Showing papers on "Superposition principle published in 2017"

Quantum test of the equivalence principle for atoms in coherent superposition of internal energy states.

Abstract: The Einstein equivalence principle (EEP) has a central role in the understanding of gravity and space-time. In its weak form, or weak equivalence principle (WEP), it directly implies equivalence between inertial and gravitational mass. Verifying this principle in a regime where the relevant properties of the test body must be described by quantum theory has profound implications. Here we report on a novel WEP test for atoms: a Bragg atom interferometer in a gravity gradiometer configuration compares the free fall of rubidium atoms prepared in two hyperfine states and in their coherent superposition. The use of the superposition state allows testing genuine quantum aspects of EEP with no classical analogue, which have remained completely unexplored so far. In addition, we measure the Eotvos ratio of atoms in two hyperfine levels with relative uncertainty in the low 10-9, improving previous results by almost two orders of magnitude.

Multibeam by Metasurface Antennas

Abstract: We explore various possibilities for designing multibeam antennas using a single metasurface (MTS) aperture. Both single-source and multisource feeding schemes are considered. For the single-source case, two approaches are investigated. In the first one, the MTS aperture is divided into several angular sectors, each one devoted to the formation of a beam in a given direction. In the second approach, the whole aperture is shared by a superposition of individual modulations, which correspond to those required to obtain beams in the desired set of directions. It is shown that the latter solution provides beams with a higher gain. The configuration based on a multisource feeding scheme is also tailored by a superposition of modulation patterns. The main advantage of the latter approach is the possibility of having one independent beam at a time when each of the sources are active, as opposed to the single-source case where all the beams coexist at the same time. Closed-form expressions are provided for the MTS surface impedance in each of the proposed solutions. The design equations include appropriate amplitude tapering to improve the beam efficiency. Numerical results based on the method of moments are presented for validation.

Enlargement of optical Schrödinger's cat states

Abstract: Superpositions of macroscopically distinct quantum states, introduced in Schrodinger's famous Gedankenexperiment, are an epitome of quantum ‘strangeness’ and a natural tool for determining the validity limits of quantum physics. The optical incarnation of Schrodinger's cat (SC)—the superposition of two opposite-amplitude coherent states—is also the backbone of continuous-variable quantum information processing. However, the existing preparation methods limit the amplitudes of the component coherent states, which curtails the state's usefulness for fundamental and practical applications. Here, we convert a pair of negative squeezed SC states of amplitude 1.15 to a single positive SC state of amplitude 1.85 with a success probability of ∼0.2. The protocol consists in bringing the initial states into interference on a beamsplitter and a subsequent heralding quadrature measurement in one of the output channels. Our technique can be realized iteratively, so arbitrarily high amplitudes can, in principle, be reached. The amplitude of a Schrodinger's cat (SC) state — superposed coherent state — is increased using a homodyne measurement. A pair of negative SC states with amplitude of 1.15 is probabilistically converted to a single positive SC state with amplitude of 1.85.

Resource Theory of Superposition.

Abstract: Resource theories of coherence are generalized to quantify the superposition of a finite number of linearly independent states.

Simultaneous generation of multiple vector beams on a single SLM.

Abstract: Complex vector light fields, classically entangled in polarization and phase, have become ubiquitous in a wide variety of research fields. This has triggered the demonstration of a wide variety of generation techniques. Of particular relevance are those based on computer-controlled devices due to their great flexibility. In particular, spatial light modulators have demonstrated their high capabilities to generate any vector beam, with various spatial profiles and polarization distributions. Here, we put forward a novel technique that exploits the superposition principle in optics to enable the simultaneous generation of many vector beams using a single digital hologram. As proof-of-principle, we demonstrated the simultaneous generation of sixteen vector vortex beams with various polarization distributions and spatial shapes on a single SLM, each with their own spatial shape and polarization distribution.

Sorting Photons by Radial Quantum Number.

