Showing papers on "Superposition principle published in 1996"

Observing the Progressive Decoherence of the 'Meter' in a Quantum Measurement

Abstract: A mesoscopic superposition of quantum states involving radiation fields with classically distinct phases was created and its progressive decoherence observed. The experiment involved Rydberg atoms interacting one at a time with a few photon coherent field trapped in a high $Q$ microwave cavity. The mesoscopic superposition was the equivalent of an `` $\mathrm{atom}+\mathrm{measuring}\mathrm{apparatus}$'' system in which the ``meter'' was pointing simultaneously towards two different directions---a ``Schr\"odinger cat.'' The decoherence phenomenon transforming this superposition into a statistical mixture was observed while it unfolded, providing a direct insight into a process at the heart of quantum measurement.

Electromagnetic dyadic Green's function in cylindrically multilayered media

Abstract: A spectral-domain dyadic Green's function for electromagnetic fields in cylindrically multilayered media with circular cross section is derived in terms of matrices of the cylindrical vector wave functions. Some useful concepts, such as the effective plane wave reflection and transmission coefficients, are extended in the present spectral domain eigenfunction expansion. The coupling coefficient matrices of the scattering dyadic Green's functions are given by applying the principle of scattering superposition. The general solution has been applied to the case of axial symmetry (n=0, n is eigenvalue parameter in /spl phi/ direction) where the scattering coefficients are decoupled between TM and TE waves. Two specific geometries, i.e., two- and three-layered media that are frequently employed to model the practical problems are considered in detail, and the coupling coefficient matrices of their dyadic Green's functions are given, respectively.

Photon Chopping: New Way to Measure the Quantum State of Light

Abstract: We propose the use of a balanced $2N$-port as a technique to measure the pure quantum state of a single-mode light field. In our scheme the coincidence signals of simple, realistic photodetectors are recorded at the output of the $2N$-port. We show that applying different arrangements both the modulus and the phase of the coefficients in a finite superposition state can be measured. In particular, the photon statistics can be so measured with currently available devices.

Wave propagation with rotating intensity distributions.

Abstract: Wave fields containing invariant features have recently stimulated the interest of the scientific community. Typical examples of such fields are Gaussian modes, Bessel beams @1#, and wave fronts containing phase dislocations @2#. Bessel beams are solutions of the wave equation that propagate with invariant intensity. Phase dislocations are discontinuities of the phase in a wave front such that the circulation of the phase around its axis is an integral multiple of 2p. Thus, they determine lines of zero intensity in space. Experimental evidences of optical dislocations can be found, for example, in Refs. @3‐5#. It was noted in Refs. @4,6# that, under certain circumstances, an array of dislocations nested in a Gaussian beam rotates by p/2 rad from the waist to the far field, expanding with the host beam. The objective of this paper is to investigate general solutions having rotating intensity distributions around and along the propagation axis. We start by demonstrating that these solutions are easily obtained in terms of the superposition of Gauss-Laguerre ~GL! modes. The rotation rate along the propagation is then derived and the set of all possible solutions presenting a specific total rotation angle is characterized. Finally, we analyze the limit of the rotation rate and present experimental results for optical beams. Let a scalar wave be represented by the function

A new coded-excitation ultrasound imaging system. I. Basic principles

Abstract: A new approach to ultrasound imaging with coded-excitation is presented. The imaging is performed by reconstruction of the scatterer strength on an assumed grid covering the region of interest (ROI). Our formulation is based on an assumed discretized signal model which represents the received sampled data vector as a superposition of impulse responses of all scatterers in the ROI. The reconstruction operator is derived from the pseudo-inverse of the linear operator (system matrix) that produces the received data vector. The singular value decomposition (SVD) method with appropriate regularization techniques is used for obtaining a robust realization of the pseudo-inverse. Under simplifying (but realistic) assumptions, the pseudo-inverse operator (PIO) can be implemented using a bank of transversal filters with each filter designed to extract echoes from a specified image line. This approach allows for the simultaneous acquisition of a large number of image lines. This could be useful in increasing frame rates for two-dimensional imaging systems or allowing for real-time implementation of three-dimensional imaging systems. When compared to the matched filtering approach to similar coded-excitation systems, our approach eliminates correlation artifacts that are known to plague such systems. Furthermore, the lateral resolution of the new system can exceed the diffraction limit imposed on conventional imaging systems utilizing delay-and-sum beamformers. The range resolution is compared to that of conventional pulse-echo systems with resolution enhancement (our PIO behaves as a pseudo-inverse Wiener filter in the range direction). Both simulation and experimental verification of these statements are given.

