Showing papers on "Superposition principle published in 2006"

Quantifying Superposition

Abstract: Measures are introduced to quantify the degree of superposition in mixed states with respect to orthogonal decompositions of the Hilbert space of a quantum system These superposition measures can be regarded as analogues to entanglement measures, but can also be put in a more direct relation to the latter By a second quantization of the system it is possible to induce superposition measures from entanglement measures We consider the measures induced from relative entropy of entanglement and entanglement of formation We furthermore introduce a class of measures with an operational interpretation in terms of interferometry We consider the superposition measures under the action of subspace preserving and local subspace preserving channels The theory is illustrated with models of an atom undergoing a relaxation process in a Mach-Zehnder interferometer

Controllable generation of highly nonclassical states from nearly pure squeezed vacua

Abstract: We present controllable generation of various kinds of highly nonclassical states of light, including the single photon state and superposition states of mesoscopically distinct components. The high nonclassicality of the generated states is measured by the negativity of the Wigner function, which is largest ever observed to our knowledge. Our scheme is based on photon subtraction from a nearly pure squeezed vacuum, generated from an optical parametric oscillator with a periodically-poled KTiOPO$_4$ crystal as a nonlinear medium. This is an important step to realize basic elements of universal quantum gates, and to serve as a highly nonclassical input probe for spectroscopy and the study of quantum memory.

Bistatic scattering from three-dimensional layered rough surfaces

Abstract: An analytical method to calculate the bistatic-scattering coefficients of a three-dimensional layered dielectric structure with slightly rough interfaces is presented. The interfaces are allowed to be statistically distinct, but possibly dependent. The waves in each region are represented as a superposition of an infinite number of up- and down-going spectral components whose amplitudes are found by simultaneously matching the boundary conditions at both interfaces. A small-perturbation formulation is used up to the first order, and the scattered fields are derived. The calculation intrinsically takes into account multiple scattering processes between the boundaries. The formulation is then validated against known solutions to special cases. New results are generated for several cases of two- and three-layer media, which will be directly applicable for modeling of the signals from radar systems and subsequent estimation of a layered medium subsurface properties, such as moisture content and layer depths

Superresolved imaging in digital holography by superposition of tilted wavefronts.

Abstract: A technique based on superresolution by digital holographic microscopic imaging is presented. We used a two dimensional (2-D) vertical-cavity self-emitting laser (VCSEL) array as spherical-wave illumination sources. The method is defined in terms of an incoherent superposition of tilted wavefronts. The tilted spherical wave originating from the 2-D VCSEL elements illuminates the target in transmission mode to obtain a hologram in a Mach-Zehnder interferometer configuration. Superresolved images of the input object above the common lens diffraction limit are generated by sequential recording of the individual holograms and numerical reconstruction of the image with the extended spatial frequency range. We have experimentally tested the approach for a microscope objective with an exact 2-D reconstruction image of the input object. The proposed approach has implementation advantages for applications in biological imaging or the microelectronic industry in which structured targets are being inspected.

Formulation of correlations for general-type beams in atmospheric turbulence

Abstract: Log-amplitude and phase correlations of general-type beams are formulated in atmospheric turbulence. A general beam is described as the superposition of many sets of multimode contents, each mode being off-axis Hermite-Gaussian. Since the Rytov solution is utilized, the formulas are valid in the weakly turbulent regime. The results are presented in integral forms that should be numerically evaluated for the specific beam type of interest. Our general beam results correctly reduce to the existing solutions for the correlations of limiting-case beams such as higher-order single-mode, multimode, off-axis Hermite-Gaussian, Hermite-sinusoidal-Gaussian, higher-order-annular, flat-topped-Gaussian, and thus naturally fundamental mode, plane, and spherical waves. Scintillation index and phase fluctuations in atmospheric optical links employing such special beams will be examined in future using the results reported here.

