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Showing papers on "Superposition principle published in 1993"


Journal ArticleDOI
TL;DR: Superposition may be the only true quantum mystery, but in multiparticle systems the principle yields phenomena that are much richer and more interesting than anything that can be seen in one-particle systems as discussed by the authors.
Abstract: Discussing the particle analog of Thomas Young's classic double‐slit experiment, Richard Feynman wrote in 1964 that it “has in it the heart of quantum mechanics In reality, it contains the only mystery” That mystery is the one‐particle superposition principle But Feynman's discussion and statement have to be generalized Superposition may be the only true quantum mystery, but in multiparticle systems the principle yields phenomena that are much richer and more interesting than anything that can be seen in one‐particle systems

297 citations


Journal ArticleDOI
TL;DR: Yan et al. as mentioned in this paper considered the control of molecular dynamics using tailored light fields, based on a phase space theory of control, which enables them to calculate, in the weak field (one-photon) limit, the globally optimal light field that produces the best overlap for a given phase space target.
Abstract: We consider the control of molecular dynamics using tailored light fields, based on a phase space theory of control [Y. J. Yan et al., J. Phys. Chem. 97, 2320 (1993)]. This theory enables us to calculate, in the weak field (one‐photon) limit, the globally optimal light field that produces the best overlap for a given phase space target. We present as an illustrative example the use of quantum control to overcome the natural tendency of quantum wave packets to delocalize on excited state potential energy curves. Three cases are studied: (i) a ‘‘molecular cannon’’ in which we focus an outgoing continuum wave packet of I2 in both position and momentum, (ii) a ‘‘reflectron’’ in which we focus an incoming bound wave packet of I2, and (iii) the focusing of a bound wave packet of Na2 at a turning point on the excited state potential using multiple light pulses to create a localized wave packet with zero momentum. For each case, we compute the globally optimal light field and also how well the wave packet produced by this light field achieves the desired target. These globally optimal fields are quite simple and robust. While our theory provides the globally optimal light field in the linear, weak field regime, experiment can in reality only provide a restricted universe of possible light fields. We therefore also consider the control of molecular quantum dynamics using light fields restricted to a parametrized functional form which spans a set of fields that can be experimentally realized. We fit the globally optimal electric field with a functional form consisting of a superposition of subpulses with variable parameters of amplitude, center time, center frequency, temporal width, relative phase, and linear and quadratic chirp. The best fit light fields produce excellent quantum control and are within the range of experimental possibility. We discuss relevant experiments such as ultrafast spectroscopy and ultrafast electron and x‐ray diffraction which can in principle detect these focused wave packets.

177 citations


Journal ArticleDOI
TL;DR: A scheme to realize an optical switch with quantum coherence between its ``open'' and ``closed'' states is presented and involves a single atom in a superposition of circular Rydberg states crossing a high Q cavity.
Abstract: A scheme to realize an optical switch with quantum coherence between its ``open'' and ``closed'' states is presented. It involves a single atom in a superposition of circular Rydberg states crossing a high Q cavity. A combination of switches could be used to prepare a quantum superposition of coherent microwave field states located simultaneously in two cavities. Such nonclassical states and their decoherence due to cavity dissipation could be studied by performing atom correlation experiments.

152 citations


Journal ArticleDOI
TL;DR: In this paper, the forward-propagating (causal) components of any homogeneous solution of the scalar-wave equation are actually recovered from either an infinite- or a finite-sized aperture in an open region.
Abstract: Several new classes of localized solutions to the homogeneous scalar wave and Maxwell’s equations have been reported recently. Theoretical and experimental results have now clearly demonstrated that remarkably good approximations to these acoustic and electromagnetic localized-wave solutions can be achieved over extended near-field regions with finite-sized, independently addressable, pulse-driven arrays. We demonstrate that only the forward-propagating (causal) components of any homogeneous solution of the scalar-wave equation are actually recovered from either an infinite- or a finite-sized aperture in an open region. The backward-propagating (acausal) components result in an evanescent-wave superposition that plays no significant role in the radiation process. The exact, complete solution can be achieved only from specifying its values and its derivatives on the boundary of any closed region. By using those localized-wave solutions whose forward-propagating components have been optimized over the associated backward-propagating terms, one can recover the desirable properties of the localized-wave solutions over the extended near-field regions of a finite-sized, independently addressable, pulse-driven array. These results are illustrated with an extreme exampl—one dealing with the original solution, which is superluminal, and its finite aperture approximation, a slingshot pulse.

