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Showing papers on "Superposition principle published in 2013"


Journal ArticleDOI
TL;DR: In this article, a review is given of an experimentally falsifiable phenomenological proposal, known as continuous spontaneous collapse, which is a stochastic nonlinear modification of the Schrodinger equation.
Abstract: Quantum mechanics is an extremely successful theory that agrees with every experimental test. However, the principle of linear superposition, a central tenet of the theory, apparently contradicts a commonplace observation: macroscopic objects are never found in a linear superposition of position states. Moreover, the theory does not explain why during a quantum measurement, deterministic evolution is replaced by probabilistic evolution, whose random outcomes obey the Born probability rule. In this article a review is given of an experimentally falsifiable phenomenological proposal, known as continuous spontaneous collapse: a stochastic nonlinear modification of the Schr\"odinger equation, which resolves these problems, while giving the same experimental results as quantum theory in the microscopic regime. Two underlying theories for this phenomenology are reviewed: trace dynamics and gravity-induced collapse. As the macroscopic scale is approached, predictions of this proposal begin to differ appreciably from those of quantum theory and are being confronted by ongoing laboratory experiments that include molecular interferometry and optomechanics. These experiments, which test the validity of linear superposition for large systems, are reviewed here, and their technical challenges, current results, and future prospects summarized. It is likely that over the next two decades or so, these experiments can verify or rule out the proposed stochastic modification of quantum theory.

901 citations


Journal ArticleDOI
19 Apr 2013-Science
TL;DR: It is demonstrated that the near-field interference of a circularly polarized dipole results in the unidirectional excitation of guided electromagnetic modes in the near field, with no preferred far-field radiation direction.
Abstract: Wave interference is a fundamental manifestation of the superposition principle with numerous applications. Although in conventional optics, interference occurs between waves undergoing different phase advances during propagation, we show that the vectorial structure of the near field of an emitter is essential for controlling its radiation as it interferes with itself on interaction with a mediating object. We demonstrate that the near-field interference of a circularly polarized dipole results in the unidirectional excitation of guided electromagnetic modes in the near field, with no preferred far-field radiation direction. By mimicking the dipole with a single illuminated slit in a gold film, we measured unidirectional surface-plasmon excitation in a spatially symmetric structure. The surface wave direction is switchable with the polarization.

626 citations


Journal ArticleDOI
07 Feb 2013-Nature
TL;DR: A general analytic approach to the characterization of diffractive imaging systems that can be described as low-rank mixed states is provided and some of the most stringent experimental conditions in ptychography can be relaxed, and susceptibility to imaging artefacts is reduced.
Abstract: Progress in imaging and metrology depends on exquisite control over and comprehensive characterization of wave fields. As reflected in its name, coherent diffractive imaging relies on high coherence when reconstructing highly resolved images from diffraction intensities alone without the need for image-forming lenses. Fully coherent light can be described adequately by a single pure state. Yet partial coherence and imperfect detection often need to be accounted for, requiring statistical optics or the superposition of states. Furthermore, the dynamics of samples are increasingly the very objectives of experiments. Here we provide a general analytic approach to the characterization of diffractive imaging systems that can be described as low-rank mixed states. We use experimental data and simulations to show how the reconstruction technique compensates for and characterizes various sources of decoherence quantitatively. Based on ptychography, the procedure is closely related to quantum state tomography and is equally applicable to high-resolution microscopy, wave sensing and fluctuation measurements. As a result, some of the most stringent experimental conditions in ptychography can be relaxed, and susceptibility to imaging artefacts is reduced. Furthermore, the method yields high-resolution images of mixed states within the sample, which may include quantum mixtures or fast stationary stochastic processes such as vibrations, switching or steady flows.