Self-mixing differential vibrometer based on electronic channel subtraction

Abstract: An instrument for noncontact measurement of differential vibrations is developed, based on the self-mixing interferometer. As no reference arm is available in the self-mixing configuration, the differential mode is obtained by electronic subtraction of signals from two (nominally equal) vibrometer channels, taking advantage that channels are servo stabilized and thus insensitive to speckle and other sources of amplitude fluctuation. We show that electronic subtraction is nearly as effective as field superposition. Common-mode suppression is 25-30 dB, the dynamic range (amplitude) is in excess of 100 μm, and the minimum measurable (differential) amplitude is 20 nm on a B=10 kHz bandwidth. The instrument has been used to measure vibrations of two metal samples kept in contact, revealing the hysteresis cycle in the microslip and gross-slip regimes, which are of interest in the study of friction induced vibration damping of gas turbine blades for aircraft applications.

Bloch?Zener oscillations

Abstract: It is well known that a particle in a periodic potential with an additional constant force performs Bloch oscillations. Modulating every second period of the potential, the original Bloch band splits into two sub- bands. The dynamics of quantum particles shows a coherent superposition of Bloch oscillations and Zener tunnelling between the sub-bands, a Bloch-Zener oscillation. Such a system is modelled by a tight-binding Hamiltonian which is a system of two minibands with an easily controllable gap. The dynamics of the system is investigated by using an algebraic ansatz leading to a differential equation of Whittaker-Hill type. It is shown that the parameters of the system can be tuned to generate a periodic reconstruction of the wave packet and thus of the occupation probability. As an application, the construction of a matter wave beam splitter and a Mach-Zehnder interferometer is briefly discussed.

Continuous-variable teleportation in the characteristic-function description

Abstract: We give a description of the continuous-variable teleportation protocol in terms of the characteristic functions of the quantum states involved The Braunstein-Kimble protocol is written for an unbalanced homodyne measurement and arbitrary input and resource states We show that the output of the protocol is a superposition between the input one-mode field and a classical one induced by measurement and classical communication We choose to describe the input state distortion through teleportation by the average photon number of the measurement-induced field Only in the case of symmetric Gaussian resource states we find a relation between the optimal added noise and the minimal EPR correlations used to define inseparability

FDTD analysis of plane wave superposition to simulate susceptibility tests in reverberation chambers

Abstract: The behavior of a device in a reverberation chamber can be analyzed as the same device irradiated by random plane waves. This work proposes an application of the finite difference time domain method to analyze the device by using a superposition of random plane waves, simulating the behavior of a reverberation chamber. The analysis of a transmission line compared with theoretical and experimental results in a reverberation chamber is reported

Entanglement of superpositions.

Abstract: Given a bipartite quantum state (in arbitrary dimension) and a decomposition of it as a superposition of two others, we find bounds on the entanglement of the superposition state in terms of the entanglement of the states being superposed. In the case that the two states being superposed are biorthogonal, the answer is simple, and, for example, the entanglement of the superposition cannot be more than one ebit more than the average of the entanglement of the two states being superposed. However, for more general states, the situation is very different.

On the Achievable Sum Rate for MIMO Interference Channels

Abstract: In this correspondence, we study some information theoretical characteristics of vector Gaussian interference channels. Resorting to the superposition code technique, a lower bound of the sum capacity for the vector Gaussian interference channel is obtained. Alternatively, orthogonal transmission via frequency division multiplexing is considered and we establish the concavity of sum rate as the bandwidth allocation factor for the vector channel case. Numerical examples indicate that the achievable sum rate via the superposition code compares favorably with orthogonal transmission: the lower bound obtained via the superposition code dominates the best achievable sum rate through orthogonal transmission. This improvement holds for all interference power levels, a sharp contrast to that of the scalar counterpart

Generation of the basis sets for multi-Gaussian ultrasonic beam models--an overview.

Abstract: By using a small number of Gaussian basis functions, one can synthesize the wave fields radiated from planar and focused piston transducers in the form of a superposition of Gaussian beams. Since Gaussian beams can be transmitted through complex geometries and media, such multi-Gaussian beam models have become powerful simulation tools. In previous studies the basis function expansion coefficients of multi-Gaussian beam models have been obtained by both spatial domain and k-space domain methods. Here, we will give an overview of these two methods and relate their expansion coefficients. We will demonstrate that the expansion coefficients that have been optimized for circular piston transducers can also be used to generate improved field simulations for rectangular probes. It will also be shown that because Gaussian beams are only approximate (paraxial) solutions to the wave equation, a multi-Gaussian beam model is ultimately limited in the accuracy it can obtain in the very near field.