A fast new method to solve inverse scattering problems

Abstract: In this paper we present a new method for solving inverse obstacle scattering problems where the far field for many incident plane waves is known. The main idea of the method is to approximate point sources by a superposition of incident plane waves, to use a characterization of the obstacle in terms of the location of these point sources and to translate and rotate the approximating function. We will describe the method and provide numerical examples.

Superposition refinement of reactive systems

Abstract: Superposition refinement enhances an algorithm by superposing one computation mechanism onto another mechanism, in a way that preserves the behavior of the original mechanism. Superposition seems to be particularly well suited to the development of parallel and distributed programs: an originally simple sequential algorithm can be extended with mechanisms that distribute control and state information to many processes, thus permitting efficient parallel execution of the algorithm. We will show in this paper how superposition of reactive systems is expressed in the refinement calculus. We illustrate the power of this method by a case study, showing how a distributed broadcasting system is derived through a sequence of superposition refinements.

Estimation of the discrete Fourier transform, a linear inversion approach

Abstract: Spatio-temporal analysis of seismic records is of particular relevance in many geophysical applications, e.g., vertical seismic profiles, plane-wave slowness estimation in seismographic array processing and in sonar array processing. The goal is to estimate from a limited number of receivers the 2-D spectral signature of a group of events that are recorded on a linear array of receivers. When the spatial coverage of the array is small, conventional f-k analysis based on Fourier transform leads to f-k panels that are dominated by sidelobes. An algorithm that uses a Bayesian approach to design an artifacts-reduced Fourier transform has been developed to overcome this shortcoming. A by-product of the method is a high-resolution periodogram. This extrapolation gives the periodogram that would have been recorded with a longer array of receivers if the data were a limited superposition of monochromatic planes waves. The technique is useful in array processing for two reasons. First, it provides spatial extrapolation of the array (subject to the above data assumption) and second, missing receivers within and outside the aperture are treated as unknowns rather than as zeros. The performance of the technique is illustrated with synthetic examples for both broad-band and narrowband data. Finally, the applicability of the procedure is assessed analyzing the f-k spectral signature of a vertical seismic profile (VSP).

Construction of quantum states of the radiation field by discrete coherent-state superpositions

Abstract: An efficient method of quantum state engineering based on discrete superpositions of coherent states is presented. A systematic method is developed for obtaining optimized superpositions from the one-dimensional representation of the desired state. It is shown that superposition of even a small number of coherent states put along a straight line or on a circle in phase space can approximate nonclassical field states with a high degree of accuracy. An experimental scheme is proposed for generating equidistant coherent-state superpositions on a circle with arbitrary coefficients. \textcopyright{} 1996 The American Physical Society.

Global Analysis of Dynamic Light Scattering Autocorrelation Functions

Abstract: Dynamic light scattering has become a standard technique for investigating colloidal suspensions and polymer solutions. The experimental field autocorrelation function g 1 (t) can often be well modelled by a Laplace transform relating g 1 (t) to a distribution of decay times A(τ). In simple systems A(τ) can usually be directly related to a distribution of molecular weights, particle sizes, diffusion coefficients or other physically relevant quantities. With constrained regularization methods, the parameter-free estimation of A(τ) has become straightforward. In complex systems, the resulting A(τ) may contain several components the identification of which is not always obvious. The problem often originates in a superposition of diffusive and angle-independent components that have different variations of their respective decay times with the scattering vector. A method is presented based on a simultaneous fit of several autocorrelation functions measured at several different scattering angles, which, using simple and reasonable assumptions, yields a robust analysis of the spectra of decay times. The application of the method is illustrated on simulated autocorrelation functions and also on real experimental data obtained on a variety of different polymer systems.