486 citations


Journal ArticleDOI
TL;DR: It is demonstrated how synthetic chemistry allows us to prepare libraries of fluorous porphyrins which can be tailored to exhibit high mass, good thermal stability and relatively low polarizability, which allows for successful superposition experiments with selected species from these molecular libraries in a quantum interferometer, which utilizes the diffraction of matter-waves at an optical phase grating.
Abstract: The quantum superposition principle, a key distinction between quantum physics and classical mechanics, is often perceived as a philosophical challenge to our concepts of reality, locality or space-time since it contrasts with our intuitive expectations with experimental observations on isolated quantum systems. While we are used to associating the notion of localization with massive bodies, quantum physics teaches us that every individual object is associated with a wave function that may eventually delocalize by far more than the body's own extension. Numerous experiments have verified this concept at the microscopic scale but intuition wavers when it comes to delocalization experiments with complex objects. While quantum science is the uncontested ideal of a physical theory, one may ask if the superposition principle can persist on all complexity scales. This motivates matter–wave diffraction and interference studies with large compounds in a three-grating interferometer configuration which also necessitates the preparation of high-mass nanoparticle beams at low velocities. Here we demonstrate how synthetic chemistry allows us to prepare libraries of fluorous porphyrins which can be tailored to exhibit high mass, good thermal stability and relatively low polarizability, which allows us to form slow thermal beams of these high-mass compounds, which can be detected using electron ionization mass spectrometry. We present successful superposition experiments with selected species from these molecular libraries in a quantum interferometer, which utilizes the diffraction of matter–waves at an optical phase grating. We observe high-contrast quantum fringe patterns of molecules exceeding a mass of 10 000 amu and having 810 atoms in a single particle.

253 citations


Journal ArticleDOI
13 Dec 2013-Science
TL;DR: An experimental system capable of detecting a single photon without destroying it is described and the large single-photon nonlinearity of the experiment should enable the development of photonic quantum gates and the preparation of exotic quantum states of light.
Abstract: All optical detectors to date annihilate photons upon detection, thus excluding repeated measurements. Here, we demonstrate a robust photon detection scheme that does not rely on absorption. Instead, an incoming photon is reflected from an optical resonator containing a single atom prepared in a superposition of two states. The reflection toggles the superposition phase, which is then measured to trace the photon. Characterizing the device with faint laser pulses, a single-photon detection efficiency of 74% and a survival probability of 66% are achieved. The efficiency can be further increased by observing the photon repeatedly. The large single-photon nonlinearity of the experiment should enable the development of photonic quantum gates and the preparation of exotic quantum states of light.

216 citations


Journal ArticleDOI
TL;DR: In this article, the authors demonstrate how synthetic chemistry can be used to prepare libraries of fluorous porphyrins which can be tailored to exhibit high mass, good thermal stability and relatively low polarizability, which allows them to form slow thermal beams of these high-mass compounds, which can then be detected in electron ionization mass spectrometry.
Abstract: The quantum superposition principle, a key distinction between quantum physics and classical mechanics, is often perceived as a philosophical challenge to our concepts of reality, locality or space-time since it contrasts our intuitive expectations with experimental observations on isolated quantum systems. While we are used to associating the notion of localization with massive bodies, quantum physics teaches us that every individual object is associated with a wave function that may eventually delocalize by far more than the body's own extension. Numerous experiments have verified this concept at the microscopic scale but intuition wavers when it comes to delocalization experiments with complex objects. While quantum science is the uncontested ideal of a physics theory, one may ask if the superposition principle can persist on all complexity scales. This motivates matter-wave diffraction and interference studies with large compounds in a three-grating interferometer configuration which also necessitates the preparation of high-mass nanoparticle beams at low velocities. Here we demonstrate how synthetic chemistry allows us to prepare libraries of fluorous porphyrins which can be tailored to exhibit high mass, good thermal stability and relatively low polarizability, which allows us to form slow thermal beams of these high-mass compounds, which can be detected in electron ionization mass spectrometry. We present successful superposition experiments with selected species from these molecular libraries in a quantum interferometer, which utilizes the diffraction of matter waves at an optical phase grating. We observe high-contrast quantum fringe patterns with molecules exceeding a mass of 10 000 amu and 810 atoms in a single particle.

161 citations


Journal ArticleDOI
Miles Blencowe1
TL;DR: It is shown that gravity as an environment induces the rapid decoherence of stationary matter superposition states when the energy differences in the superposition exceed the Planck energy scale.
Abstract: Adopting the viewpoint that the standard perturbative quantization of general relativity provides an effective description of quantum gravity that is valid at ordinary energies, we show that gravity as an environment induces the rapid decoherence of stationary matter superposition states when the energy differences in the superposition exceed the Planck energy scale.

