scispace - formally typeset
Search or ask a question

Showing papers on "Superposition principle published in 2002"


01 Jan 2002
TL;DR: In this article, a Schrodinger cat-like state of matter was generated at the single atom level by applying a sequence of laser pulses, which entangles internal and external states of the ion.
Abstract: A "Schrodinger cat"-like state of matter was generated at the single atom level. A trapped 9Be+ ion was laser-cooled to the zero-point energy and then prepared in a superposition of spatially separated coherent harmonic oscillator states. This state was created by application of a sequence of laser pulses, which entangles internal (electronic) and external (motional) states of the ion. The Schrodinger cat superposition was verified by detection of the quantum mechanical interference between the localized wave packets. This mesoscopic system may provide insight into the fuzzy boundary between the classical and quantum worlds by allowing controlled studies of quantum measurement and quantum decoherence.

799 citations


Journal ArticleDOI
TL;DR: In this paper, a linear superposition state of three basis kets was proposed, where a photon split to three pulses is sent from Alice to Bob, where the phase difference between sequential two pulses carries bit information.
Abstract: A novel quantum cryptography scheme is proposed, in which a single photon is prepared in a linear superposition state of three basis kets. A photon split to three pulses is sent from Alice to Bob, where the phase difference between sequential two pulses carries bit information. Bob measures the phase difference by passive differential phase detection. This scheme is suitable for fiber transmission systems and offers a key creation efficiency higher than conventional fiber-based BB84.

363 citations


Journal ArticleDOI
TL;DR: Under these conditions and in the absence of orientational selection, the dipolar time evolution data can be quantitatively simulated for arbitrary radial distribution functions by shell factorization, i.e., by performing the orientational average separately for thin spherical shells and multiplying the signals of all the shells.

224 citations


Journal ArticleDOI
TL;DR: The results of numerical micromagnetic calculations exhibit excellent agreement with experiment and show that a comprehensive account of spatial nonuniformity and propagation is necessary to accurately measure the intrinsic damping rate.
Abstract: We measure the propagation of spatially localized spin waves in NiFe thin films through local inductive detection of the dynamic magnetization. A pulsed magnetic field excites a linear superposition of spin wave modes with a distribution that is predominantly driven by the spatial dependence of the in-plane excitation field. The results of numerical micromagnetic calculations exhibit excellent agreement with experiment and show that a comprehensive account of spatial nonuniformity and propagation is necessary to accurately measure the intrinsic damping rate.

185 citations


Journal ArticleDOI
TL;DR: The single photon plays a role of a "catalyst:" it is explicitly present in both the input and the output channels of the interaction yet facilitates generation of a nonclassical state of light.
Abstract: We report preparation and characterization of coherent superposition states t[0>+alpha]1> of the electromagnetic field by conditional measurements on a beam splitter. This state is generated in one of the beam splitter output channels if a coherent state [alpha> and a single-photon Fock state [1> are present in the two input ports and a single photon is registered in the other beam splitter output. The single photon thus plays a role of a "catalyst:" it is explicitly present in both the input and the output channels of the interaction yet facilitates generation of a nonclassical state of light.

182 citations


Journal ArticleDOI
TL;DR: It is shown herein that both theories describe available nonlinear experimental ligament data well and hence can account for both elastic and viscous nonlinearities and modified superposition allows for a more direct interpretation of the relationship between model parameters and physical behavior than does Schapery's theory.
Abstract: Recent experiments in rat medial collateral ligament revealed that the rate of stress relaxation is strain dependent and the rate of creep is stress dependent. This nonlinear behavior requires a more general description than the separable quasilinear viscoelasticity theory commonly used in tissue biomechanics. The purpose of this study was to determine whether the nonlinear theory of Schapery or the modified superposition method could adequately model the strain-dependent stress-relaxation behavior of ligaments. It is shown herein that both theories describe available nonlinear experimental ligament data well and hence can account for both elastic and viscous nonlinearities. However, modified superposition allows for a more direct interpretation of the relationship between model parameters and physical behavior, such as elastic and viscous nonlinearities, than does Schapery's theory. Hence, the modified superposition model is suggested to describe ligament data demonstrating both elastic nonlinearity and strain-dependent relaxation rate behavior. The behavior of the modified superposition model under a sinusoidal strain history is also examined. The model predicts that both elastic and viscous behaviors are dependent on strain amplitude and frequency.