149 citations


Journal ArticleDOI
TL;DR: In this article, the authors present two-dimensional and three-dimensional forward modeling in linear viscoelastic media, which implements Boltzmann's superposition principle based on a spectrum of relaxation mechanisms.
Abstract: Anelasticity is usually caused by a large number of physical mechanisms which can be modeled by different microstructural theories. A general way to take all these mechanisms into account is to use a phenomenologic model. Such a model which is consistent with the properties of anelastic media can be represented mechanically by a combination of springs and dash‐pots. A suitable system can be constructed by the parallel connection of several standard linear elements and is referred to as the general standard linear solid rheology. Two relaxation functions that describe the dilatational and shear dissipation mechanisms of the medium are needed. This model properly describes the short and long term behaviors of materials with memory and is the basis for describing viscoelastic wave propagation. This work presents two‐dimensional (2-D) and three‐dimensional (3-D) forward modeling in linear viscoelastic media. The theory implements Boltzmann’s superposition principle based on a spectrum of relaxation mechanisms...

134 citations


Journal ArticleDOI
TL;DR: A free monochromatic electromagnetic field is investigated which is the superposition of a squeezed thermal radiation and a coherent one and an analytic formula is established for an arbitrary correlation function, as well as its strong-squeezing limit.
Abstract: We investigate a free monochromatic electromagnetic field which is the superposition of a squeezed thermal radiation and a coherent one The main tool in our analysis is the characteristic function that has a Gaussian form We establish an analytic formula for an arbitrary correlation function, as well as its strong-squeezing limit Besides the usual quasiprobability densities, the coherent-state, number-state, coordinate, and momentum representations of the density operator are derived We point out the non-classical oscillations of the photon-number distribution and find its generating function Collaterally, displaced thermal states and squeezed thermal states are revisited as nontrivial particular cases

131 citations


Journal ArticleDOI
TL;DR: The observation of light amplification without population inversion is reported, where a linear superposition of an m=1 and an m=-1 magnetic substate is populated coherently and an inverse transition is used for amplification of light.
Abstract: We report the observation of light amplification without population inversion. A linear superposition of an m=1 and an m=-1 magnetic substate is populated coherently. Absorption from this superposition to a higher state is canceled by interference of channels, a so-called dark resonance. An inverse transition is used for amplification of light. The temporal behavior of the amplified pulse and the gain are studied as a function of the energy splitting due to a magnetic field. In a vapor of cadmium-112 gain factors of up to 4.3 are observed

102 citations


Journal ArticleDOI
TL;DR: It is shown that simple superpositions of Schrodinger cats exhibit amplitude squeezing, similarly to the case of a superposition of several coherent states along a straight line that shows quadrature squeezing.
Abstract: As a generalization of the optical Schrodinger cats, discrete sets of coherent states are considered on a circle in the a plane. It is shown that simple superpositions of Schrodinger cats exhibit amplitude squeezing, similarly to the case of a superposition of several coherent states along a straight line that shows quadrature squeezing. The interference fringes between the coherent states form the annuli of the Fock states in the Wigner-function picture. It is also shown that a continuous superposition of coherent states on a circle can serve as a basis for the representation of any state