158 citations


Journal ArticleDOI
TL;DR: In this paper, a phase-matching condition for enhancement of sensitivity in a Mach-Zehnder interferometer illuminated by an arbitrary state in one input port and an odd (even) state in the other port was found.
Abstract: We find a phase-matching condition for enhancement of sensitivity in a Mach-Zehnder interferometer illuminated by an arbitrary state in one input port and an odd (even) state in the other port. Under this condition, the Fisher information becomes maximal with respect to the relative phase of two modes, and the phase sensitivity is enhanced. For the case with photon losses, we further find that the phase-matching condition remains unchanged with a coherent state and a coherent superposition state as the input states.

143 citations


Journal ArticleDOI
TL;DR: A theoretical approach is developed to calculate the radiation force of an arbitrary acoustic beam on an elastic sphere in a liquid or gas medium by employing conventional angular spectrum decomposition to derive expressions for components of the radiation stress tensor.
Abstract: A theoretical approach is developed to calculate the radiation force of an arbitrary acoustic beam on an elastic sphere in a liquid or gas medium. First, the incident beam is described as a sum of plane waves by employing conventional angular spectrum decomposition. Then, the classical solution for the scattering of a plane wave from an elastic sphere is applied for each plane-wave component of the incident field. The net scattered field is expressed as a superposition of the scattered fields from all angular spectrum components of the incident beam. With this formulation, the incident and scattered waves are superposed in the far field to derive expressions for components of the radiation stress tensor. These expressions are then integrated over a spherical surface to analytically describe the radiation force on an elastic sphere. Limiting cases for particular types of incident beams are presented and are shown to agree with known results. Finally, the analytical expressions are used to calculate radiation forces associated with two specific focusing transducers.

143 citations


Posted Content
TL;DR: Solving a tractable convex program is shown to locate the elements of the support with high precision as long as they are separated by 2/f and the noise level is small with respect to the amplitude of the signal.
Abstract: We study the problem of super-resolving a superposition of point sources from noisy low-pass data with a cut-off frequency f. Solving a tractable convex program is shown to locate the elements of the support with high precision as long as they are separated by 2/f and the noise level is small with respect to the amplitude of the signal.

120 citations


Journal ArticleDOI
TL;DR: The first experimental results on SOP evolution of vector soliton molecules with periodic polarisation switching between two and three SOPs and superposition of polarisation Switching with SOP precessing are presented.
Abstract: Two fundamental laser physics phenomena - dissipative soliton and polarisation of light are recently merged to the concept of vector dissipative soliton (VDS), viz. train of short pulses with specific state of polarisation (SOP) and shape defined by an interplay between anisotropy, gain/loss, dispersion, and nonlinearity. Emergence of VDSs is both of the fundamental scientific interest and is also a promising technique for control of dynamic SOPs important for numerous applications from nano-optics to high capacity fibre optic communications. Using specially designed and developed fast polarimeter, we present here the first experimental results on SOP evolution of vector soliton molecules with periodic polarisation switching between two and three SOPs and superposition of polarisation switching with SOP precessing. The underlying physics presents an interplay between linear and circular birefringence of a laser cavity along with light induced anisotropy caused by polarisation hole burning.

Journal ArticleDOI
TL;DR: In this paper, a class of trilinear differential operators is introduced through a technique of assigning signs to derivatives and used to create triliear differential equations, which are characterized by the Bell polynomials and applied to the construction of resonant solutions of exponential waves.
Abstract: A class of trilinear differential operators is introduced through a technique of assigning signs to derivatives and used to create trilinear differential equations. The resulting trilinear differential operators and equations are characterized by the Bell polynomials, and the superposition principle is applied to the construction of resonant solutions of exponential waves. Two illustrative examples are made by an algorithm using weights of dependent variables.

