Showing papers on "Superposition principle published in 2008"
TL;DR: In this article, the role of quantum coherence in the efficiency of excitation transfer in a ring-hub arrangement of interacting two-level systems was investigated, mimicking a light harvesting antenna connected to a reaction center as it is found in natural photosynthetic systems.
Abstract: We investigate the role of quantum coherence in the efficiency of excitation transfer in a ring-hub arrangement of interacting two-level systems, mimicking a light-harvesting antenna connected to a reaction center as it is found in natural photosynthetic systems. By using a quantum jump approach, we demonstrate that in the presence of quantum coherent energy transfer and energetic disorder, the efficiency of excitation transfer from the antenna to the reaction center depends intimately on the quantum superposition properties of the initial state. In particular, we find that efficiency is sensitive to symmetric and asymmetric superposition of states in the basis of localized excitations, indicating that initial-state properties can be used as an efficiency control parameter at low temperatures.
315 citations
TL;DR: In this paper, a single electron spin on a single quantum dot has been demonstrated for a variety of photonic and information processing applications, including quantum information storage and quantum repeaters.
Abstract: Coherent population trapping is a process by which a particle is induced to exist in a superposition of two ground states. This has now been demonstrated for an electron spin on a single quantum dot, which could prove useful in a variety of photonic and information-processing applications. Coherent population trapping (CPT) refers to the steady-state trapping of population in a coherent superposition of two ground states that are coupled by coherent optical fields to an intermediate state in a three-level atomic system1. Recently, CPT has been observed in an ensemble of donor-bound spins in GaAs (ref. 2) and in single nitrogen-vacancy centres in diamond3 by using a fluorescence technique. Here, we report the demonstration of CPT of an electron spin in a single quantum dot. The observation demonstrates both the CPT of an electron spin and the successful generation of Raman coherence between the two spin ground states of the electron4,5,6. This technique can be used to initialize, at about a gigahertz rate, an electron spin state in an arbitrary superposition by varying the ratio of the Rabi frequencies between the driving and probe fields. The results show the potential importance of charged quantum dots for a solid-state approach to the implementation of electromagnetically induced transparency7,8, slow light9, quantum information storage10 and quantum repeaters11,12.
202 citations
TL;DR: The presented method was found to be accurate in a wide range of conditions making it suitable for clinical planning purposes and compared against Monte Carlo simulations in several phantoms including lung- and bone-type heterogeneities.
Abstract: In this work, a novel three-dimensional superposition algorithm for photon dose calculation is presented. The dose calculation is performed as a superposition of pencil beams, which are modified based on tissue electron densities. The pencil beams have been derived from Monte Carlo simulations, and are separated into lateral and depth-directed components. The lateral component is modeled using exponential functions, which allows accurate modeling of lateral scatter in heterogeneous tissues. The depth-directed component represents the total energy deposited on each plane, which is spread out using the lateral scatter functions. Finally, convolution in the depth direction is applied to account for tissue interface effects. The method can be used with the previously introduced multiple-source model for clinical settings. The method was compared against Monte Carlo simulations in several phantoms including lung- and bone-type heterogeneities. Comparisons were made for several field sizes for 6 and 18 MV energies. The deviations were generally within (2%, 2 mm) of the field central axis dmax. Significantly larger deviations (up to 8%) were found only for the smallest field in the lung slab phantom for 18 MV. The presented method was found to be accurate in a wide range of conditions making it suitable for clinical planning purposes.
126 citations
TL;DR: Analytical formulas for the elements of the 2x2 cross-spectral density matrix of a kind of stochastic electromagnetic array beam propagating through the turbulent atmosphere are derived with the help of vector integration and it is shown that for the array beam composed by isotropic Gaussian-Schell model sources, the spectral degree of polarization in the sufficiently far field returns to the value of the array source.
Abstract: Analytical formulas for the elements of the 2×2 cross-spectral density matrix of a kind of stochastic electromagnetic array beam propagating through the turbulent atmosphere are derived with the help of vector integration. Two types of superposition (i.e. the correlated superposition and the uncorrelated superposition) are considered. The changes in the spectral density and in the spectral degree of polarization of such an array beam generated by isotropic or anisotropic electromagnetic Gaussian Schell-model sources on propagation are determined by the use of the analytical formulas. It is shown by numerical calculations that for the array beam composed by isotropic Gaussian-Schell model sources, the spectral degree of polarization in the sufficiently far field returns to the value of the array source; for the array beam composed by anisotropic sources, the spectral degree of polarization in the far field approaches a fixed value that is different from the source.
