Showing papers on "Superposition principle published in 2003"

Quantum computation with optical coherent states

Abstract: We show that quantum computation circuits using coherent states as the logical qubits can be constructed from simple linear networks, conditional photon measurements, and "small" coherent superposition resource states.

Improved recursive algorithm for light scattering by a multilayered sphere.

Abstract: An improved recurrence algorithm to calculate the scattering field of a multilayered sphere is developed. The internal and external electromagnetic fields are expressed as a superposition of inward and outward waves. The alternative yet equivalent expansions of fields are proposed by use of the first kind of Bessel function and the first kind of Hankel function instead of the first and the second kinds of Bessel function. The final recursive expressions are similar in form to those of Mie theory for a homogeneous sphere and are proved to be more concise and convenient than earlier forms. The new algorithm avoids the numerical difficulties, which give rise to significant errors encountered in practice by previous methods, especially for large, highly absorbing thin shells. Various calculations and tests show that this algorithm is efficient, numerically stable, and accurate for a large range of size parameters and refractive indices.

Nonlinear evolution of quantum states in the adiabatic regime.

Abstract: We investigate adiabatic evolution of quantum states as governed by the nonlinear Schrodinger equation and provide examples of applications with a nonlinear tunneling model for Bose-Einstein condensates. Our analysis not only spells out conditions for adiabatic evolution of eigenstates but also characterizes the motion of noneigenstates which cannot be obtained from the former in the absence of the superposition principle. We find that Aharonov-Anandan phases play the role of classical canonical actions and are conserved in the adiabatic evolution of noneigenstates.

Switched wave packets: a route to nonperturbative quantum control.

Abstract: The dynamic Stark effect due to a strong nonresonant but nonionizing laser field provides a route to quantum control via the creation of novel superposition states. We consider the creation of a field-free "switched" wave packet through adiabatic turn-on and sudden turn-off of a strong dynamic Stark interaction. There are two limiting cases for such wave packets. The first is a Raman-type coupling, illustrated by the creation of field-free molecular axis alignment. An experimental demonstration is given. The second case is that of dipole-type coupling, illustrated by the creation of charge localization in an array of quantum wells.

Coherent-mode decomposition of partially polarized, partially coherent sources.

Abstract: It is shown that any partially polarized, partially coherent source can be expressed in terms of a suitable superposition of transverse coherent modes with orthogonal polarization states. Such modes are determined through the solution of a system of two coupled integral equations. An example, for which the modal decomposition is obtained in closed form in terms of fully linearly polarized Hermite Gaussian modes, is given.

ULF wave identification in the magnetosheath: The k-filtering technique applied to Cluster II data

Abstract: The magnetic fluctuations in the magnetosheath are studied, thanks to Cluster II data. The k-filtering technique is applied to explore ULF magnetic fluctuations using STAFF (Spatio-Temporal Analysis of a Field Fluctuations) data. Based on multipoint measurements, the k-filtering technique allows, for the first time, to estimate the Magnetic Field Energy Distribution (MFED) in both the angular frequency and wave vector space. We show how the localisation of the magnetic energy in the (ω, k) domain can be used to identify the linear modes that can propagate in the magnetosheath. A comparison between k-filtering results and prediction of the linear theory is performed. For the frequencies examined the magnetic energy seems to be distributed over the low frequency modes: mirror, Alfven, and slow modes. Estimation of Doppler shift shows that each frequency observed is the superposition of different frequencies in the plasma frame. This ``mixture of modes'' at a given observed frequency explains why the fluctuations are generally not observed to be polarized, as shown in previous studies. Some other implications on a weak turbulence approach of the magnetic fluctuations in the magnetosheath are discussed.

Oblique frozen modes in periodic layered media.