100 citations


Journal ArticleDOI
TL;DR: In this article, a frequency and short-pulse (SP) time-domain (TD) study of two-dimensional plane wave scattering from a finite periodic array of thin, flat, coplanar perfectly conducting strips is presented.
Abstract: A frequency and short-pulse (SP) time-domain (TD) study of two-dimensional plane wave scattering from a finite periodic array of thin, flat, coplanar perfectly conducting strips is presented. Rigorous analytical-numerical reference solutions are established by spatial spectral wave number decomposition and the method of moments (MOM), followed by frequency inversion. The analytical portion is approximated so as to yield via high-frequency asymptotics, for a sufficiently large number of strips, a hybrid ray-Floquet-mode-MOM algorithm that not only explains the phenomena in physical terms but is also numerically efficient and reasonably accurate when compared with the reference solution. Of special interest are the TD Floquet modes with their space-time-dependent frequencies and wave numbers. By superposition, they can synthesize the highly resolved pulse train return under SP conditions. Attention is given also to direct SP-TD synthesis, and to processing options for SP-TD data. >

92 citations


Journal ArticleDOI
TL;DR: In this paper, a non-linear ion trap is generated by the superposition of weak higher multiple fields on the basic quadrupolar field, which is called nonlinear ion traps.

79 citations



Journal ArticleDOI
TL;DR: It is demonstrated that substantial coherence is retained when such light interacts with a two-photon-absorbing reservoir and is responsible for the preservation of squeezing in the steady state despite the effect of dissipation.
Abstract: We investigate the dynamical evolution of nonclassical states of light undergoing a two-photon absorption process. We consider two distinct cases of initial states, a squeezed coherent state and an eigenstate of the two-photon annihilation operator (a superposition of macroscopically distinct coherent states). We analyze the fluctuations in the photon-number operator and in the quadrature components of the field. Whereas one-photon linear damping rapidly destroys quantum features such as squeezing, we demonstrate that substantial coherence is retained when such light interacts with a two-photon-absorbing reservoir. This surviving coherence is responsible for the preservation of squeezing in the steady state despite the effect of dissipation. We relate the origin of squeezing of initially unsqueezed light interacting with two-photon absorbers with the squeezing generated by simple superposition states of light.

Journal ArticleDOI
TL;DR: In this article, a perturbation wave form for reliable electrochemical impedance spectroscopy measurements based on the fast Fourier transformation is proposed using numerical simulation, arguments and results are presented for the choice and the optimization of the perturbations signal constructed as a superposition of discrete sine waves with selected frequencies.
Abstract: The choice of the perturbation wave form is of crucial importance for reliable electrochemical impedance spectroscopy measurements based on the fast Fourier transformation. Using numerical simulation, arguments and results are presented for the choice and the optimization of a perturbation signal constructed as a superposition of discrete sine waves with selected frequencies. Two possible ways to optimize the perturbation for better noise immunity are described: choosing proper values for the phases of the individual sine waves, minimal perturbation signal amplitudes can be obtained which improve the quality of impedance data by 25%. By introducing response‐sensitive amplitudes an improvement in the quality of data by a factor of 4–5 can be reached in the low frequency range. A new technique for single‐pulse measurements with continuous perturbations that assures a steady‐state response and better accuracy at high capacitive and/or inductive samples is also described.

Journal ArticleDOI
F. Moussu1, M. Nivoit1
TL;DR: In this paper, the elastic constants of an orthotropic material were determined by studying the free vibrations of a rectangular plate in completely free boundary conditions, based on series expansions of the deformed plate shape and requiring the boundary conditions to be satisfied.

Journal ArticleDOI
TL;DR: A new type of finite-amplitude traveling or standing wave with an exact sinusoidal form and a short commensurate wavelength is predicted to exist in lattices with cubic and/or quartic anharmonic potential between any arbitrary number of nearest and non-nearest neighbors.
Abstract: A new type of finite-amplitude traveling or standing wave with an exact sinusoidal form and a short commensurate wavelength is predicted to exist in lattices with cubic and/or quartic anharmonic potential between any arbitrary number of nearest and non-nearest neighbors. Fast traveling nonlinear sinusoidal waves (NSW) can generate sinusoidal lattice solitons. Superposition of two NSW or sinusoidal solitons propagating in opposite directions can result in the formation of an extended or a localized standing-wave eigenmode. New exact solutions for localized standing-wave structures are found within a rigorous discrete-lattice approach.