109 citations
TL;DR: In this article, an approximate free energy surface and transition rates for alanine dipeptide for a variety of force fields and implicit solvent models are presented based upon local minima, transition states and pathways characterised for each potential energy surface using geometry optimisation.
108 citations
TL;DR: It was found that neurons track unexpectedly fast transients, as their response amplitude has no attenuation up to 200 Hz, higher than the limits set by passive membrane properties and average firing rate and is not affected by the rate of change of the input.
Abstract: Cortical neurons are often classified by current-frequency relationship. Such a static description is inadequate to interpret neuronal responses to time-varying stimuli. Theoretical studies suggested that single-cell dynamical response properties are necessary to interpret ensemble responses to fast input transients. Further, it was shown that input-noise linearizes and boosts the response bandwidth, and that the interplay between the barrage of noisy synaptic currents and the spike-initiation mechanisms determine the dynamical properties of the firing rate. To test these model predictions, we estimated the linear response properties of layer 5 pyramidal cells by injecting a superposition of a small-amplitude sinusoidal wave and a background noise. We characterized the evoked firing probability across many stimulation trials and a range of oscillation frequencies (1-1000 Hz), quantifying response amplitude and phase-shift while changing noise statistics. We found that neurons track unexpectedly fast transients, as their response amplitude has no attenuation up to 200 Hz. This cut-off frequency is higher than the limits set by passive membrane properties (approximately 50 Hz) and average firing rate (approximately 20 Hz) and is not affected by the rate of change of the input. Finally, above 200 Hz, the response amplitude decays as a power-law with an exponent that is independent of voltage fluctuations induced by the background noise.
107 citations
TL;DR: This work considers the superoscillatory area fraction of random optical speckle patterns, which follows from the joint probability density function of intensity and phase gradient for isotropic Gaussian random wave superpositions.
Abstract: Waves are superoscillatory where their local phase gradient exceeds the maximum wavenumber in their Fourier spectrum. We consider the superoscillatory area fraction of random optical speckle patterns. This follows from the joint probability density function of intensity and phase gradient for isotropic Gaussian random wave superpositions. Strikingly, this fraction is 1/3 when all the waves in the two-dimensional superposition have the same wavenumber. The fraction is 1/5 for a disk spectrum. Although these superoscillations are weak compared with optical fields with designed superoscillations, they are more stable on paraxial propagation.
104 citations
TL;DR: In this article, an enhanced spectral finite element (SFE) formulation is proposed to calculate the time-transient response in cylindrical waveguides, in which material damping is included allowing for complex stress-strain viscoelastic constitutive relations in force of the correspondence principle.
100 citations
TL;DR: In this paper, the authors considered the initial value problem for a nonlinear version of the dissipative Timoshenko system and employed the time weighed L2 energy method which is combined with the optimal L2 decay estimates for lower order derivatives of solutions.
Abstract: We consider the initial value problem for a nonlinear version of the dissipative Timoshenko system. This syetem verifies the decay property of regularity-loss type. To overcome this difficulty caused by the regularity-loss property, we employ the time weighed L2 energy method which is combined with the optimal L2 decay estimates for lower order derivatives of solutions. Then we show the global existence and asymptotic decay of solutions under smallness and enough regularity conditions on the initial data. Moreover, we show that the solution approaches the linear diffusion wave expressed in terms of the superposition of the heat kernels as time tends to infinity.
90 citations
TL;DR: In this paper, the authors show that one can form integral superpositions of such Gaussian beams to generate more general high frequency solutions to PDEs and show that the observed behavior is in agreement with the predictions of Maslov theory.