Abstract: We study the classical scattering problem of a plane electromagnetic wave incident on the surface of semi-infinite periodic stratified media incorporating anisotropic dielectric layers with special oblique orientation of the anisotropy axes. We demonstrate that an obliquely incident light, upon entering the periodic slab, gets converted into an abnormal grazing mode with huge amplitude and zero normal component of the group velocity. This mode cannot be represented as a superposition of extended and evanescent contributions. Instead, it is related to a general (non-Bloch) Floquet eigenmode with the amplitude diverging linearly with the distance from the slab boundary. Remarkably, the slab reflectivity in such a situation can be very low, which means an almost 100% conversion of the incident light into the axially frozen mode with the electromagnetic energy density exceeding that of the incident wave by several orders of magnitude. The effect can be realized at any desirable frequency, including optical and UV frequency range. The only essential physical requirement is the presence of dielectric layers with proper oblique orientation of the anisotropy axes. Some practical aspects of this phenomenon are considered.

The self-imaging phenomenon and its applications

Abstract: The self-imaging effect can be obtained as the result of the diffraction of a plane wave by the periodic structure. It is known as the Talbot effect. The self-imaging phenomenon is discussed here also from the new viewpoint as a class of the propagation-invariant wavefields. The repetition of an object can be achieved by the superposition of nondiffracting beams.

2D dynamic response of unlined and lined tunnels in poroelastic soil to harmonic body waves

Abstract: The problem of harmonic wave diffraction by tunnels in an infinite poroelastic saturated soil obeying Biot's theory is studied numerically under conditions of plane strain and the effect of poroelasticity on the response is assessed through some parametric studies. The method is based on the theory of Mei and Foda, which considers the total field to be approximated by the superposition of an elastodynamic problem with modified elastic constants and mass density for the whole domain and a diffusion problem for the pore fluid pressure confined to a boundary layer at the free boundaries. Both problems are solved numerically by the boundary element method in the frequency domain. Results dealing with the response of a circular tunnel with and without an elastic concrete liner in an infinite poroelastic medium to incident harmonic P and SV plane waves are provided and compared against analytical ones as well as to those corresponding to linear elastic soil behaviour. Copyright © 2002 John Wiley & Sons, Ltd.

Creation and Measurement of a Coherent Superposition of Quantum States

Abstract: We demonstrate experimental techniques for creating and measuring a coherent superposition of two degenerate atomic states with equal amplitudes in metastable neon. Starting from state (3)P(0), we create adiabatically a coherent superposition of the magnetic sublevels M=+/-1 of the state (3)P(2) using a tripod stimulated Raman adiabatic passage scheme. The measurement is based on the coupling of the levels (3)P(2) (3)P(1) by a linearly polarized laser, followed by the detection of the population in the (3)P(2)(M=+/-2) states as a function of the polarization angle of that laser.

Use of quadrupolar nuclei for quantum-information processing by nuclear magnetic resonance: Implementation of a quantum algorithm

Abstract: Physical implementation of quantum-information processing by liquid-state nuclear magnetic resonance, using weakly coupled spin- 1/2 nuclei of a molecule, is well established. Nuclei with spin.1/2 oriented in liquid-crystalline matrices is another possibility. Such systems have multiple qubits per nuclei and large quadrupolar couplings resulting in well separated lines in the spectrum. So far, creation of pseudopure states and logic gates has been demonstrated in such systems using transition selective radio-frequency pulses. In this paper we report two developments. First, we implement a quantum algorithm that needs coherent superposition of states. Second, we use evolution under quadrupolar coupling to implement multiqubit gates. We implement the Deutsch-Jozsa algorithm on a spin- 3/2 (2 qubit) system. The controlled-NOT operation needed to implement this algorithm has been implemented here by evolution under the quadrupolar Hamiltonian. To the best of our knowledge, this method has been implemented for the first time in quadrupolar systems. Since the quadrupolar coupling is several orders of magnitude greater than the coupling in weakly coupled spin- 1/2 nuclei, the gate time decreases, increasing the clock speed of the quantum computer.