Multimode squeezing of frequency combs

Abstract: We have developed a full multimode theory of a synchronously pumped type-I optical parametric oscillator. We calculate the output quantum fluctuations of the device and find that, in the degenerate case (coincident signal and idler set of frequencies), significant squeezing is obtained when one approaches threshold from below for a set of well-defined ``supermodes,'' or frequency combs, consisting of a coherent linear superposition of signal modes of different frequencies which are resonant in the cavity.

Predicting surface scatter using a linear systems formulation of non-paraxial scalar diffraction

Abstract: Scattering effects from rough surfaces are non-paraxial diffraction phenomena resulting from random phase variations in the reflected wavefront. The ability to predict these effects is important in a variety of applications including x-ray and EUV imaging, the design of stray light rejection systems, and reflection modeling for rendering realistic scenes and animations of physical objects in computer graphics. Rayleigh-Rice (small perturbation method) and Beckmann-Kirchoff (Kirchhoff approximation) theories are commonly used to predict surface scatter effects. In addition, Harvey and Shack developed a linear systems formulation of surface scatter phenomena in which the scattering behavior is characterized by a surface transfer function. This treatment provided insight and understanding not readily gleaned from the two previous theories, and has been incorporated into a variety of computer software packages (ASAP, Zemax, Tracepro). However, smooth surface and paraxial approximations have severely limited the range of applicability of each of the above theoretical treatments. In this dissertation, a linear systems formulation of non-paraxial scalar diffraction theory is first developed and then applied to sinusoidal phase gratings, resulting in diffraction efficiency predictions far more accurate than those provided by classical scalar theories. The application of the theory to these gratings was motivated by the fact that rough surfaces are frequently modeled as a superposition of sinusoidal surfaces of different amplitudes, periods, and orientations. The application of the non-paraxial scalar diffraction theory to surface scatter phenomena resulted first in a modified Beckmann-Kirchhoff surface scattering model, then a generalized Harvey-Shack theory, both of which produce accurate results for rougher surfaces than the Rayleigh-Rice theory and for larger incident and scattering angles than the classical Beckmann-Kirchhoff theory. These new developments enable the analysis and simplify the understanding of wide-angle scattering behavior from rough surfaces illuminated at large incident angles. In addition, they provide an improved BRDF (Bidirectional Reflectance Distribution Function) model, particularly for the smooth surface inverse scattering problem of determining surface power spectral density (PSD) curves from BRDF measurements.

The classification of traveling wave solutions and superposition of multi-solutions to Camassa-Holm equation with dispersion

Abstract: Under the traveling wave transformation, Camassa-Holm equation with dispersion is reduced to an integrable ODE whose general solution can be obtained using the trick of one-parameter group. Furthermore combining complete discrimination system for polynomial, the classifications of all single traveling wave solutions to the Camassa-Holm equation with dispersion is obtained. In particular, an affine subspace structure in the set of the solutions of the reduced ODE is obtained. More general, an implicit linear structure in Camassa-Holm equation with dispersion is found. According to the linear structure, we obtain the superposition of multi-solutions to Camassa-Holm equation with dispersion.

Holographic spectral filter

Abstract: Method and apparatus are contemplated for receiving from an input, an optical signal in a volume hologram comprising a transfer function that may comprise temporal or spectral information, and spatial transformation information; diffracting the optical signal; and transmitting the diffracted optical signal to an output. A plurality of inputs and outputs may be coupled to the volume hologram. The transformation may be a linear superposition of transforms, with each transform acting on an input signal or on a component of an input signal. Each transform may act to focus one or more input signals to one or more output ports. A volume hologram may be made by various techniques, and from various materials. A transform function may be calculated by simulating the collision of a design input signal with a design output signal.

Self-consistent models of cuspy triaxial galaxies with dark matter haloes

Abstract: We have constructed realistic, self-consistent models of triaxial elliptical galaxies embedded in triaxial dark matter haloes. We examined three different models for the shape of the dark matter halo: (i) the same axis ratios as the luminous matter (0.7:0.86:1); (ii) a more prolate shape (0.5:0.66:1); (iii) a more oblate shape (0.7:0.93:1). The models were obtained by means of the standard orbital superposition technique introduced by Schwarzschild. Self-consistent solutions were found in each of the three cases. Chaotic orbits were found to be important in all of the models,and their presence was shown to imply a possible slow evolution of the shapes of the haloes. Our results demonstrate for the first time that triaxial dark matter haloes can co-exist with triaxial galaxies.