Abstract: High frequency solutions to partial differential equations (PDEs) are notoriously difficult to simulate numerically due to the large number of grid points required to resolve the wave oscillations. In applications, one often must rely on approximate solution methods to describe the wave field in this regime. Gaussian beams are asymptotically valid high frequency solutions concen- trated on a single curve through the domain. We show that one can form integral superpositions of such Gaussian beams to generate more general high frequency solutions to PDEs. As a particular example, we look at high frequency solutions to the constant coefficient wave equation and construct Gaussian beam solutions with Taylor expansions of several orders. Since this PDE can be solved via a Fourier transform, we use the Fourier transform solution to gauge the error of the constructed Gaussian beam superposition solutions. Furthermore, we look at an example for which the solution exhibits a cusp caustic and investigate the order of magnitude of the wave amplitude as a function of frequency at the tip of the cusp. We show that the observed behavior is in agreement with the predictions of Maslov theory.
88 citations
22 Aug 2008
TL;DR: This paper substantially extended the operation range of deep-submicron CMOS for terahertz applications by using a linear superposition method, in which a 324GHz frequency generator in 90nm digital CMOS with 4GHz tuning range under 1V supply voltage is realized.
Abstract: This paper presents CMOS for terahertz applications, substantially extended the operation range of deep-submicron CMOS by using a linear superposition method, in which we have realized a 324GHz frequency generator in 90nm digital CMOS with 4GHz tuning range under 1V supply voltage.
TL;DR: In this article, a multiconfiguration method with a large electronic basis set is used to compute the response of all the electrons of LiH to a few-cycle intense pump field followed by a probe pulse.
Abstract: A time-dependent multiconfiguration method with a large electronic basis set is used to compute the response of all the electrons of LiH to a few-cycle intense pump field followed by a probe pulse. The ultrashort pump pulse excites a coherent superposition of stationary electronic states and, by changing the pump parameters such as intensity, duration, polarization and phase of carrier frequency, one can steer the motion of the electrons. Particular attention is given to the control provided by the polarization and by the phase. For example, a change in polarization is used to select an electronic wave packet that is rotating in a plane perpendicular to the bond or rotation in a plane containing the bond. The electronic wave packet can be probed by a delayed second pulse. This delayed probe pulse is also included in the Hamiltonian with the result that the frequency dispersed probe spectrum can be computed and displayed as a two-dimensional plot.
TL;DR: It is shown that the motion of the plate is indeed a superposition of bending waves following the theoretical dispersion relation of the linear wave equation and the nonlinearities seem to efficiently break the coherence of the waves so that no modal structure is observed.
Abstract: An thin elastic steel plate is excited with a vibrator and its local velocity displays a turbulentlike Fourier spectrum. This system is believed to develop elastic wave turbulence. We analyze here the motion of the plate with a two-point measurement in order to check, in our real system, a few hypotheses required for the Zakharov theory of weak turbulence to apply. We show that the motion of the plate is indeed a superposition of bending waves following the theoretical dispersion relation of the linear wave equation. The nonlinearities seem to efficiently break the coherence of the waves so that no modal structure is observed. Several hypotheses of the weak turbulence theory seem to be verified, but nevertheless the theoretical predictions for the wave spectrum are not verified experimentally.
TL;DR: A novel, fast, and accurate method to simulate the time-domain system response using multiple edge responses (MER) based on linear superposition and peak distortion analysis, which is commonly used to find the worst-case data pattern based on SBR, is extended for DER and MER using dynamic programming.
Abstract: High-speed input/output (I/O) link performance is limited by random noise as well as signal integrity issues such as dispersion, reflections, and crosstalk. Hence, accurate prediction of system performance including these random and deterministic noise is crucial in high-speed link design. This paper presents a novel, fast, and accurate method to simulate the time-domain system response. The presented method calculates the system response using multiple edge responses (MER) based on linear superposition. Being able to take into account system nonlinearity more accurately, the presented method significantly improves simulation accuracy compared with the other published fast simulation techniques based on either single bit response (SBR) or double edge responses (DER), while at the same time maintaining equivalent numerical efficiency. Furthermore, peak distortion analysis, which is commonly used to find the worst-case data pattern based on SBR, is extended for DER and MER using dynamic programming. A multiphase worst-case data pattern approach is also introduced in this paper in order to determine the worst-case system performance under both timing and voltage consideration.
TL;DR: In this article, a measure for the size of a quantum superposition of two many-body states with (supposedly) macroscopically distinct properties by counting how many single-particle operations are needed to map one state onto the other is proposed.