Journal ArticleDOI
TL;DR: Novel intensity and polarization patterns obtained from the superposition of two vector LG beams may find applications in the field of molecular imaging, optical manipulation, atom optics, and optical lattices.
Abstract: We present a systematic study of the superposition of two vector Laguerre-Gaussian (LG) beams. Propagation depended field distribution obtained from the superposition of two vector LG beams has many interesting features of intensity and polarization. Characteristic inhomogeneous polarization distribution of the vector LG beam appears in the form of azimuthally modulated intensity and polarization distributions in the superposition of the beams. We found that the array of polarization singular points, whose number depends upon the azimuthal indices of the two beams, evolves during propagation of the field. The position and number of C-points generated in the field were analyzed using Stokes singularity relations. Novel intensity and polarization patterns obtained from the superposition of two vector LG beams may find applications in the field of molecular imaging, optical manipulation, atom optics, and optical lattices.

Journal ArticleDOI
TL;DR: A practical method enabling us to infer the optimal temporal mode directly from experimental data acquired via homodyne detection, without any assumptions on the state is reported.
Abstract: The characterization or subsequent use of a propagating optical quantum state requires the knowledge of its precise temporal mode. Defining this mode structure very often relies on a detailed a priori knowledge of the used resources, when available, and can additionally call for an involved theoretical modeling. In contrast, here we report on a practical method enabling us to infer the optimal temporal mode directly from experimental data acquired via homodyne detection, without any assumptions on the state. The approach is based on a multimode analysis using eigenfunction expansion of the autocorrelation function. This capability is illustrated by experimental data from the preparation of Fock states and coherent state superposition.

Journal ArticleDOI
TL;DR: In this paper, a closed-form solution for evaluating the dynamical behavior of a general multi-span Bernoulli-Euler beam is derived by applying the boundary conditions to the characteristic function of a beam.

Journal ArticleDOI
TL;DR: In this article, the authors present a methodology to determine the horizontal and vertical shift coefficients to be applied to the isotherms of storage and loss moduli measured using the Bueche-Rouse theory.

Journal ArticleDOI
TL;DR: In this paper, the Winkler model was used to obtain analytic bending solutions of free rectangular thin plates resting on elastic foundations, based on a new symplectic superposition method, which was able to solve the problem analytically.

Journal ArticleDOI
TL;DR: The aim of this paper is to investigate the main aspects of the synthesis of plane wave generators (PWGs), i.e., arrays capable of emulating a plane wave, or a superposition of plane waves, in a given region.
Abstract: The aim of this paper is to investigate the main aspects of the synthesis of plane wave generators (PWGs) i.e., arrays capable of emulating a plane wave, or a superposition of plane waves, in a given region. In particular, we introduce new figures of merit, particularly suitable for PWG synthesis procedures, and simple guidelines regarding size and shape of the PWG, as well as the number of radiating sources needed to synthesize the required plane waves. The performance limits of a PWG are analyzed, in terms of indexes related to the stability of the solution and to the level of the field amplitude on the lateral walls of the anechoic chamber in which the PWG is placed. Finally we present a synthesis method for PWGs, based on a planar sparse array architecture. Starting from the previously achieved results, a novel effective synthesis procedure is introduced. By means of such a procedure we are also able to take explicitly into account the mechanical and electrical tolerances in the PWG realization. In such a way we can assure the best performances, given the unavoidable errors in the positioning and excitation of the radiating elements.

Journal ArticleDOI
TL;DR: In this work, a fragment-orbital density functional theory-based method is combined with two different non-adiabatic schemes for the propagation of the electronic degrees of freedom to perform unbiased simulations of electron transfer processes in complex media.
Abstract: In this work, a fragment-orbital density functional theory-based method is combined with two different non-adiabatic schemes for the propagation of the electronic degrees of freedom. This allows us to perform unbiased simulations of electron transfer processes in complex media, and the computational scheme is applied to the transfer of a hole in solvated DNA. It turns out that the mean-field approach, where the wave function of the hole is driven into a superposition of adiabatic states, leads to over-delocalization of the hole charge. This problem is avoided using a surface hopping scheme, resulting in a smaller rate of hole transfer. The method is highly efficient due to the on-the-fly computation of the coarse-grained DFT Hamiltonian for the nucleobases, which is coupled to the environment using a QM/MM approach. The computational efficiency and partial parallel character of the methodology make it possible to simulate electron transfer in systems of relevant biochemical size on a nanosecond time scale. Since standard non-polarizable force fields are applied in the molecular-mechanics part of the calculation, a simple scaling scheme was introduced into the electrostatic potential in order to simulate the effect of electronic polarization. It is shown that electronic polarization has an important effect on the features of charge transfer. The methodology is applied to two kinds of DNA sequences, illustrating the features of transfer along a flat energy landscape as well as over an energy barrier. The performance and relative merit of the mean-field scheme and the surface hopping for this application are discussed.