Relaxation processes in coherent-population trapping

Abstract: The role played by a buffer gas in the ground-state superposition created in coherent-population-trapping experiments is investigated theoretically. The density matrix equations are solved on the basis of the coupled-noncoupled states. The velocity-changing collisions are examined in the limit of strong collisions. The relaxation rate for transfer of the ground-state superposition between atoms with different velocities is derived from a fit of available experimental results. {copyright} {ital 1996 The American Physical Society.}

Superposition dose calculation incorporating Monte Carlo generated electron track kernels.

Abstract: The superposition/convolution method and the transport of pregenerated Monte Carlo electron track data have been combined into the Super-Monte Carlo (SMC) method, an accurate 3-D x-ray dose calculation algorithm. The primary dose (dose due to electrons ejected by primary photons) is calculated by transporting pregenerated (in water) Monte Carlo electron tracks from each primary photon interaction site, weighted by the terma for that site. The length of each electron step is scaled by the inverse of the density of the medium at the beginning of the step. Because the density scaling of the electron tracks is performed for each individual transport step, the limitations of the macroscopic scaling of kernels (in the superposition algorithm) are overcome. This time-consuming step-by-step transport is only performed for the primary dose calculation, where current superposition methods are most lacking. The scattered dose (dose due to electrons set in motion by scattered photons) is calculated by superposition. In both a water-lung-water phantom and a two lung-block phantom, SMC dose distributions are more consistent with Monte Carlo generated dose distributions than are superposition dose distributions, especially for small fields and high energies-for an 18-MV, 5 X 5-cm(2) beam, the central axis dose discrepancy from Monte Carlo is reduced from 4.5% using superposition to 1.5% using SMC. The computation time for this technique is approximately 2 h (depending on the simulation history), 20 times slower than superposition, but 15 times faster than a full Monte Carlo simulation (on our platform).

Ray tracing in non-constant media

Abstract: In this paper, we explore the theory of optical deformations due to continuous variations of the refractive index of the air, and present several efficient implementations. We introduce the basic equations from geometrical optics, outlining a general method of solution. Further, we model the fluctuations of the index of refraction both as a superposition of blobs and as a stochastic function. Using a well known perturbation technique from geometrical optics, we compute linear approximations to the deformed rays. We employ this approximation and the blob representation to efficiently ray trace non linear rays through multiple environments. In addition we present a stochastic model for the ray deviations derived from an empirical model of air turbulence. We use this stochastic model to precompute deformation maps.

Harmonic-generation control

Abstract: In this paper we examine some effects of quantum interference on high harmonic generation. We demonstrate in particular that preparing the initial state in a coherent superposition of bound states leads to a harmonic spectrum with distinct plateaus with different conversion efficiencies. We show how this scheme may provide a way of controlling the coherent output that is produced in an experiment. \textcopyright{} 1996 The American Physical Society.

Effects of wave superposition on the polarization of electromagnetic ion cyclotron waves

Abstract: Using data from the Active Magnetospheric Particle Tracer Explorers/Charge Composition Explorer spacecraft, we make a detailed comparison between the observed polarization properties of electromagnetic ion cyclotron (EMIC) waves and those predicted by theory. The polarization can be described by three parameters: the ellipticity e, the ratio of parallel (to the background magnetic field B0) magnetic fluctuations δBz to the major axis component of the elliptical perturbation in the perpendicular plane δBmajor, and the phase angle between δBz and δBmajor. On the basis of the plasma parameters observed during EMIC events, we have calculated the linear properties of the theoretical modes and compared these to the observations. The result is that two and in some cases, three of the observed polarization properties are inconsistent with the assumption that the waves result from a single linear mode. We use a simple model with two constituent waves in various azimuthal orientations (around B0) and temporal phase relations and show that the distribution of observed polarization properties can be understood as resulting from the superposition of more than one mode. When there is superposition, the instantaneous polarization characteristics of the fluctuations do not reliably reflect the constituent wave properties and the minimum variance direction cannot be associated with a wave vector direction. Nonetheless, we have shown that the constituent wave properties can be inferred from the distribution of observed properties. For superposition of two waves with only slightly dissimilar characteristics, the constituent wave e is approximately the median observed e, e, and the constituent θkB (angle between the wave vector k and B0) is approximately given by tan θkB = δBz/δBmajor/e, with the overbar on δBz/δBmajor again indicating a median value.