Journal ArticleDOI
TL;DR: In this paper, a technique which enables a dispersive Lamb wave to be propagated over a considerable distance to give a simple waveform at the receiver position is described, which works by launching a signal which, by superposition of its frequency components, will recombine to form a signal with a simple shape (a pulse or tone burst) at the measurement position.

Journal ArticleDOI
TL;DR: In this article, a large set of hourly-averaged air infiltration measurements using a constant concentration tracer gas injection system were sorted to separate stack-driven, wind-driven and wind-direction shelter effects.

Journal ArticleDOI
TL;DR: An approximate solution is given for the Jaynes-Cummings model with cavity losses, i.e., the problem of a two-level atom interacting with a single mode of the quantized radiation field, in the rotating-wave approximation, when the field is damped by a reservoir at zero temperature.
Abstract: An approximate solution is given for the Jaynes-Cummings model with cavity losses, i.e., the problem of a two-level atom interacting with a single mode of the quantized radiation field, in the rotating-wave approximation, when the field is damped by a reservoir at zero temperature. The approximate solution is derived for initial coherent field states with moderately large numbers of photons. It is simpler in form than earlier results derived by other authors and, over the appropriate parameter range, substantially more accurate than some of them, as shown by direct numerical integration of the master equation. In particular, it is found that an earlier treatment of this problem based on a secular approximation is seriously flawed, in that the conditions for its validity are much more restrictive than was previously believed. Among the results derived it is shown that, just as for the lossless case, when the atom is initially prepared in one of the semiclassical eigenstates the evolution is very simple, with the field and the atomic dipole drifting together in phase. For moderate losses this leads, as in the lossless case, to a ``state preparation''; i.e., to a good approximation, the state of the atom at a specific time can be made independent of its initial state. The effect of losses on the recently discovered ``Schr\"odinger cat'' state of the field is also analyzed. It is found that, although the dissipation destroys the coherence of the macroscopic superposition very rapidly, preparation and observation of the ``cat'' should be possible with the cavity quality factors reported in recent micromaser experiments.

Journal ArticleDOI
TL;DR: In this article, it was shown that the resonant interaction between a two-level atom and a quantized field via two-photon transitions leads to extreme quantum entanglement between the atom and quantum field.
Abstract: We show that the resonant interaction between a two-level atom and a quantized field mode via two-photon transitions leads to extreme quantum entanglement between the atom and quantum field. Nevertheless during the time evolution there are moments at which the atom-field system becomes asymptotically disentangled. We investigate statistical properties of the pure-field states generated at such times. We show that at the quarter of the revival time the field is produced in the pure superposition state (Schrodinger cat state) composed of two coherent states with the same amplitude but which are out of phase by 90° (we obtain approximate analytical solution for this superposition state). We show that the interference between component states leads to non-classical oscillations in the photon number distribution. At the revival time the field is again in the pure state (we present an approximate analytical solution for the corresponding state vector). This pure state is not a superposition state. Neve...

Journal ArticleDOI
TL;DR: In this paper, a Fourier transform technique is employed to express the scattered field in the spectral domain as a superposition of the parallel-plate waveguide modes, and the boundary conditions are enforced on the conducting surface and the groove apertures to obtain simultaneous equations for the transmitted field inside the grooves.
Abstract: TM-wave scattering from rectangular grooves in a perfectly conducting plane is investigated. A Fourier-transform technique is employed to express the scattered field in the spectral domain as a superposition of the parallel-plate waveguide modes. The boundary conditions are enforced on the conducting surface and the groove apertures to obtain simultaneous equations for the transmitted field inside the grooves. The simultaneous equations are solved to obtain the transmitted field in a series representation that reduces to a closed form in a high-frequency scattering regime. With the use of the stationary phase approximation, the far-zone scattered field is obtained, and its scattering behavior is studied in terms of the scattering angle. The diffraction efficiency for the finite grating as the number of grooves increases is presented.