Physical wavelets and their sources: real physics in complex spacetime

Abstract: A thorough review of acoustic and electromagnetic wavelets is given, including a first account of recent progress in understanding their sources. These physical wavelets, introduced in 1994, are families of 'small' solutions of the wave and Maxwell equations generated from a single member by group operations including translations, Lorentz transformations, and scaling. They are parametrized by complex spacetime points z = x − iy, where x gives the centre of their region of origin and y gives the extension and orientation of this region in spacetime. They are thus pulsed beams whose origin, direction and focus are all governed by z and which give, by superposition, 'wavelet representations' of acoustic and electromagnetic waves. Recently this idea has been developed substantially by the rigorous understanding of the source distributions required to launch and absorb the wavelets, defined as extended delta functions. The unexpected simplicity and complex structure of the sources in the Fourier domain suggests their potential use in the construction of fast algorithms for the analysis and synthesis of acoustic and electromagnetic waves. The review begins with a brief account of the physical wavelets associated with massive (Klein–Gordon and Dirac) fields, which are relativistic coherent states.

Brownian motion in confinement.

Abstract: This research modifies an earlier approach based on the single-wall reflection method to predict the perpendicular and parallel diffusion coefficients of a Brownian sphere in confinement. The modified version provides predictions that match experimental data reported in the literature more accurately than those provided by other available models, including the linear superposition approximation, the coherent superposition approximation, and Oseen's equation.

ac relaxation in silver vanadate glasses

Abstract: The frequency dependent ac conductivity of semiconducting silver vanadate glasses has been studied in the temperature range 87--423 K and in the frequency range 10 Hz--2 MHz. The experimental results have been analyzed with reference to various theoretical models based on quantum mechanical tunneling and classical barrier hopping. The analysis shows that the temperature dependence of the ac conductivity is consistent with the overlapping large polaron tunneling model at temperatures below 275 K in the measured frequency range. The frequency exponent data show a departure from the theoretically expected values above 275 K. A scaling of the conductivity spectra with respect to temperature is attempted for these glasses at high temperatures. It is observed that at temperatures above 275 K the conductivity spectra show a time-temperature superposition principle consistent with the temperature independence of the frequency exponent in this temperature region.

Some extensions of the Gaussian beam expansion: Radiation fields of the rectangular and the elliptical transducer

Abstract: A straightforward extension of Gaussian beam expansion is presented for calculation of the Fresnel field integral [J. J. Wen and M. A. Breazeale, J. Acoust. Soc. Am. 83, 1752–1756 (1988)]. The source distribution function is expanded into the superposition of a series of two-dimensional Gaussian functions. The corresponding radiation field is expressed as the superposition of these two-dimensional Gaussian beams and is then reduced to the computation of these simple functions. This treatment overcomes the limit that the shape of source is of circular axial-symmetry. The numerical examples are presented for the field of the (uniform) elliptical and the rectangular piston transducers and agree well with the results given by complicated computation.

Laser excitation of surface wave motion

Abstract: A simplified analysis of surface wave generation by laser irradiation of a homogeneous, isotropic, linearly elastic body is presented. The thermoelastic process of expansion of a surface element is examined, and a direct derivation of equivalent mechanical surface loading is presented. A novel representation of surface wave motion is given in terms of a single-wave potential for a carrier wave propagating on the free surface. Finally, for time-harmonic laser irradiation the elastodynamic reciprocity theorem is used to relate the generated surface wave motion to a virtual surface wave, which leads to a straightforward analytical determination of the generated surface waves for the cases of laser line- and point-focused illumination. The surface-wave pulses for pulsed irradiation are obtained by Fourier superposition. For the line-focus case the surface-wave pulse is proportional to the laser pulse, while for point-focus illumination the surface-wave pulse consists of a principal pulse followed by a smaller pulse of opposite sign.

Particle-like solutions to higher-order curvature Einstein–Yang–Mills systems in d dimensions

Abstract: We consider the superposition of the first two members of the gravitational hierarchy (Einstein plus first Gauss–Bonnet (GB)) interacting with the superposition of the first two members of the Yang–Mills (YM) hierarchy, in d dimensions. The YM fields are taken to be in the chiral representations of the gauge groups, (i) SO(±)(d), and (ii) SO(±)(d − 1), respectively, for (i) even d and (ii) odd d. Such systems can occur in the low energy effective action of string theory. Particle-like solutions in dimensions d = 6, 8, and d = 7, are constructed, respectively. Our results reveal qualitatively new properties featuring double-branch solutions with critical behaviour. In this preliminary study, we have restricted numerical study to one-node solutions.