174 citations


Book ChapterDOI
01 Jan 2002
TL;DR: Pseudoanalysis uses many mathematical tools from different fields, such as functional equations, variational calculus, measure theory, functional analysis, optimization theory, and semiring theory.
Abstract: This chapter discusses the pseudoadditive measures and and the corresponding integrals, which give a base for pseudoanalysis. The pseudoadditive measures are applied in optimization problems, nonlinear partial differential equations, nonlinear difference equations, optimal control, and fuzzy systems.Pseudoanalysis uses many mathematical tools from different fields, such as functional equations, variational calculus, measure theory, functional analysis, optimization theory, and semiring theory. The advantage of the pseudoanalysis is that the problems from many different fields are covered with one theory and unified methods. This approach gives solutions in such a form that are not achieved by other theories. In some cases, it enables nonlinear equations to obtain exact solutions in the similar form as for linear equations. Some obtained principles such as the pseudolinear superposition principle allows transferring methods of linear equations to nonlinear equations. Pseudointegral that is defined as the limits of the corresponding idempotent Riemannian sums is also elaborated in the chapter.

162 citations


Journal ArticleDOI
TL;DR: In this article, the utility of nonclassical states of simple harmonic oscillators, particularly a superposition of coherent states, for sensitive force detection was investigated, and it was shown that like squeezed states, such states allow displacement measurements at the Heisenberg limit.
Abstract: We investigate the utility of nonclassical states of simple harmonic oscillators, particularly a superposition of coherent states, for sensitive force detection. We find that like squeezed states, a superposition of coherent states allows displacement measurements at the Heisenberg limit. Entangling many superpositions of coherent states offers a significant advantage over a single-mode superposition state with the same mean photon number.

161 citations


Journal ArticleDOI
TL;DR: This work presents a simple yet accurate analytical model for the focusing of the pinhole photon sieve, applicable to arbitrary paraxial illumination with arbitrary complex amplitude distribution at the photon sieving plane.
Abstract: Recently, a new class of diffractive optical element called a photon sieve, which consists of a great number of pinholes, was developed for the focusing and imaging of soft x rays. In terms of the closed-form formula for the far field of individual pinholes and the linear superposition principle, we present a simple yet accurate analytical model for the focusing of the pinhole photon sieve. This model is applicable to arbitrary paraxial illumination with arbitrary complex amplitude distribution at the photon sieve plane. We check the validity range of this model by comparing it with the exact Fresnel diffraction integral. Some special problems, such as the individual quasi-far-field correction for very large pinholes and the related phase shift induced by this correction, are also discussed.

106 citations


Proceedings ArticleDOI
02 Jun 2002
TL;DR: In this paper, the authors present novel coupling schemes for microwave resonator filters, which are shown to obtain higher-order filter characteristics from lower-order sections connected in parallel between the source and the load by proper superposition of the individual lowerorder responses.
Abstract: The paper presents novel coupling schemes for microwave resonator filters. Some of these solutions contain more than one main path between the input and output. These paths may be interacting or non-interacting. In other solutions, only some of the direct (main) couplings are zero. It is shown that higher-order filter characteristics can be obtained from lower-order sections, which are connected in parallel between the source and the load, by proper superposition of the individual lower-order responses. Possible applications of these solution to actual design problems are discussed.

88 citations


Journal ArticleDOI
TL;DR: In this paper, a new partial differential technique based on the segment projection method in phase space is introduced, where the superposition problem is perfectly resolved and so is the problem of computing amplitudes in the neighborhood of caustics.

Journal ArticleDOI
TL;DR: The Deutsch-Jozsa algorithm for three-qubit functions using pure coherent superpositions of rovibrational eigenstates is described in this paper. But it is not suitable for the case where the function's character, either constant or balanced, is evaluated by first imprinting the function, using a phase-shaped femtosecond pulse, on a coherent superposition of the molecular states, and then projecting the superposition onto an ionic final state, with a specific time delay.
Abstract: The Deutsch-Jozsa algorithm is experimentally demonstrated for three-qubit functions using pure coherent superpositions of ${\mathrm{Li}}_{2}$ rovibrational eigenstates. The function's character, either constant or balanced, is evaluated by first imprinting the function, using a phase-shaped femtosecond pulse, on a coherent superposition of the molecular states, and then projecting the superposition onto an ionic final state, using a second femtosecond pulse at a specific time delay.