Journal ArticleDOI
TL;DR: In this article, the sensitivity analysis of structural acoustic performance in presence of non-proportional damping and optimal layout design of the damping layer of vibrating shell structures under harmonic excitations are discussed.

Journal ArticleDOI
TL;DR: In this article, the authors derived quantum master and filter equations for systems coupled to fields in certain non-classical continuous-mode states, such as single photon states and superpositions of coherent states.
Abstract: The purpose of this paper is to determine quantum master and filter equations for systems coupled to fields in certain non-classical continuous-mode states. Specifically, we consider two types of field states (i) single photon states, and (ii) superpositions of coherent states. The system and field are described using a quantum stochastic unitary model. Master equations are derived from this model and are given in terms of systems of coupled equations. The output field carries information about the system, and is continuously monitored. The quantum filters are determined with the aid of an embedding of the system into a larger non-Markovian system, and are given by a system of coupled stochastic differential equations.

Journal ArticleDOI
TL;DR: In this article, the exact configurations of the four dimensional Skyrme model are presented and the static configurations have the profile which behaves as a kink and the corresponding energy momentum tensor describes a domain wall.
Abstract: Exact configurations of the four dimensional Skyrme model are presented The static configurations have the profile which behaves as a kink and, consequently, the corresponding energy momentum tensor describes a domain wall Furthermore, a class of exact time periodic Skyrmions is discovered Within such class, it is possible to disclose a remarkable phenomenon which is a genuine effect of the Skyrme term For a special value of the frequency the Skyrmions admit a non linear superposition principle One can combine two or more exact elementary Skyrmions (which may depend in a non trivial way on all the space like coordinates) into a new exact composite Skyrmion Due to such superposition law, despite the explicit presence of non linear effects in the energy momentum tensor, the interaction energy between the elementary Skyrmions can be computed exactly The relations with the appearance of Skyrme crystals is discussed

Journal ArticleDOI
TL;DR: In this paper, the existence of time-periodic, small amplitude solutions of autonomous quasi-linear or fully nonlinear completely resonant pseudo-PDEs of Benjamin-Ono type in Sobolev class was proved.

Proceedings ArticleDOI
12 May 2013
TL;DR: In this paper, a mechanically-dark mode is proposed to overcome the thermal motion of a mechanical oscillator to its motional ground state. But it is not suitable for quantum information processing.
Abstract: Summary form only given. Thermal mechanical motion hinders the use of a mechanical system in applications such as quantum information processing. A straightforward, but technically challenging, approach to overcome the thermal motion is to cool the mechanical oscillator to its motional ground state. An alternative approach, as proposed recently, is to exploit the use of a mechanically-dark mode, which is a special coherent superposition of two optical modes [1, 2]. The cancellation in the mechanical coupling induced by the superposition decouples the dark mode from the mechanical oscillator. The formation of the dark mode, however, also induces a conversion of the optical field from one optical mode to the other. This type of mechanically-mediated coupling is immune to thermal mechanical motion, providing a promising mechanism for interfacing hybrid quantum systems. Here, we report the experimental demonstration of such a dark mode by coupling two optical modes in a silica resonator to one of its mechanical breathing modes in the regime of weak optomechanical coupling [3].