Abstract: The Laguerre-Gaussian (LG) modes constitute a complete basis set for representing the transverse structure of a paraxial photon field in free space. Earlier workers have shown how to construct a device for sorting a photon according to its azimuthal LG mode index, which describes the orbital angular momentum (OAM) carried by the field. In this paper we propose and demonstrate a mode sorter based on the fractional Fourier transform to efficiently decompose the optical field according to its radial profile. We experimentally characterize the performance of our implementation by separating individual radial modes as well as superposition states. The reported scheme can, in principle, achieve unit efficiency and thus can be suitable for applications that involve quantum states of light. This approach can be readily combined with existing OAM mode sorters to provide a complete characterization of the transverse profile of the optical field.

Approximate Message-Passing Decoder and Capacity Achieving Sparse Superposition Codes

Abstract: We study the approximate message-passing decoder for sparse superposition coding on the additive white Gaussian noise channel and extend our preliminary work. We use heuristic statistical-physics-based tools, such as the cavity and the replica methods, for the statistical analysis of the scheme. While superposition codes asymptotically reach the Shannon capacity, we show that our iterative decoder is limited by a phase transition similar to the one that happens in low density parity check codes. We consider two solutions to this problem, that both allow to reach the Shannon capacity: 1) a power allocation strategy and 2) the use of spatial coupling, a novelty for these codes that appears to be promising. We present, in particular, simulations, suggesting that spatial coupling is more robust and allows for better reconstruction at finite code lengths. Finally, we show empirically that the use of a fast Hadamard-based operator allows for an efficient reconstruction, both in terms of computational time and memory, and the ability to deal with very large messages.

Weighted Superposition Attraction (WSA)

Abstract: A novel swarm intelligence based algorithm inspired by superposition principle and field attraction for global optimization.High converging capability.Extensive computational study is presented for solving many test problems with success. This paper is the first one of the two papers entitled Weighted Superposition Attraction (WSA), which is based on two basic mechanisms, superposition and attracted movement of agents, that are observable in many systems. Dividing this paper into two parts raised as a necessity because of their individually comprehensive contents. If we wanted to write these papers as a single paper we had to write more compact as distinct from its current versions because of the space requirements. So, writing them as a single paper would not be as effective as we desired.In many natural phenomena it is possible to compute superposition or weighted superposition of active fields like light sources, electric fields, sound sources, heat sources, etc.; the same may also be possible for social systems as well. An agent (particle, human, electron, etc.) may be supposed to move towards superposition if it is attractive to it. As systems status changes the superposition also changes; so it needs to be recomputed. This is the main idea behind the WSA algorithm, which mainly attempts to realize this superposition principle in combination with the attracted movement of agents as a search procedure for solving optimization problems in an effective manner. In this current part, the performance of the proposed WSA algorithm is tested on the well-known unconstrained continuous optimization functions, through a set of computational study. The comparison with some other search algorithms is performed in terms of solution quality and computational time. The experimental results clearly indicate the effectiveness of the WSA algorithm.

Optimised Signal Processing for Nonlinear Ultrasonic Nondestructive testing of Complex Materials and Biological Tissues

Abstract: In this thesis the possibility of nonlinear ultrasonic NDT is investigated for complex materials and biological tissues. The delayed TR-NEWS signal processing methodis developed, which is based on the TR-NEWS method. TR-NEWS is a method well-suited for materials with complex structure: it allows spatio-temporal focusing of a long ultrasonic chirp signal to the region near the receiving transducer, forming an impulse pulse. The received signal power and SNR are increased as a result.Delayed TR-NEWS allows the use of this focused wave pulse as a new basis for either the signal optimisation or, alternatively, for the detection of nonlinearity by the breakdown of linear superposition. This method is used in physical experiments and simulations. The physical experiments are made on an undamaged CFRP block and a porcine skin sample. The skin is tested in a synchronised acoustomechanical setup specially designed in the course of this thesis. In 1D pseudospectral simulations for CFRP, it is determined that while classical nonlinearity cannot probably be detected in ultrasonic NDT, it could be possible to detect nonclassical nonlinear effects such as those from cracks and microdamage.Physical experiments and 2D FEM simulations of linear, undamaged CFRP are compared for studying the delayed TR-NEWS method, its applicability in optimising the focused wave, and also for creating an interaction of waves at the focusing region with a linear superposition prediction. This suggests the possibility of detecting nonlinearities by comparing the actual signal from interaction to the linear prediction.Finally, more 2D simulations are conducted for CFRP with a single contact gap nonlinearity near the focusing region. The nonlinearity is measured by PI and delayed TR-NEWS. It is determined that delayed TR-NEWS is able to detect the defect at least as well as the PI method. It is ascertained that the PM hysteresis model could describe the nonclassical nonlinearity of damaged materials and biological tissues. Asynchronised acoustomechanical test setup is created to test such multiscale nonlinearity. The simultaneous mechanical load test and ultrasonic delayed TR-NEWS test can be used to measure the mechanical properties of skin