A time-space decomposition method for calculating the nearfield pressure generated by a pulsed circular piston

Abstract: A time-space decomposition approach is derived for numerical calculations of the transient nearfield pressure generated by a circular piston. Time-space decomposition analytically separates the temporal and spatial components of a rapidly converging single integral expression, thereby converting transient nearfield pressure calculations into the superposition of a small number of fast-converging spatial integrals that are weighted by time-dependent factors. Results indicate that, for the same peak error value, time-space decomposition is at least one or two orders of magnitude faster than the Rayleigh-Sommerfeld integral, the Schoch integral, the Field II program, and the DREAM program. Time-space decomposition is also faster than methods that directly calculate the impulse response by at least a factor of 3 for a 10% peak error and by a factor of 17 for a 1% peak error. The results show that, for a specified maximum error value, time-space decomposition is significantly faster than the impulse response and other analytical integrals evaluated for computations of transient nearfield pressures generated by circular pistons.

The discontinuous enrichment method for elastic wave propagation in the medium‐frequency regime

Abstract: The discontinuous enrichment method (DEM) is specified and developed for the solution of two-dimensional elastic wave propagation problems in the frequency domain. The classical finite element polynomial approximation of the displacement field is enriched by the superposition of discontinuous pressure and shear wave functions. The continuity of the solution across the element interfaces is weakly enforced by suitable Lagrange multipliers. Higher-order rectangular DEM elements are constructed and benchmarked against the standard higher-order polynomial Galerkin elements for two-dimensional problems in the medium frequency regime. In general, it is found that for such applications, DEM can achieve the same accuracy as the p finite element method using a similar computational complexity but with about 10 times fewer degrees of freedom. This highlights the potential of this hybrid method for problems where the scale of vibrations is very small compared to the characteristic dimension of the physical medium. Copyright © 2006 John Wiley & Sons, Ltd.

Polarization operator approach to electron-positron pair production in combined laser and Coulomb fields

Abstract: The optical theorem is applied to the process of electron-positron pair creation in the superposition of a nuclear Coulomb and a strong laser field. We derive representations for the total production rate as twofold integrals, both for circular laser polarization and for the general case of elliptic polarization. Our approach allows us to obtain, by analytical means, the asymptotic behavior of the pair creation rate for various limits of interest. In particular, we consider pair production by two-photon absorption and show that, close to the energetic threshold of this process, the rate obeys a power law in the laser frequency with different exponents for linear and circular laser polarization. With the help of the upcoming x-ray laser sources, our results could be tested experimentally.

Multiple Edge Responses for Fast and Accurate System Simulations

Abstract: Fast and accurate simulation of the system response is important in high-speed I/O system design because performance is severely limited by channel ISI and random noise. This paper presents a novel way to simulate the signal response given an arbitrary bit pattern using multiple edge responses (MER). The presented method provides an accuracy improvement over the traditional approaches which either uses the superposition of single bit response (SBR) or double edge response (DER), while maintaining the equivalent numerical efficiency.

Macroscopic superpositions of superfluid flows

Abstract: We present a scheme for creating macroscopic superpositions of the direction of superfluid flow around a loop. Using the Bose-Hubbard model we study an array of Bose-Einstein condensates trapped in optical potentials and coupled to one another to form a ring. By rotating the ring so that each particle acquires on average half a quantum of superfluid flow, it is possible to create a multiparticle superposition of all the particles rotating and all the particles stationary. Under certain conditions it is possible to scale up the number of particles to form a macroscopic superposition. The simplicity of the model has allowed us to study macroscopic superpositions at an atomic level for different variables. Here we concentrate on the tunnelling strength between the potentials. Further investigation remains important, because it could lead us to making an ultra-precise quantum-limited gyroscope.

Vector mode analysis of a young interferometer.

Abstract: It is proved that, when the vector modal theory of coherence is applied to a pair of fixed points, exact results are obtained for the mode structure. In particular, it is shown that the field radiated by the pinholes of a Young interferometer can always be represented by the incoherent superposition of no more than four perfectly correlated and polarized modes. The role of such modes is illustrated through a simple example.