory fails. We suggest a different technique to measure the temperature of our simulations in these circumstances. Using this approach we determine the dependence of the condensate fraction and specific heat on temperature for several interaction strengths, and observe the appearance of vortex networks. Interesting behavior near the critical point is observed and discussed.

Quantum dynamics of two coupled qubits

We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the initial state. The difference appears as nonpositive-definite diffusion terms in the quantum evolution equation of an appropriate positive phase-space probability density. Thus, it is not possible to express the dynamics in terms of a convolution of a positive transition probability function and the initial condition as can be done in the classical case. It is this feature that enables the quantum system to evolve to an entangled state. We conclude that the dynamics are a quantum element of nuclear magnetic resonance quantum-information processing. There are two limits where our quantum evolution coincides with the classical one: the short-time limit before spin-spin interaction sets in and the long-time limit when phase diffusion is incorporated.

Comparative study of power converter topologies and control strategies for the harmonic performance of variable-speed wind turbine generator systems

Power converters play a vital role in the integration of wind power into the electrical grid. Variable-speed wind turbine generator systems have a considerable interest of application for grid connection at constant frequency. In this paper, comprehensive simulation studies are carried out with three power converter topologies: matrix, two-level and multilevel. A fractional-order control strategy is studied for the variable-speed operation of wind turbine generator systems. The studies are in order to compare power converter topologies and control strategies. The studies reveal that the multilevel converter and the proposed fractional-order control strategy enable an improvement in the power quality, in comparison with the other power converters using a classical integer-order control strategy. (C) 2010 Elsevier Ltd. All rights reserved.

Assessment of data-driven modeling strategies for water delivery canals

The aim of this paper is to develop models for experimental open-channel water delivery systems and assess the use of three data-driven modeling tools toward that end. Water delivery canals are nonlinear dynamical systems and thus should be modeled to meet given operational requirements while capturing all relevant dynamics, including transport delays. Typically, the derivation of first principle models for open-channel systems is based on the use of Saint-Venant equations for shallow water, which is a time-consuming task and demands for specific expertise. The present paper proposes and assesses the use of three data-driven modeling tools: artificial neural networks, composite local linear models and fuzzy systems. The canal from Hydraulics and Canal Control Nucleus (A parts per thousand vora University, Portugal) will be used as a benchmark: The models are identified using data collected from the experimental facility, and then their performances are assessed based on suitable validation criterion. The performance of all models is compared among each other and against the experimental data to show the effectiveness of such tools to capture all significant dynamics within the canal system and, therefore, provide accurate nonlinear models that can be used for simulation or control. The models are available upon request to the authors.

Symbolic fractional dynamics

Fractional dynamics reveals long range memory properties of systems described by means of signals represented by real numbers. Alternatively, dynamical systems and signals can adopt a representation where states are quantified using a set of symbols. Such signals occur both in nature and in man made processes and have the potential of a aftermath as relevant as the classical counterpart. This paper explores the association of Fractional calculus and symbolic dynamics. The results are visualized by means of the multidimensional technique and reveal the association between the fractal dimension and one definition of fractional derivative.

Complex dynamics of financial indices

This paper presents a novel method for the analysis of nonlinear financial and economic systems. The modeling approach integrates the classical concepts of state space representation and time series regression. The analytical and numerical scheme leads to a parameter space representation that constitutes a valid alternative to represent the dynamical behavior. The results reveal that business cycles can be clearly revealed, while the noise effects common in financial indices can elegantly be filtered out of the results.