Journal ArticleDOI
TL;DR: A linear-superposition scheme for the wave function is proposed which reduces the number of full multiple-scattering calculations needed for the structure optimization drastically and allows for a parameter space with a much higher dimension than before, which will improve the reliability of structure determinations considerably.
Abstract: Direct methods in low-energy-photoelectron diffraction can provide only approximate locations of atoms close to the emitter. More detailed structural information has to be extracted from the photoelectron diffraction spectra in the traditional way by comparing the results of multiple-scattering calculations for possible structure models to the experimental data. In this paper we propose a linear-superposition scheme for the wave function which reduces the number of full multiple-scattering calculations needed for the structure optimization drastically. This method allows us to explore a parameter space with a much higher dimension than before, which will improve the reliability of structure determinations considerably

Journal ArticleDOI
01 Nov 1993
TL;DR: In this paper, an approach for efficient control of the population dynamics in the presence of competing multiphoton transitions is developed and demonstrated for the state-selective vibrational excitation of the OH bond on a femtosecond time scale.
Abstract: An approach for efficient control of the population dynamics in the presence of competing multiphoton transitions is developed and demonstrated for the state-selective vibrational excitation of the OH bond on a femtosecond time scale. The controlling scheme includes coherent superposition of properly optimized infrared laser pulses.

Journal ArticleDOI
TL;DR: In this paper, a computational technique using the boundary element method for the prediction of sound radiated by axisymmetric bodies with arbitrary boundary conditions is presented, where the arbitrary boundary condition is expanded in a Fourier series with respect to the angle of revolution.
Abstract: This paper presents a computational technique using the boundary element method for the prediction of sound radiated by axisymmetric bodies with arbitrary boundary conditions. By taking advantage of the axisymmetric property of the body, the three‐dimensional integral formulation is reduced to a one‐dimensional integral along the generator of the body. The arbitrary boundary condition is expanded in a Fourier series with respect to the angle of revolution. The integral equation is solved using a superposition principle involving each term of the series. A numerical procedure is implemented using a curvilinear isoparametric element representation. Examples are given involving an oscillating sphere and a half vibrating sphere. The results are compared with the analytical solutions in which good agreement has been obtained.

Journal ArticleDOI
TL;DR: In this paper, a new family of mode-superposition methods for the computation of the forced response of proportionally damped systems with and without rigid body modes is investigated, which may be considered to be an extension of the mode-acceleration method.

Journal ArticleDOI
TL;DR: Nondegenerate oscillation is studied in the limit of a fast-decaying pump mode and states of definite signal-idler photon-number difference are generated, enabling preparation of a macroscopic superposition state.
Abstract: Nondegenerate oscillation is studied in the limit of a fast-decaying pump mode. The study is facilitated by analytic solutions of the positive P representation. In the absence of all individual signal and idler losses, states of definite signal-idler photon-number difference are generated. Determination of this photon number enables preparation of a macroscopic superposition state.

Journal ArticleDOI
TL;DR: In this article, the Gaussian beam approach is applied to atmospheric sound propagation in the presence of refraction above a ground surface, where a superposition of Gaussian beams along nearby rays is constructed.
Abstract: The Gaussian beam approach solves the wave equation in the neighborhood of the conventional rays using the parabolic approximation. The solution associates with each ray a beam having a Gaussian amplitude profile normal to the ray. The approximate overall solution for a given source is then constructed by a superposition of Gaussian beams along nearby rays. The solution removes ray‐tracing artifacts such as perfect shadows and infinite energy at caustics without the computational difficulties of numerical solutions to the wave equation. In this paper, the Gaussian beam approach is applied to atmospheric sound propagation in the presence of refraction above a ground surface. A brief overview of the method is presented. Calculations obtained from Gaussian beam tracing are compared to those obtained from the fast field program (FFP) and to experimental measurements. The experiments were made above a concave surface indoors that simulates propagation under downward refraction (inversion or downwind) in the cases of a hard and finite impedance surface. These experiments include measurements in the presence of a barrier. Measurements were also made in a wind tunnel in the presence of wind and temperature gradients. The results suggest that beam tracing can be applied to complex atmospheric sound propagation problems with advantages over conventional ray tracing and full‐wave solutions.