Coherent Frequency Shift of Atomic Matter Waves.

Abstract: We demonstrate how Bragg diffraction of atomic matter waves at a time-modulated thick standing light wave can be used to coherently shift the de Broglie frequency of the diffracted atoms. The coherent frequency shift is experimentally confirmed by interferometric superposition of modulated and unmodulated atoms resulting in time-dependent interference fringes. Our frequency shifter for atomic matter waves is a generalization of an acousto-optic frequency shifter for photons. [S0031-9007(96)01871-6]

Derivative superposition-a linearisation technique for ultra broadband systems

Abstract: This paper summarises progress on a distortion reduction and nonlinear function synthesis technique called derivative superposition. The paper starts by reviewing the idea of derivative superposition. We show how low distortion amplifiers and function circuits such as frequency triplers can be designed. We review the results of a 4 HEMT low 3rd order distortion amplifier demonstrator. We consider the effect of the strong 2-port nonlinearity of a MESFET and show its effect on a 2 MESFET demonstrator. We describe progress on a software tool called "Super Deriv" that provides CAD support. We describe some alternative implementations of derivative superposition.

Quantum state measurement by realistic heterodyne detection.

Abstract: The determination of the quantum properties of a single-mode radiation field by heterodyne or double homodyne detection is studied. The realistic case of not fully efficient photodetectors is considered. It is shown that a large amount of quite precise information is available, whereas the completeness of such information is also discussed. Some examples are given and the special case of states expressed as a finite superposition of number states is considered in some detail. \textcopyright{} 1996 The American Physical Society.

A method to study the characteristics of 3D dose distributions created by superposition of many intensity-modulated beams delivered via a slit aperture with multiple absorbing vanes

Abstract: Highly conformal dose distributions can be created by the superposition of many radiation fields from different directions, each with its intensity spatially modulated by the method known as tomotherapy. At the planning stage, the intensity of radiation of each beam element (or bixel) is determined by working out the effect of superposing the radiation through all bixels with the elemental dose distribution specified as that from a single bixel with all its neighbours closed (the `independent-vane' (IV) model). However, at treatment-delivery stage, neighbouring bixels may not be closed. Instead the slit beam is delivered with parts of the beam closed for different periods of time to create the intensity modulation. As a result, the 3D dose distribution actually delivered will differ from that determined at the planning stage if the elemental beams do not obey the superposition principle. The purpose of this paper is to present a method to investigate and quantify the relation between planned and delivered 3D dose distributions. Two modes of inverse planning have been performed: (i) with a fit to the measured elemental dose distribution and (ii) with a `stretched fit' obeying the superposition principle as in the PEACOCK 3D planning system. The actual delivery has been modelled as a series of component deliveries (CDs). The algorithm for determining the component intensities and the appropriate collimation conditions is specified. The elemental beam from the NOMOS MIMiC collimator is too narrow to obey the superposition principle although it can be `stretched' and fitted to a superposition function. Hence there are differences between the IV plans made using modes (i) and (ii) and the raw and the stretched elemental beam, and also differences with CD delivery. This study shows that the differences between IV and CD dose distributions are smaller for mode (ii) inverse planning than for mode (i), somewhat justifying the way planning is done within PEACOCK. Using a stretched elemental beam is a useful adjustment to improve the accuracy of inverse planning but the 3D dose distribution actually delivered will display characteristics of the collimation.