Abstract: We propose a measure for the ``size'' of a quantum superposition of two many-body states with (supposedly) macroscopically distinct properties by counting how many single-particle operations are needed to map one state onto the other This definition gives sensible results for simple, analytically tractable cases and is consistent with a previous definition restricted to Greenberger-Horne-Zeilinger-like states We apply our measure to the experimentally relevant, nontrivial example of a superconducting three-junction flux qubit put into a superposition of left- and right-circulating supercurrent states, and we find the size of this superposition to be surprisingly small
TL;DR: The effects of phase holography artifacts on quantum-state generation are quantified and a prescription for avoiding these artifacts by preconditioning the hologram function is presented.
Abstract: There has been considerable interest recently in the generation of azimuthal phase functions associated with photon orbital angular momentum (OAM) for high-dimensional quantum key distribution. The generation of secure quantum keys requires not only this pure phase basis but also additional bases comprised of orthonormal superposition states formed from the pure states. These bases are also known as mutually unbiased bases (MUBs) and include quantum states whose wave functions are modulated in both phase and amplitude. Although modulo 2π optical path control with high-resolution spatial light modulators (SLMs) is well suited to creating the azimuthal phases associated with the pure states, it does not introduce the amplitude modulation associated with the MUB superposition states. Using computer-generated holography (CGH) with the Leith-Upatnieks approach to hologram recording, however, both phase and amplitude modulation can be achieved. We present a description of the OAM states of a three-dimensional MUB system and analyze the construction of these states via CGH with a phase-modulating SLM. The effects of phase holography artifacts on quantum-state generation are quantified and a prescription for avoiding these artifacts by preconditioning the hologram function is presented. Practical effects associated with spatially isolating the first-order diffracted field are also quantified, and a demonstration utilizing a liquid-crystal SLM is presented.
TL;DR: In this paper, a reduced-order-modeling approach for nonlinear, multi-degree-of-freedom aerodynamic systems using multi-input Volterra theory is presented.
Abstract: This paper presents a reduced-order-modeling approach for nonlinear, multi-degree-of-freedom aerodynamic systems using multi-input Volterra theory. The method is applied to a two-dimensional, 2 degree-of-freedom transonic airfoil undergoing simultaneous forced pitch and heave harmonic oscillations. The so-called Volterra cross kernels are identified and shown to successfully model the aerodynamic nonlinearities associated with the simultaneous pitch and heave motions. The improvements in accuracy over previous approaches that effectively ignored the cross kernels by using superposition are demonstrated.
TL;DR: In this article, the authors compared three widely used pull-in theoretical models (i.e., one-dimensional lumped model, linear supposition model and planar model) by considering both cantilever and fixed-fixed type mi cro and nano-switches.
Abstract: The existing three widely used pull-in theoretical models (i.e., one-dimensional lumped model, linear supposition model and planar model) are compared with the nonlinear beam mode in this paper by considering both cantilever and fixed-fixed type mi cro and nano-switches. It is found that the error o f the pull-in parameters between one-dimensional lumped model and the nonlinear beam model is large because the denominator of the electrostatic force is minim al when the electrostatic force is computed at the maximum deflection along the beam. Since both the linear superposition model and the slender planar model consider the variation of electrostatic force with the beam’s deflection, these two models not o nly are of the same type but also own little error of the pull-in parameters with the nonlinear beam model, the error brought by these two models attributes to tha t the boundary conditions are not completely satisf ied when computing the numerical integration of the def lection.
TL;DR: In this paper, exact solutions to the nonlinear Schr\"odinger equation (NLSE) in the presence of self-steepening and a self-frequency shift are found.
Abstract: We find exact solutions to the nonlinear Schr\"odinger equation (NLSE) in the presence of self-steepening and a self-frequency shift. These include periodic solutions and localized solutions of dark-bright type which can be chiral, the chirality being controlled by the sign of the self-steepening term. A form of self-phase-modulation that can be tuned by higher-order nonlinearities as well as by the initial conditions, distinct from the nonlinear Schr\"odinger equation, characterizes these solutions. In certain nontrivial parameter domains, solutions are found to satisfy the linear Schr\"odinger equation, indicating the possibility of linear superposition in this nonlinear system. Dark and bright solitons exist in both the anomalous and normal dispersion regimes, and a duality between the dark-bright type of solution and kinematic higher-order chirping is also seen. Localized kink solutions similar to NLSE solitons, but with very different self-phase-modulation, are identified.