High-Performance Coherent Population Trapping Clock with Polarization Modulation

Abstract: The authors use a single laser beam with synchronously modulated polarization and phase to trap atoms in a superposition state, decoupled from the light. Thanks to the linear architecture of this setup, it can serve as a compact, high-performance vapor-cell atomic clock. Such systems based on coherent population trapping are desired as successors to the well-known rubidium clock, particularly for applications in navigation and telecommunication. This setup offers frequencies an order of magnitude more stable than from a typical industrial clock.

Quantifying the Coherence between Coherent States

Abstract: In this Letter, we detail an orthogonalization procedure that allows for the quantification of the amount of coherence present in an arbitrary superposition of coherent states The present construction is based on the quantum coherence resource theory introduced by Baumgratz, Cramer, and Plenio and the coherence resource monotone that we identify is found to characterize the nonclassicality traditionally analyzed via the Glauber-Sudarshan P distribution This suggests that identical quantum resources underlie both quantum coherence in the discrete finite dimensional case and the nonclassicality of quantum light We show that our construction belongs to a family of resource monotones within the framework of a resource theory of linear optics, thus establishing deeper connections between the class of incoherent operations in the finite dimensional regime and linear optical operations in the continuous variable regime

Integrability, solitons, periodic and travelling waves of a generalized (3+1)-dimensional variable-coefficient nonlinear-wave equation in liquid with gas bubbles

Abstract: Under investigation in this paper is a generalized (3+1)-dimensional varible-coefficient nonlinear-wave equation, which has been presented for nonlinear waves in liquid with gas bubbles. The bilinear form, Backlund transformation, Lax pair and infinitely-many conservation laws are obtained via the binary Bell polynomials. One-, two- and three-soliton solutions are generated by virtue of the Hirota method. Travelling-wave solutions are derived with the aid of the polynomial expansion method. The one-periodic wave solutions are constructed by the Hirota-Riemann method. Discussions among the soliton, periodic- and travelling-wave solutions are presented: I) the soliton velocities are related to the variable coefficients, while the soliton amplitudes are unaffected; II) the interaction between the solitons is elastic; III) there are three cases of the travelling-wave solutions, i.e., the triangle-type periodical, bell-type and soliton-type travelling-wave solutions, while we notice that bell-type travelling-wave solutions can be converted into one-soliton solutions via taking suitable parameters; IV) the one-periodic waves approach to the solitary waves under some conditions and can be viewed as a superposition of overlapping solitary waves, placed one period apart.

Multichannel Metasurface for Simultaneous Control of Holograms and Twisted Light Beams

Abstract: In terms of system integration and device miniaturization, a single optical device that can possess more tunable functionalities in multiple channels is desirable. As a proof of concept, we experimentally demonstrate such an ultrathin optical device that can simultaneously realize polarization-controllable hologram and superposition of orbital angular momentum (OAM) in multiple channels. By continuously controlling the polarization state of the incident light, the polarization-dependent holographic images in two channels along the horizontal direction and the continuous control of OAM superposition in two channels along the vertical direction are realized. The uniqueness of the device lies in that both the superpositions of OAM states and the holographic images are controlled at the same time. This novel device provides a fast and efficient tool for simultaneous control of hologram and manipulation of OAM supposition in various channels, which significantly simplifies the experimental system and is of imp...