Journal ArticleDOI
TL;DR: In this article, a model of the self-fields associated with the charge density and current of the electron beam is incorporated into three-dimensional nonlinear formulations of the interaction in free-electron lasers for both planar and helical wiggler configurations.
Abstract: A model of the self‐fields associated with the charge density and current of the electron beam is incorporated into three‐dimensional nonlinear formulations of the interaction in free‐electron lasers for both planar and helical wiggler configurations. The model assumes the existence of a cylindrically symmetric electron beam with a flat‐top density profile and a uniform axial velocity, and the self‐electric and self‐magnetic fields are determined from Poisson’s equation and Ampere’s law. Diamagnetic and paramagnetic effects due the electron beam interaction with the wiggler field are neglected; hence, the model breaks down when the wiggler‐induced transverse displacement is comparable to the beam radius. The nonlinear formulations are based upon the arachne and wigglin codes, which represent slow‐time‐scale formulations for the evolution of the amplitudes and phases of a multimode superposition of vacuum waveguide modes. The electron dynamics in these codes are treated by means of the complete three‐dimen...

Journal ArticleDOI
TL;DR: In this paper, it was shown that multiphoton coherent states can be expressed as linear quantum superpositions of a finite number of generalized coherent states, which can be used to express non-classical effects such as oscillations in the photon number distribution, quadrature squeezing, SU(1, 1) squeezing and SU(2, 2) squeezing.
Abstract: We show that multiphoton coherent states can be expressed as linear quantum superpositions of a finite number of generalized coherent states. Quantum interferences between component states lead to appearance of non-classical effects such as oscillations in the photon number distribution, quadrature squeezing, SU(1, 1) squeezing and others.

Journal ArticleDOI
TL;DR: In this paper, a 2D Green's function is integrated to yield exact analytic expressions for the vector magnetic fields and Fourier transforms associated with thin film heads, which accurately represent the fields at all corners, both at the gap and at the pole edges.
Abstract: Analytical expressions for the vector magnetic fields and Fourier transforms associated with thin film heads are presented. These results are derived from accurate, approximate expressions for the surface field of an asymmetric thin film head determined from conformal mapping solutions. A 2D Green's function is integrated to yield exact analytic expressions for the fields, which are of no more complexity than the Karlqvist field approximations. In spite of their simplicity, these expressions accurately represent the fields at all corners, both at the gap and at the pole edges. These results are only approximate at spatial distances beyond the head edges and at wavelengths beyond about ten times the total head length. The Fourier transform of the surface field is also given in simple analytic form. As an example of the use of these expressions, it is shown how the effect of pole length to gap length ratio an pulse superposition can be easily estimated. >

Journal ArticleDOI
A. Saha1, Chuan-Lin Wu, Dun-Sung Tang
TL;DR: The authors derive some key properties of RBF networks that provide suitable grounds for implementing efficient search strategies for nonconvex optimization within the same framework.
Abstract: This paper concerns neural network approaches to function approximation and optimization using linear superposition of Gaussians (or what are popularly known as radial basis function (RBF) networks). The problem of function approximation is one of estimating an underlying function f, given samples of the form ((y/sub i/, x/sub i/); i=1,2,...,n; with y/sub i/=f(x/sub i/)). When the dimension of the input is high and the number of samples small, estimation of the function becomes difficult due to the sparsity of samples in local regions. The authors find that this problem of high dimensionality can be overcome to some extent by using linear transformations of the input in the Gaussian kernels. Such transformations induce intrinsic dimension reduction, and can be exploited for identifying key factors of the input and for the phase space reconstruction of dynamical systems, without explicitly computing the dimension and delay. They present a generalization that uses multiple linear projections onto scalars and successive RBF networks (MLPRBF) that estimate the function based on these scaler values. They derive some key properties of RBF networks that provide suitable grounds for implementing efficient search strategies for nonconvex optimization within the same framework. >