TL;DR: It is shown that improvements in resolution are obtained at the expense of sensitivity to noise and a method of quantifying this sensitivity is presented and generalization of the technique for the case of multimode media is suggested.
Abstract: The paper describes a general approach for processing data from a guided wave transducer array on a plate-like structure. The raw data set from such an array contains time-domain signals from each transmitter–receiver combination. The technique is based on linear superposition of signals in the frequency domain with some amplitude and phase factors and can be applied to any array geometry and any types of array elements. The problem of finding optimal coefficients, which allow the best resolution to be achieved with the minimum number of array elements, is investigated. It is shown that improvements in resolution are obtained at the expense of sensitivity to noise. A method of quantifying this sensitivity is presented. Results are shown that illustrate the application of the technique to a linear array and an array of circular geometry (containing a single ring of elements). Experimental data obtained from a guided wave array containing electromagnetic acoustic transducer elements for exciting and detecti...
TL;DR: In this article, the entanglement of superposition of multi-state states is investigated in three cases when the states in the superposition are mutually biorthogonal, mutually orthogonal and non-orthogonal.
Abstract: In this letter, we investigate the entanglement of superposition of multi-states. Three cases are considered when the states in the superposition are mutually biorthogonal, mutually orthogonal and nonorthogonal. The relations between the entanglement of superposition and the entanglements of the superposed states are explored.
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TL;DR: In this paper, various strategies have been devised to discriminate optimally between non-orthogonal states and some of the optical experiments that have been performed to realize these, as a fundamental consequence of the superposition principle for quantum states.
Abstract: It is a fundamental consequence of the superposition principle for quantum states that there must exist non-orthogonal states, that is states that, although different, have a non-zero overlap. This finite overlap means that there is no way of determining with certainty in which of two such states a given physical system has been prepared. We review the various strategies that have been devised to discriminate optimally between non-orthogonal states and some of the optical experiments that have been performed to realise these.
TL;DR: In this paper, a non-force-free magnetic field is derived from vector magnetograms, where the boundary conditions are at least two layers of vector magnetogram, one at the photospheric level and the other at the chromospheric scale.
Abstract: We develop an approach to deriving the three-dimensional non-force-free coronal magnetic field from vector magnetograms. Based on the principle of minimum dissipation rate, a general non-force-free magnetic field is expressed as the superposition of one potential field and two constant-α (linear) force-free fields. Each is extrapolated from its bottom boundary data, providing the normal component only. The constant-α parameters are distinct and determined by minimizing the deviations between the numerically computed and measured transverse magnetic field at the bottom boundary. The boundary conditions required are at least two layers of vector magnetograms, one at the photospheric level and the other at the chromospheric level, presumably. We apply our approach to a few analytic test cases, especially to two nonlinear force-free cases examined by Schrijver et al. (Solar Phys.235, 161, 2006). We find that for one case with small α parameters, the quantitative measures of the quality of our result are better than the median values of those from a set of nonlinear force-free methods. The reconstructed magnetic-field configuration is valid up to a vertical height of the transverse scale. For the other cases, the results remain valid to a lower vertical height owing to the limitations of the linear force-free-field solver. Because our method is based on the fast-Fourier-transform algorithm, it is much faster and easy to implement. We discuss the potential usefulness of our method and its limitations.
TL;DR: Considering the simultaneous propagation of multicomponent fields in an isotropic medium, an N-coupled nonlinear Schrödinger system with the self- phase modulation, cross-phase modulation, and energy exchange terms is investigated and shows that such a system admits the Painlevé property.