Orbital-Angular-Momentum Mode Selection by Rotationally Symmetric Superposition of Chiral States with Application to Electron Vortex Beams.

Abstract: A general orbital-angular-momentum (OAM) mode selection principle is put forward involving the rotationally symmetric superposition of chiral states. This principle is not only capable of explaining the operation of vortex generating elements such as spiral zone plate holograms, but more importantly, it enables the systematic and flexible generation of structured OAM waves in general. This is demonstrated both experimentally and theoretically in the context of electron vortex beams using rotationally symmetric binary amplitude chiral sieve masks.

Permutation-blocking path-integral Monte Carlo approach to the static density response of the warm dense electron gas.

Abstract: The static density response of the uniform electron gas is of fundamental importance for numerous applications. Here we employ the recently developed ab initio permutation blocking path integral Monte Carlo (PB-PIMC) technique [T. Dornheim et al., New J. Phys. 17, 073017 (2015)] to carry out extensive simulations of the harmonically perturbed electron gas at warm dense matter conditions. In particular, we investigate in detail the validity of linear response theory and demonstrate that PB-PIMC allows us to obtain highly accurate results for the static density response function and, thus, the static local field correction. A comparison with dielectric approximations to our new ab initio data reveals the need for an exact treatment of correlations. Finally, we consider a superposition of multiple perturbations and discuss the implications for the calculation of the static response function.

Shaped Beam Synthesis Based on Superposition Principle and Taylor Method

Abstract: A technique for the synthesis of shaped beam radiation patterns is proposed. The new synthesis method is based on superposition principle and Taylor method. The method may control the sidelobe level of the shaped beam. The approach includes four steps: 1) get the distribution of pencil beam array with low sidelobe by Taylor method; 2) let the beams scan as a phased array to the specific angles according to the requirement of the shaped beam, The sum pattern is close to the shaping beam; 3) determine the value of angles and weights; and 4) count the distribution of the shaped beam array according to the new array factor function. Numerical results are provided to assess the capabilities of the proposed design method. The method develops an effective approach for the synthesis of shaped beams via uniform linear arrays. Both the ripple and sidelobe level of shaped beam may be controlled by the new synthesis method.

Flat-band light dynamics in Stub photonic lattices.

Abstract: We experimentally study a Stub photonic lattice and excite their localized linear states originated from an isolated Flat Band at the center of the linear spectrum. By exciting these modes in different regions of the lattice, we observe that they do not diffract across the system and remain well trapped after propagating along the crystal. By using their wave nature, we are able to combine – in phase and out of phase – two neighbor states into a coherent superposition. These observations allow us to propose a novel setup for performing three different all-optical logical operations such as OR, AND, and XOR, positioning Flat Band systems as key setups to perform all-optical operations at any level of power.

A deterministic detector for vector vortex states.

Abstract: Encoding information in high-dimensional degrees of freedom of photons has led to new avenues in various quantum protocols such as communication and information processing. Yet to fully benefit from the increase in dimension requires a deterministic detection system, e.g., to reduce dimension dependent photon loss in quantum key distribution. Recently, there has been a growing interest in using vector vortex modes, spatial modes of light with entangled degrees of freedom, as a basis for encoding information. However, there is at present no method to detect these non-separable states in a deterministic manner, negating the benefit of the larger state space. Here we present a method to deterministically detect single photon states in a four dimensional space spanned by vector vortex modes with entangled polarisation and orbital angular momentum degrees of freedom. We demonstrate our detection system with vector vortex modes from the |[Formula: see text]| = 1 and |[Formula: see text]| = 10 subspaces using classical and weak coherent states and find excellent detection fidelities for both pure and superposition vector states. This work opens the possibility to increase the dimensionality of the state-space used for encoding information while maintaining deterministic detection and will be invaluable for long distance classical and quantum communication.