Computational analysis of quality reduction during drying of lumber due to irrecoverable deformation. I: Orthotropic viscoelastic-mechanosorptive-plastic material model for the transverse plane of wood

Abstract: This paper presents the development of an orthotropic material model for the mechanical analysis of wood in the plane perpendicular to the growth direction. It is based on an earlier uniaxial development and experimental verification. The novel features are the biaxial extension and the description of partially irrecoverable creep deformation by enhancing a viscoelastic-mechanosorptive creep model by coupling it with orthotropic plasticity. The mathematical description of both the equations of state and the evolution laws are formulated on a thermodynamical basis. A semianalytical solution algorithm is derived for the obtained nonlinear system of differential equations. The model is applicable over a wide range of temperature as well as moisture content (20–120°C; nearly 0% moisture content to fiber saturation), which is achieved through application of the time-temperature-moisture superposition principle and the introduction of a moisture-change-temperature superposition principle. A set of material parameters suitable for this range of conditions is given for \IPinus silvestris\N.

Terahertz beam propagation measured through three-dimensional amplitude profile determination

Abstract: To determine the spatio-temporal field distribution of freely propagating terahertz bandwidth pulses, we measure the time-resolved electric field in two spatial dimensions with high resolution. The measured, phase-coherent electric-field distributions are compared with an analytic model in which the radiation from a dipole antenna near a dielectric interface is coupled to free space through a spherical lens. The field external to the lens is limited by reflection at the lens–air dielectric interface, which is minimized at Brewster’s angle, leading to an annular field pattern. Field measurements compare favorably with theory. Propagation of terahertz beams is determined both by assuming a TEM0,0 Gaussian profile as well as expanding the beam into a superposition of Laguerre–Gauss modes. The Laguerre–Gauss model more accurately describes the beam profile for free-space propagation and after propagating through a simple optical system. The accuracy of both models for predicting far-field beam patterns depend upon accurately measuring complex field amplitudes of terahertz beams.

Orthogonal polynomials of a discrete variable as expansion basis sets in quantum mechanics: Hyperquantization algorithm

Abstract: In recent years, orthogonal polynomials of a discrete variable have been widely investigated both as tools of numerical analysis for the representation of functions on grids and as the superposition coefficients that appear as matrix elements of the overlap between spherical and hyperspherical harmonics corresponding to alternative coordinate systems. This article reviews our work concerning the extension of their use to quantum mechanical problems. By exploiting both their connection with coupling and recoupling coefficients of angular momentum theory and their asymptotic relationships (semiclassic limit) with spherical and hyperspherical harmonics, a discretization procedure, the hyperquantization algorithm, has been developed and applied to the study of anisotropic interactions and of reactive scattering as a quantum mechanical n-body problem. One of the most appealing features of this method has turned out to be a drastic reduction of memory requirements and computing time for extensive dynamic calculations as obtained by a diagonal matrix formulation of the interparticle interaction (the stereodirected representation). Use for fitting of potential energy surfaces has been also proposed and further applications have been made to stereodirected dynamics via an exact representation for the scattering matrix as well as to the characterization of molecular beam polarization. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Separation of the geomagnetic variation field on the ground into external and internal parts using the spherical elementary current system method

Abstract: Traditionally the separation of the ground geomagnetic field variations into external and internal parts is carried out by applying methods using harmonic functions However, these methods may require a separate field interpolation and extrapolation, can be computationally slow, and require a minimum wavelength to be specified to which the spatial resolution is limited globally A novel method that utilizes elementary current systems can overcome these shortcomings The basis is the fact that inside a domain free of current flow, the magnetic field can be continued to any selected plane in terms of equivalent currents Two layers of equivalent currents, each composed of superposition of spherical elementary systems, are placed to reproduce the ground magnetic field: One above the surface of the Earth representing the field of ionospheric origin, and one below it representing the field caused by induced currents in the Earth The method can be applied for single time steps and the solution of the associated underdetermined linear system is found to be fast and reliable when using singular value decomposition The applicability of the method is evaluated using synthetic magnetic data computed from different ionospheric current models and associated image currents placed below the surface of the Earth Following these tests, the method is applied to the measurements of Baltic Electromagnetic Array Research (BEAR) (June–July 1998) External and internal components of geomagnetic variations were computed for the entire measurement period Also the adequacy of the sparser IMAGE magnetometer network for the full field separation was tested

