Showing papers on "Superposition principle published in 2004"

Negativity of the Wigner function as an indicator of nonclassicality

Abstract: A measure of nonclassicality of quantum states based on the volume of the negative part of the Wigner function is proposed. We analyze this quantity for Fock states, squeezed displaced Fock states and cat-like states defined as coherent superposition of two Gaussian wave packets.

Diffuse fields in open systems and the emergence of the Green’s function (L)

Abstract: As is now well known, the relation between diffuse field correlations and the Green’s function follows directly from a definition of a diffuse field as an uncorrelated smooth spectral superposition of normal modes. Such a definition is, however, inapplicable in most open structures, the earth in particular. A preferable definition might be that of room acoustics: a diffuse field is an uncorrelated isotropic superposition of plane waves. But that definition is inapplicable to heterogeneous structures, or near boundaries. Here, a definition of a local diffuse field applicable to open heterogeneous systems is proposed. A local diffuse field is taken to be one in steady‐state equilibrium with the field in a homogeneous region having an uncorrelated isotropic superposition of incident plane waves. This definition is applicable to both heterogeneous and open systems, and is shown using a reciprocity argument to lead to the familiar identity between the local Green’s function of the structure and the diffuse fields correlations.

Parabolic nondiffracting optical wave fields

Abstract: We demonstrate the existence of parabolic beams that constitute the last member of the family of fundamental nondiffracting wave fields and determine their associated angular spectrum. Their transverse structure is described by parabolic cylinder functions, and contrary to Bessel or Mathieu beams their eigenvalue spectrum is continuous. Any nondiffracting beam can be constructed as a superposition of parabolic beams, since they form a complete orthogonal set of solutions of the Helmholtz equation. A novel class of traveling parabolic waves is also introduced for the first time.

Conditional production of superpositions of coherent states with inefficient photon detection

Abstract: It is shown that a linear superposition of two macroscopically distinguishable optical coherent states can be generated using a single photon source and simple all-optical operations. Weak squeezing on a single photon, beam mixing with an auxiliary coherent state, and photon detecting with imperfect threshold detectors are enough to generate a coherent state superposition in a free propagating optical field with a large coherent amplitude (alpha>2) and high fidelity (F>0.99). In contrast to all previous schemes to generate such a state, our scheme does not need photon number resolving measurements nor Kerr-type nonlinear interactions. Furthermore, it is robust to detection inefficiency and exhibits some resilience to photon production inefficiency.

Push-Pull Optical Pumping of Pure Superposition States

Abstract: A new optical pumping method, "push-pull pumping," can produce very nearly pure, coherent superposition states between the initial and the final sublevels of the important field-independent 0-0 clock resonance of alkali-metal atoms. The key requirement for push-pull pumping is the use of D1 resonant light which alternates between left and right circular polarization at the Bohr frequency of the state. The new pumping method works for a wide range of conditions, including atomic beams with almost no collisions, and atoms in buffer gases with pressures of many atmospheres.

Signal modeling for low-coherence height-scanning interference microscopy

Abstract: We propose a computationally efficient theoretical model for low-coherence interferometric profilers that measure surface heights by scanning the optical path difference of the interferometer. The model incorporates both geometric and spectral effects by means of an incoherent superposition of ray bundles through the interferometer spanning a range of wavelengths, incident angles, and pupil plane coordinates. This superposition sum is efficiently performed in the frequency domain, followed by a Fourier transform to generate the desired simulated interference signal. Example applications include white-light interferometry, high-numerical-aperture microscopy with a near-monochromatic light source, and interference microscopy for thickness and topography analysis of thin-film structures and other complex surface features.

Remote preparation of a single-mode photonic qubit by measuring field quadrature noise.

Abstract: An electromagnetic field quadrature measurement, performed on one of the modes of the nonlocal single-photon state alpha|1,0>-beta|0,1>, collapses it into a superposition of the single-photon and vacuum states in the other mode. We use this effect to implement remote preparation of arbitrary single-mode photonic qubits conditioned on observation of a preselected quadrature value. The preparation efficiency of the resulting qubit can be higher than that of the initial single photon.