Journal ArticleDOI
TL;DR: In this paper, the variation of the vorticity of the superposition of two Bessel singular beams under free-space propagation is analyzed, and it is shown that in the near field the combined beam creates light pattern with much richer vortex content than that of individual beams.

Journal ArticleDOI
Maria A. Heckl1
TL;DR: In this article, a mathematical model for the propagation of structural waves on an infinitely long, periodically supported Timoshenko beam is presented, where the wave types that can exist on the beam are bending waves with displacements in the horizontal and vertical directions, compressional waves and torsional waves.

Journal ArticleDOI
TL;DR: In this paper, a compact thermal model for the transient hot spot (junction) temperatures and contact heat flow development of electronic systems with multiple thermal ports is presented, which is exact provided that the heat conduction equation is linear and the temperature distribution along the thermal contact areas is uniform.

Journal ArticleDOI
TL;DR: In this paper, a self-consistent large-signal beam-field interaction model for vacuum electronic microwave sources with external cavities is described, which includes a selfconsistent solution of the three-dimensional equations of electron motion and the time-dependent field equations.
Abstract: A self-consistent large-signal beam-field interaction model for vacuum electronic microwave sources with external cavities is described. The model includes a self-consistent solution of the three-dimensional equations of electron motion and the time-dependent field equations. The RF fields are decomposed into the fields inside the beam region and the fields inside outer resonators. The RF fields inside the beam region are represented as a superposition of local waveguide modes. The RF fields inside resonators are represented as a sum over resonator modes. The various modes are coupled together due to gaps connecting cavities with each other and with the beam region. The numerical implementation of the model requires additional analytical steps to obtain an effective, convergent, and stable numerical solution. The modified version of the code MAGY has been tested by a comparison with known results and also with measured data.

Journal ArticleDOI
TL;DR: In this paper, structured decompositions of unitary operators can be employed to derive control schemes for finite-level quantum systems that require only sequences of simple control pulses such as square wave pulses with finite rise and decay times or Gaussian wavepackets.
Abstract: We demonstrate how structured decompositions of unitary operators can be employed to derive control schemes for finite-level quantum systems that require only sequences of simple control pulses such as square wave pulses with finite rise and decay times or Gaussian wavepackets. To illustrate the technique, it is applied to find control schemes to achieve population transfers for pure-state systems, complete inversions of the ensemble populations for mixed-state systems, create arbitrary superposition states and optimize the ensemble average of dynamic observables.

Journal ArticleDOI
TL;DR: In this paper, the authors explore the laser-pulse propagation dynamics when one, two, or three pulses resonantly drive a coherently prepared four-level medium in a tripod configuration.
Abstract: We explore the laser-pulse propagation dynamics when one, two, or three pulses resonantly drive a coherently prepared four-level medium in a tripod configuration. If the system is prepared in a coherent superposition of two of the lower levels, we show that two incident resonant pulses can parametrically generate a third pulse in the medium. Over short distances, the propagation of this generated pulse can be partially controlled by varying the Rabi frequency of one of the driving fields. For a medium prepared in a coherent superposition of the three lower levels, we obtain a general expression for a three-photon Beer's length. Under specific conditions, the medium can either become completely opaque or completely transparent to three incident resonant pulses. Moreover, a single incident pulse can be used to parametrically generate two additional pulses. Finally, a general relationship is found that links the amplitudes of the initial superposition of states and the amplitudes of the pulses at large distances in the medium, implying that the initial superposition can be used to engineer the amplitudes of the exiting pulses.