Non-Markovian effects on quantum optimal control of dissipative wave packet dynamics

Abstract: Optimal control within the density matrix formalism is applied to the creation of a specified superposition state in condensed phases. The primary system modeled by a displaced harmonic oscillator is surrounded by a boson heat bath, the dynamics of which is described by a non-Markovian master equation. A newly developed monotonically convergent algorithm is used to solve the pulse design equations. The control mechanisms are strongly dependent on the bath correlation time that is characterized by the inverse of an exponential decay constant, γ. If the correlation time is shorter than the temporal width of a typical subpulse involved in an optimal pulse, the solution is reduced to that in the Markovian case. If we assume a longer correlation time, by weighing less physical significance on the penalty due to pulse fluence, an optimal pulse with high intensity is obtained, the temporal width of which approaches ∼1/γ. We also see considerable changes in the shape of the optimal pulse with increasing intensity, suggesting that strong fields open up control mechanisms that are qualitatively different from those in weak fields.

Measuring properties of superposed light beams carrying different frequencies.

Abstract: When two electromagnetic fields of different frequencies are physically superposed, the linear superposition equation implies that the fields readjust themselves into a new mean frequency whose common amplitude undulates at half their difference frequency. Neither of these mathematical frequencies are measurable quantities. We present a set of experiments underscoring that optical fields do not interfere with each other or modify themselves into a new frequency even when they are physically superposed. The multi-frequency interference effects are manifest only in materials with broad absorption bands as their constituent diploes attempt to respond collectively and simultaneously to all the optical frequencies of the superposed fields. Interference is causal and real since the dipoles carry out the operation of summation dictated by their quantum mechanical properties.

Signals of new physics in global event properties in pp collisions in the TeV energy domain

Abstract: In the framework of the weighted superposition mechanism of different classes of minimum bias events (or substructures), described by the negative binomial multiplicity distribution, in possible scenarios for pp collisions in the TeV energy domain, we explore global properties of an eventual new class of events, characterized by high hadron and clan densities, to be added to the soft (without minijets) and semihard (with minijets) ones. It turns out that the main signal of the mentioned new physical expectations at 14 TeV c.m. energy would be an ``elbow structure'' in the tail of the total charged particle multiplicity distribution in complete disagreement with the second shoulder structure predicted by PYTHIA Monte Carlo calculations: a challenging problem for new experimental work.

An approach for reducing adjacent element crosstalk in ultrasound arrays

Abstract: A method is presented for active cancellation of crosstalk effects in ultrasonic arrays. The approach makes use of the programmable transmitter waveform generators that are now being used with growing prevalence in diagnostic ultrasound systems. The array's transmit mode transfer function is represented by a transfer function matrix. Elements of this matrix are determined by exciting a single, central element with a wideband waveform and determining the resulting pressure output from the central element and adjacent elements. The desired output then is defined (e.g., finite output from a single, central element) and zero output from all other elements. The transfer function matrix equation can be solved to determine the required excitation functions on both the central array element and its neighbors. These excitation functions result in reduced evidence of crosstalk on the output signals. Therefore, the single-element, angular-response function is improved. Using superposition, the approach can be extended to beamformed array excitation. A variety of theoretical and experimental results are shown. The method also can be used in the receive mode but with a less satisfactory solution. A transmitting mode experiment based on a prototype five-element transducer has provided results indicating that sidelobes in the angular response can be reduced using this technique.

Spatial coherence wavelets

Abstract: It is shown that the cross-spectral density at a plane in the Fresnel—Fraunhofer domain can be expressed as a certain diffraction pattern, which is generated by the superposition of second-order spatial coherence wavelets that emerge from the aperture. The amplitude of each coherence wavelet exhibits units of power density (average energy) and the power spectrum at the far zone plane will be the summation of the amplitudes of such wavelets. Thus, the spatial coherence wavelet constitutes a vehicle for both correlation and energy transport in free space. Some simulation results are discussed to illustrate these ideas.