Magnetic damping of buoyant convection during semiconductor crystal growth in microgravity. Continuous random g‐jitters

Abstract: This paper treats the buoyant convection of a liquid metal in a circular cylinder with a uniform, steady, axial magnetic field and with the random residual accelerations encountered on earth‐orbiting vehicles. The objective is to model the magnetic damping of the melt motion during semiconductor crystal growth by the Bridgman process in space. For a typical process with a magnetic flux density of 0.2 T, the convective heat transfer and the nonlinear inertial effects are negligible, so that the governing equations are linear. Therefore, for residual accelerations or ‘‘g‐jitters’’ whose directions are random functions of time, the buoyant convection is given by a superposition of the convections for two unidirectional accelerations: an axial acceleration which is parallel to the cylinder’s axis and a transverse acceleration which is perpendicular to this axis. Similarly, the response to accelerations whose amplitudes are random functions of time is given by a Fourier‐transform superposition of the buoyant c...

A simple calculation approach for the second harmonic sound field generated by an arbitrary axial‐symmetric source

Abstract: In a linear approximation, an arbitrary axial‐symmetric source can be expressed as the linear superposition of a set of Gaussian sources and the corresponding radiated sound field can be represented as the superposition of this set of Gaussian beams. The analysis is extended to the second harmonic generation due to nonlinear effects under a quasilinear approximation, then the second harmonic sound field could be considered as a sum of self‐ and cross‐interaction terms produced by a series of Gaussian beams. Therefore, the calculation of the second harmonic sound field of an axial‐symmetric source can be reduced to a simple linear combination of a set of exponential integral functions, instead of a complicated triple integral. In order to verify this calculation approach, the second harmonic generation of a focused and a simple piston source is examined, and the result is in good agreement with that in earlier paper by complicated computation.

On metric observers for nonlinear systems

Abstract: While observer design is well understood and widely used for linear systems, extensions to nonlinear systems have lacked generality. Motivated by fluid dynamics, this paper shows that the use of so-called Euler coordinates in general nonlinear, non-autonomous systems allows major simplifications such as a superposition principle, and leads to new analysis and design methods. A system's dynamic equations may be systematically shaped through a change of metric based on the available measurements, rather than by explicit error feedback. This in turn leads to new deterministic observer design techniques for general nonlinear non-autonomous systems.

An efficient computational model for the stress analysis of smart plate structures

Abstract: A variable kinematic finite element (VKFE) model based on an hierarchical, multiple assumed displacement field is combined with the mesh superposition technique to determine local stress fields in surface-bonded piezoelectric actuated plates The displacement field hierarchy contains both a conventional 2D plate expansion and the full layerwise expansion of Reddy The combination of VKFE and the mesh superposition technique further increases the computational efficiency and robustness of the computational algorithm to determine local stress fields and global response accurately

Theory of helix traveling wave tubes with dielectric and vane loading

Abstract: A time‐dependent nonlinear analysis of a helix traveling wave tube (TWT) is presented for a configuration where an electron beam propagates through a sheath helix surrounded by a conducting wall. The effects of dielectric and vane loading are included in the formulation as is efficiency enhancement by tapering the helix pitch. Dielectric loading is described under the assumption that the gap between the helix and the wall is uniformly filled by a dielectric material. The vane‐loading model describes the insertion of an arbitrary number of vanes running the length of the helix, and the polarization of the field between the vanes is assumed to be an azimuthally symmetric transverse‐electric mode. The field is represented as a superposition of azimuthally symmetric waves in a vacuum sheath helix. An overall explicit sinusoidal variation of the form exp(ikz−iωt) is assumed (where ω denotes the angular frequency corresponding to the wave number k in the vacuum sheath helix), and the polarization and radial variation of each wave is determined by the boundary conditions in a vacuum sheath helix. The propagation of each wave in vacuo as well as the interaction of each wave with the electron beam is included by allowing the amplitudes of the waves to vary in z and t. A dynamical equation for the field amplitudes is derived analogously to Poynting’s equation, and solved in conjunction with the three‐dimensional Lorentz force equations for an ensemble of electrons. Electron beams with a both a continuous and emission‐gated pulse format are analyzed, and the model is compared with linear theory of the interaction as well as with the performance of a TWTs operated at the Naval Research Laboratory and at Northrop–Grumman Corporation.