Posted Content
TL;DR: In this article, a nonlinear semi-classical Schrodinger equation with quadratic oscillations is considered, and it is shown that the associate solution is the superposition of the nonlinear evolution of each of them, up to a small remainder term.
Abstract: We consider a nonlinear semi-classical Schrodinger equation for which it is known that quadratic oscillations lead to focusing at one point, described by a nonlinear scattering operator. If the initial data is an energy bounded sequence, we prove that the nonlinear term has an effect at leading order only if the initial data have quadratic oscillations; the proof relies on a linearizability condition (which can be expressed in terms of Wigner measures). When the initial data is a sum of such quadratic oscillations, we prove that the associate solution is the superposition of the nonlinear evolution of each of them, up to a small remainder term. In an appendix, we transpose those results to the case of the nonlinear Schrodinger equation with harmonic potential.

Journal ArticleDOI
TL;DR: In this paper, the authors presented analytical solutions for the calculation of the acoustic insulation provided by an infinite single panel wall when subjected to a spatially sinusoidal harmonic line load or a point pressure load.

Journal ArticleDOI
TL;DR: A time-domain method on an overlapped lattice is presented for the accurate and efficient simulation of electromagnetic wave propagation through inhomogeneous media and is shown to be a generalization and reinterpretation of the Yee algorithm.
Abstract: A time-domain method on an overlapped lattice is presented for the accurate and efficient simulation of electromagnetic wave propagation through inhomogeneous media. The method comprises a superposition of complementary approximations to electromagnetic theory on a lattice. The discrete space-time (DST) method, is set on a pair of dual lattices whose field components are collocated on their respective lattice sites. The other, the time-domain element (TDE) method, is set on overlapping dual lattices whose field components are noncollocated. The TDE method is shown to be a generalization and reinterpretation of the Yee algorithm. The benefits of the combined algorithm over comparable methods include: (1) increased accuracy over larger bandwidths; (2) increased stability allowing larger time steps; (3) local stencil-satisfying boundary conditions on interfaces; (4) self-contained mathematical framework; (5) it is physically intuitive.


Journal ArticleDOI
TL;DR: In this paper, two distinct nonlinear phenomena in a four-level quantum system having a tripod configuration were analyzed and it was shown that the system can become transparent at two different frequencies of a probe laser field.
Abstract: We analyse two distinct nonlinear phenomena in a four-level quantum system having a tripod configuration. First, we show that the system can become transparent at two different frequencies of a probe laser field. The potential for parametric generation in this medium is also investigated. We show that, if the system is prepared in a coherent superposition of two or three of the lower levels, one or two new fields can be generated.

Journal ArticleDOI
TL;DR: In this article, the effect of large amplitude on the dissipative nature as well as on the natural frequency of viscoelastic laminated plates is investigated. But the authors focus on the nonlinear and hereditary type governing equations.

Journal ArticleDOI
TL;DR: In this article, a compromise between analytical rigor and analysis features (e.g., multiple wheels, seasonal property variations, material nonlinearity) is made to approximate multiple wheel effects via superposition.
Abstract: Flexible pavement structural analysis for design usage must consider (as a minimum) multiple wheel/axle loading configurations, seasonal variations of material layer properties, and the nonlinear behavior of unbound materials. Although these requirements are all easily within the capabilities of three-dimensional finite element analysis, the required computation times may be impracticably long for routine design. Compromises between analytical rigor (e.g., three-dimensionality) and analysis features (e.g., multiple wheels, seasonal property variations, material nonlinearity) must be made. One compromise is to retain seasonal property variations and material nonlinearity within an axisymmetric single wheel finite element model and to approximate multiple wheel effects via superposition. Although this superposition of nonlinear solutions is undeniably invalid from a rigorous theoretical viewpoint, the errors may be well within acceptable magnitudes for practical design. The paper investigates this ...

Journal ArticleDOI
TL;DR: In this article, a wave mechanics approach is used to solve the Timoshenko beam equation, revealing that two waves exist: the s a -wave and the s b -wave.
Abstract: A wave mechanics approach is used to solve the Timoshenko beam equation, revealing that two waves exist. One is called the s a –wave and the other the s b –wave. These two waves are found to be the basic constituent components of the mode shapes of the beam. An experiment was carried out and the measured mode shapes of a free–free beam are shown to consist of one s a –wave and one s b –wave in superposition for each of the modes. The measured s a –wave and s b –wave exhibit the Rayleigh–Lamb first (with anomalous dispersion) and Rayleigh–Lamb second (with normal dispersion) flexural modes, respectively. The issue of the second spectrum is addressed and it is shown that, within the measurable frequency range, Rayleigh–Lamb second flexural modes are present in the free–free beam. The s b –wave is identified as the second–spectrum mode. The role of shear deformation is also investigated in explaining the basic difference in the behaviour of the s a – and s b –waves. This paper also contributes to a physical interpretation of the hyperbolic functions in the classical solution of beam vibration problems.