Journal ArticleDOI
TL;DR: Huang et al. as discussed by the authors presented an open-source implementation of the Hilbert Huang transform (HHT), an alternative spectral method designed to avoid the linearity and stationarity constraints of Fourier analysis.
Abstract: Online Material: Color versions of spectrogram figures; R and hht code installation instructions with examples The Fourier transform remains one of the most popular spectral methods in time‐series analysis, so much so that the word “spectrum” is virtually equivalent to “Fourier spectrum” (Huang et al , 2001) This method assumes that a time series extends from positive to negative infinity (stationarity) and consists of a linear superposition of sinusoids (linearity) However, geophysical signals are never stationary and are not necessarily linear This results in a trade‐off between time and frequency resolution for nonstationary signals and the creation of spurious harmonics for nonlinear signals We present an open‐source implementation of the Hilbert–Huang transform (HHT), an alternative spectral method designed to avoid the linearity and stationarity constraints of Fourier analysis The HHT defines instantaneous frequency as the time derivative of phase, illuminating previously inaccessible spectral details in transient signals Nonlinear signals become frequency modulations rather than a series of fitted sinusoids, eliminating artificial harmonics in the resulting spectrogram In this paper, we describe the HHT algorithm and present our recently‐developed hht package for the R programming language This package includes routines for empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD) and Hilbert spectral analysis It also comes with high‐level plotting functions for easy and accurate visualization of the resulting waveforms and spectra We demonstrate this code by applying it to three signals: a synthetic nonlinear waveform, a transient signal recorded at Deception Island volcano, Antarctica, and quasi‐harmonic tremor from Reventador volcano, Ecuador The synthetic signal shows how the EMD method breaks complex time series into simpler modes It also illustrates how the Hilbert transforms of nonlinear signals produce frequency oscillations rather than harmonics The transient signal demonstrates the high‐time/frequency resolution of the HHT method The volcanic‐tremor signal has high‐frequency harmonics in the …

Journal ArticleDOI
TL;DR: It is shown empirically that after proper randomization, the structure of the operators does not significantly affect the performances of the solver, and for some specially designed spatially coupled operators, this allows a computationally fast and memory efficient reconstruction in compressed sensing up to the information-theoretical limit.
Abstract: We study the behavior of Approximate Message-Passing, a solver for linear sparse estimation problems such as compressed sensing, when the i.i.d matrices -for which it has been specifically designed- are replaced by structured operators, such as Fourier and Hadamard ones. We show empirically that after proper randomization, the structure of the operators does not significantly affect the performances of the solver. Furthermore, for some specially designed spatially coupled operators, this allows a computationally fast and memory efficient reconstruction in compressed sensing up to the information-theoretical limit. We also show how this approach can be applied to sparse superposition codes, allowing the Approximate Message-Passing decoder to perform at large rates for moderate block length.

Journal ArticleDOI
TL;DR: In this article, the authors provided a systematic analysis of a prototypical nonlinear oscillator system respecting PT-symmetry, i.e., one has gain and the other an equal and opposite amount of loss.
Abstract: We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT-symmetry, i.e., one of them has gain and the other an equal and opposite amount of loss. We first discuss various symmetries of the model. We show that both the linear system as well as a special case of the nonlinear system can be derived from a Hamiltonian, whose structure is similar to the Pais–Uhlenbeck Hamiltonian. Exact solutions are obtained in a few special cases. We show that the system is a superintegrable system within the rotating wave approximation (RWA). We also obtain several exact solutions of these RWA equations. Further, we point out a novel superposition in the context of periodic solutions in terms of Jacobi elliptic functions that we obtain in this problem. Finally, we briefly mention numerical results about the stability of some of the solutions.

Journal ArticleDOI
TL;DR: In this paper, an improved version of the band superposition approach is proposed, introducing a rheological model for high frequency unsteady forces, and the numerical model is validated against wind tunnel tests performed by means of an active turbulence generator and a multi-box deck sectional model.

Journal ArticleDOI
TL;DR: In this article, a beam finite element is presented, with an accurate representation of normal stresses caused by "shear lag" or restrained torsion, using an enriched kinematics, representing cross-section warping as the superposition of "warping modes".

Journal ArticleDOI
TL;DR: It is proved that the synchrosqueezed wave packet transform identifies these components and estimates their local wavevectors for a function that is a superposition of several wave-like components with a highly oscillatory pattern satisfying certain separation conditions.
Abstract: This paper introduces the synchrosqueezed wave packet transform as a method for analyzing two-dimensional images. This transform is a combination of wave packet transforms of a certain geometric scaling, a reallocation technique for sharpening phase space representations, and clustering algorithms for modal decomposition. For a function that is a superposition of several wave-like components with a highly oscillatory pattern satisfying certain separation conditions, we prove that the synchrosqueezed wave packet transform identifies these components and estimates their local wavevectors. A discrete version of this transform is discussed in detail, and numerical results are given to demonstrate the properties of the proposed transform.