Casimir-Polder forces: A nonperturbative approach

Abstract: Within the frame of macroscopic QED in linear, causal media, we study the radiation force of Casimir-Polder type acting on an atom which is positioned near dispersing and absorbing magnetodielectric bodies and initially prepared in an arbitrary electronic state. It is shown that minimal and multipolar coupling lead to essentially the same lowest-order perturbative result for the force acting on an atom in an energy eigenstate. To go beyond perturbation theory, the calculations are based on the exact center-of-mass equation of motion. For a nondriven atom in the weak-coupling regime, the force as a function of time is a superposition of force components that are related to the electronic density matrix elements at a chosen time. Even the force component associated with the ground state is not derivable from a potential in the ususal way, because of the position dependence of the atomic polarizability. Further, when the atom is initially prepared in a coherent superposition of energy eigenstates, then temporally oscillating force components are observed, which are due to the interaction of the atom with both electric and magnetic fields.

Mixed vortex states of light as information carriers

Abstract: An original method for encoding of information into the spatial structure of mixed vortex states of light is proposed. It is based on the creation of pseudo-nondiffracting vortex patterns representing a controllable superposition of optical vortices with different topological charges. Weight coefficients of the superposition serve as carriers of information. The different topological charges of the vortices are used as 'markers' enabling vortex spatial separation and information decoding. The proposed concept of information encoding is verified experimentally by means of a spatial light modulator.

Hollow elliptical Gaussian beam and its propagation through aligned and misaligned paraxial optical systems.

Abstract: A new mathematical model called hollow elliptical Gaussian beam (HEGB) is proposed to describe a dark-hollow laser beam with noncircular symmetry in terms of a tensor method. The HEGB can be expressed as a superposition of a series of elliptical Hermite–Gaussian modes. By using the generalized diffraction integral formulas for light passing through paraxial optical systems, analytical propagation formulas for HEGBs passing through paraxial aligned and misaligned optical systems are obtained through vector integration. As examples of applications, evolution properties of the intensity distribution of HEGBs in free-space propagation were studied. Propagation properties of HEGBs through a misaligned thin lens were also studied. The HEGB provides a convenient way to describe elliptical dark-hollow laser beams and can be used conveniently to study the motion of atoms in a dark-hollow laser beam.

The complex equivalent source method for sound propagation over an impedance plane.

Abstract: The sound field caused by a monopole source above an impedance plane can be calculated by using a superposition of equivalent point sources located along a line in the mirror space below the plane. Originally, such an approach for representing the half-space Green’s function was described by Sommerfeld at the beginning of the last century, in order to treat half-space problems of heat conduction. However, the representation converges only for masslike impedances and cannot be used for the more important case of reflecting planes with springlike surface impedances. The singular part of the line integral can be transformed into a Hankel function, which shows that surface waves are contained in the whole solution. Unfortunately, this representation suffers from the lack of validity at certain receiver points and from restrictions on wave number and impedance range to ensure the necessary convergence. The main idea of the present method is to use also a superposition of equivalent point sources, but to allow that these sources can be located at complex source points. The corresponding form of the half-space Green’s function is suitable for both masslike and springlike surface impedances, and can be used as a cornerstone for a boundary element method.

Tailoring photonic entanglement in high-dimensional Hilbert spaces

Abstract: We present an experiment where two photonic systems of arbitrary dimensions can be entangled. The method is based on spontaneous parametric down-conversion with trains of d pump pulses with a fixed phase relation, generated by a mode-locked laser. This leads to a photon pair created in a coherent superposition of d discrete emission times, given by the successive laser pulses. Entanglement is shown by performing a two-photon interference experiment and by observing the visibility of the interference fringes increasing as a function of the dimension d. Factors limiting the visibility, such as the presence of multiple pairs in one train, are discussed.

Two-photon interference with thermal light

Abstract: The study of entangled states has greatly improved the basic understanding about two-photon interferometry. Two-photon interference is not the interference of two photons but the result of superposition among indistinguishable two-photon amplitudes. The concept of two-photon amplitude, however, has generally been restricted to the case of entangled photons. In this letter we report an experimental study that may extend this concept to the general case of independent photons. The experiment also shows interesting practical applications regarding the possibility of obtaining high-resolution interference patterns with thermal sources.