Journal ArticleDOI
TL;DR: The conditions to realize parallel recording and reading databases of Grover algorithms in molecular magnet Mn-12 are discussed in detail in this article, where it is found that an accurate time duration of the magnetic pulse as well as the discrete frequency spectrum and the amplitudes are required to design a quantum computing device.
Abstract: Quantum computation in molecular magnets is studied by solving the time-dependent Schrodinger equation numerically Following Leuenberger and Loss [Nature (London) 410, 789 (2001)], an external alternating magnetic field is applied to populate and manipulate a superposition of single-spin states in molecular magnet Mn-12 The conditions to realize parallel recording and reading databases of Grover algorithms in molecular magnets are discussed in detail It is found that an accurate time duration of the magnetic pulse as well as the discrete frequency spectrum and the amplitudes are required to design a quantum computing device

Journal ArticleDOI
TL;DR: The frequency response of a fiber-optic hydrophone that uses a dielectric multilayer system as the sensing element for ultrasound detection is investigated and the transfer function obtained was interpreted as the result of the superposition of longitudinal, edge diffraction and lateral waves with a resonant vibration mode of the fiber body representing an elastic rod.
Abstract: The frequency response of a fiber-optic hydrophone that uses a dielectric multilayer system as the sensing element for ultrasound detection is investigated. A primary interferometric calibration technique is applied to determine by experiment the frequency-dependent pressure-voltage transfer function up to 45 MHz. The interaction between an incident pressure wave and the fiber end is analyzed by finite element methods. The simulation yields the response of the sensor to a short Gaussian impulse in the time domain from which the transfer function is calculated. The results of the model simulations allowed the transfer function obtained to be interpreted as the result of the superposition of longitudinal, edge diffraction and lateral waves with a resonant vibration mode of the fiber body representing an elastic rod.

Journal ArticleDOI
TL;DR: A comprehensive theoretical analysis of the occurrence of omnidirectional reflection in one-dimensional phononic crystal structures and the appropriate choices of the material and geometrical properties to realize such structures is presented.
Abstract: This paper presents a comprehensive theoretical analysis of the occurrence of omnidirectional reflection in one-dimensional phononic crystal structures. We discuss the conditions for a one-dimensional layered structure, made of elastic materials, to exhibit total reflection of acoustic incident waves in a given frequency range, for all incident angles and all polarizations. The property of omnidirectional reflection can be fulfilled with a simple finite superlattice if the substrate from which the incident waves are launched is made of a material with high acoustic velocities (this is very similar to the case of omnidirectional optical mirror where the incident light is generated in vacuum). However, if the substrate is made of a material with low acoustic velocities, we propose two solutions to obtain an omnidirectional band gap, namely, the cladding of a superlattice with a layer of high acoustic velocities, which acts like a barrier for the propagation of phonons, or the association in tandem of two different superlattices in such a way that the superposition of their band structures exhibits an absolute acoustic band gap. We discuss the appropriate choices of the material and geometrical properties to realize such structures. The behavior of the transmission coefficients are discussed in relation with the dispersion curves of the finite structure embedded between two substrates. Both transmission coefficients and densities of states (from which we derive the dispersion curves) are calculated in the framework of a Green's function method.

Journal ArticleDOI
TL;DR: In this paper, the generalized Wei-Norman method and the reduction method are used to deal with systems of differential equations admitting a superposition function allowing us to write the general solution in terms of any fundamental set of particular solutions.
Abstract: The characterization of systems of differential equations admitting a superposition function allowing us to write the general solution in terms of any fundamental set of particular solutions is discussed. These systems are shown to be related with equations on a Lie group and with some connections in fiber bundles. We develop two methods for dealing with such systems: the generalized Wei–Norman method and the reduction method, which are very useful when particular solutions of the original problem are known. The theory is illustrated with some applications in both classical and quantum mechanics.