Abstract: Considering the simultaneous propagation of multicomponent fields in an isotropic medium, an $N$-coupled nonlinear Schr\"odinger system with the self-phase modulation, cross-phase modulation, and energy exchange terms is investigated in this paper. First, via symbolic computation, the Painlev\'e singularity structure analysis shows that such a system admits the Painlev\'e property. Then, with the Ablowitz-Kaup-Newell-Segur scheme, the linear eigenvalue problem (Lax pair) associated with this model is constructed in the frame of the block matrices. With the Hirota bilinear method, the bright one- and two-soliton solutions of this system are presented. In addition, the bright multisoliton solutions of the system for $N=2$ are straightforwardly derived by the linear superposition of soliton solutions of two independent scalar nonlinear Schr\"odinger equations. Furthermore, through the analysis for the soliton solutions, the corresponding propagation behavior and applications for soliton pulses in nonlinear optical fibers are considered. Finally, three significant conserved quantities, i.e., energy, momentum, and Hamiltonian, are also given.
TL;DR: It is argued that the emergence of the asymmetry provides a useful probe of nonequilibrium solvation on the excited state potential surface of heterodyne-detected and time-resolved nonlinear time-domain rephasing and nonrephasing signals generated in three-pulse experiments and the corresponding frequency-domain two-dimensional spectra.
Abstract: Optical response functions are known to reflect quantum dynamics in a superposition state and as such, lack a well-defined classical limit. In a previous paper we considered the importance of accounting for the quantum nature of the dynamics by comparing the linear absorption spectrum and homodyne-detected time-integrated two-pulse photon-echo signal as calculated via the semiclassical forward-backward approach, linearized semiclassical approach, and standard approach which is based on equilibrium ground state dynamics [Shi and Geva, J. Chem. Phys. 122, 064506 (2005)]. In the present paper, we extend the comparison to the case of heterodyne-detected and time-resolved nonlinear time-domain rephasing and nonrephasing signals generated in three-pulse experiments and the corresponding frequency-domain two-dimensional spectra. The comparison is performed in the context of a two-state chromophore solvated in a nonpolar liquid. It is shown that the inherent insensitivity of the standard method to the nonequilibrium dynamics on the excited state potential surface gives rise to two-dimensional spectra which are symmetrical relative to the diagonal. In contrast, accounting for the effect of nonequilibrium excited state dynamics, as is the case within the forward-backward and linearized semiclassical methods, is found to give rise to two-dimensional spectra that become increasingly asymmetrical relative to the diagonal as the waiting time between the second and third pulses becomes larger. It is argued that the emergence of the asymmetry provides a useful probe of nonequilibrium solvation on the excited state potential surface.
TL;DR: In this paper, the ultra-weak variational formulation (UWVF) for fluid-solid vibration problems is introduced, where the authors consider the scattering of time-harmonic acoustic pressure waves from solid, elastic objects.
TL;DR: In this article, the authors describe the numerical prediction of noise transmission loss (TL) through sandwich plates subjected to an acoustic plane wave or a diffuse sound field excitation, based on a finite element formulation for the sandwich plate coupled to a boundary element method for the acoustic medium.
Abstract: This study describes the numerical prediction of noise transmission loss (TL) through sandwich plates subjected to an acoustic plane wave or a diffuse sound field excitation. The sandwich plate considered is made up of a viscoelastic core sandwiched between two elastic faces. The model presented is based on a finite element formulation for the sandwich plate coupled to a boundary element method for the acoustic medium. The plate formulation is derived from Kirchhoff's theory for the elastic faces and Mindlin's theory for the core. The strain and kinetic energies of the sandwich plates are written in terms of the mean and relative in-plane displacements of the faces and the transverse deflection of the plate. The diffuse sound field is modeled as a superposition of uncorrelated plane waves with equal amplitude. The vibroacoustic equations obtained are discretized using a triangular finite element. The accuracy of the present model is demonstrated by comparing it with analytical and experimental results ava...
TL;DR: In this paper, the authors proposed a modal analysis of complex three-dimensional framed structures, optionally with lumped masses and/or elastic supports, and established orthogonal conditions for different natural modes, and hence transient response analysis based on mode superposition.
TL;DR: In this paper, the centers of solitons were treated as point particles and their discrete dynamics were studied by using variational calculus, and the authors showed that the dynamics of the quasi-particles obey a pseudo-Newtonian law.
TL;DR: Kolařik et al. as discussed by the authors derived a new type of internal time-tensile strain superposition for a series of single-step nonlinear tensile creeps.