Generation of macroscopic superposition states with small nonlinearity

Abstract: We suggest a scheme to generate a macroscopic superposition state (Schrodinger cat state) of a free-propagating optical field using a beam splitter, homodyne measurement, and a very small Kerr nonlinear effect. Our scheme makes it possible to reduce considerably the required nonlinear effect to generate an optical cat state using simple and efficient optical elements.

Controlled rotation in a double quantum dot structure

Abstract: The coherent manipulation of a double quantum dot system by an external driving field is analyzed. Using a controlled rotation method a general superposition state of the lower states is formed. Several interaction schemes are discussed and analytic results are presented. These are found to agree very well with the results of numerical simulations.

Generation and selection of laser beams represented by a superposition of two angular harmonics

Abstract: The properties of fields generated by diffractive phase-only optical elements that generate combinations of two angular harmonic fields with different harmonic indices in Fraunhofer and Fresnel regions are investigated theoretically and experimentally Camomile shaped diffraction patterns are predicted and observed It is shown that multi-order diffractive phase elements can be used to both generate these beams and to identify the weights of different angular harmonics in a given incident laser beam

A size criterion for macroscopic superposition states

Abstract: An operational measure to quantify the sizes of some 'macroscopic quantum superpositions', realized in recent experiments, is proposed. The measure is based on the fact that a superposition presents greater sensitivity in interferometric applications than its superposed constituent states. This enhanced sensitivity, or 'interference utility', may then be used as a size criterion among superpositions.

Complex mode superposition algorithm for seismic responses of non-classically damped linear mdof system

Abstract: This paper deals with a complex mode superposition method for the seismic responses of general multiple degrees of freedom (MDOF) discrete system with complex eigenvectors and eigenvalues. A delicate general solution, completely in real value form, for calculating seismic time history response of the MDOF system which cannot be uncoupled by normal modes, is deduced based on the algorithms of the complex superposition method. This solution comprises of two parts which are in relation to the Duhamel integration to sine and cosine function respectively. The related term of the Duhamel integration to sine function is actually the displacement response of the oscillator with corresponding modal frequency and the damping ratio. The other can be transferred into a combination of the displacement and velocity responses of the same oscillator. In order to meet the practical needs of seismic design based on code design spectra for various kinds of structures equipped by viscous dampers, the complex complete quadratic combination (CCQC) method is deduced following similar procedures such as the well-known CQC method, in which a new modal velocity correlation coefficient, together with a new modal displacement-velocity correlation coefficient are involved besides the modal displacement correlation coefficient in normal CQC formula. The new algorithm of CCQC is not only as concise as that of the normal CQC but also has explicit physical meaning. The results obtained from complex mode superposition approaches are discussed and verified in some examples through step by step integration computation under a prescribed earthquake motion input. From these examplary analyses, it may be pointed that the CCQC algorithm normally yields conservative outcome and that the forced mode uncoupling approach has good approximation even the discussed examplary structures are strongly non-proportional.

Modeling the Excitation of Lamb and SH Waves by Point and Line Sources

Abstract: The guided wave field excited in a plate‐like structure from any weakly coupled transducer can be calculated from the superposition of the guided wave fields due to a number of suitable point or line excitation sources. In this paper, the fields from various point and line excitation sources are reviewed and relationships between them are demonstrated. The performance of pancake coil EMATs is modeled using the superposition of the fields from point sources and the results compared with experiment.

Effect of time-dependent basis functions and their superposition error on atom-centered density matrix propagation (ADMP): connections to wavelet theory of multiresolution analysis.

Abstract: We present a rigorous analysis of the primitive Gaussian basis sets used in the electronic structure theory. This leads to fundamental connections between Gaussian basis functions and the wavelet theory of multiresolution analysis. We also obtain a general description of basis set superposition error which holds for all localized, orthogonal or nonorthogonal, basis functions. The standard counterpoise correction of quantum chemistry is seen to arise as a special case of this treatment. Computational study of the weakly bound water dimer illustrates that basis set superposition error is much less for basis functions beyond the 6-31+G(*) level of Gaussians when structure, energetics, frequencies, and radial distribution functions are to be calculated. This result will be invaluable in the use of atom-centered Gaussian functions for ab initio molecular dynamics studies using Born-Oppenheimer and atom-centered density matrix propagation.