Finite-horizon covariance control of linear time-varying systems

Abstract: We consider the problem of finite-horizon optimal control of a discrete linear time-varying system subject to a stochastic disturbance and fully observable state. The initial state of the system is drawn from a known Gaussian distribution, and the final state distribution is required to reach a given target Gaussian distribution, while minimizing the expected value of the control effort. We derive the linear optimal control policy by first presenting an efficient solution for the diffusion-less case, and we then solve the case with diffusion by reformulating the system as a superposition of diffusion-less systems. We show that the resulting solution coincides with a LQG problem with particular terminal cost weight matrix.

Fast superposition T-matrix solution for clusters with arbitrarily-shaped constituent particles☆

Abstract: A fast superposition T-matrix solution is formulated for electromagnetic scattering by a collection of arbitrarily-shaped inhomogeneous particles. The T-matrices for individual constituents are computed by expanding the Green's dyadic in the spherical vector wave functions and formulating a volume integral equation, where the equivalent electric current is the unknown and the spherical vector wave functions are treated as excitations. Furthermore, the volume integral equation and the superposition T-matrix are accelerated by the precorrected-FFT algorithm and the fast multipole algorithm, respectively. The approach allows for an efficient scattering analysis of the clusters and aggregates consisting of a large number of arbitrarily-shaped inhomogeneous particles.

Applications of linear superposition principle to resonant solitons and complexitons

Abstract: We apply the linear superposition principle to Hirota bilinear equations and generalized bilinear equations. By extending the linear superposition principle to complex field, we construct complex exponential wave function solutions first and then get complexions by taking pairs of conjugate parameters. A few examples of mixed resonant solitons and complexitons to Hirota and generalized bilinear differential equations are presented.

Hamiltonian simulation with optimal sample complexity

Abstract: We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd, Mohseni, and Rebentrost [Nat. Phys., 10(9):631–633, 2014] is optimal for this task. We further extend their method to the case of multiple input states, showing how to simulate any Hermitian polynomial of the states provided. As applications, we derive optimal algorithms for commutator simulation and orthogonality testing, and we give a protocol for creating a coherent superposition of pure states, when given sample access to those states. We also show that this sample-based Hamiltonian simulation can be used as the basis of a universal model of quantum computation that requires only partial swap operations and simple single-qubit states. One of the hallmarks of quantum computation is the storage and extraction of information within quantum systems. Recently, Lloyd, Mohseni and Rebentrost created a protocol to treat multiple identical copies of a quantum state as “quantum software”, specifying a quantum program to be run on any other state. They use this approach to do principal component analysis of the software state. Here, we expand on their results, providing protocols for running more-complex quantum programs specified by several different states. Our protocols can be used to analyze the relationship between different states (for example, deciding whether states are orthogonal) and to create new states (such as coherent linear combinations of two states). We also outline the optimality of Lloyd et al.’s original protocol, as well as our new protocols.

Fast and slow thermal processes in harmonic scalar lattices

Abstract: An approach for analytical description of thermal processes in harmonic lattices is presented. We cover longitudinal and transverse vibrations of chains and out-of-plane vibrations of two-dimensional lattices with interactions of an arbitrary number of neighbors. Motion of each particle is governed by a single scalar equation and therefore the notion "scalar lattice" is used. Evolution of initial temperature field in an infinite lattice is investigated. An exact equation describing the evolution is derived. Continualization of this equation with respect to spatial coordinates is carried out. The resulting continuum equation is solved analytically. The solution shows that the kinetic temperature is represented as the sum of two terms, one describing short time behavior, the other large time behavior. At short times, the temperature performs high-frequency oscillations caused by redistribution of energy among kinetic and potential forms (fast process). Characteristic time of this process is of order of ten periods of atomic vibrations. At large times, changes of the temperature are caused by ballistic heat transfer (slow process). The temperature field is represented as a superposition of waves having the shape of initial temperature distribution and propagating with group velocities dependent on the wave vector. Expressions describing fast and slow processes are invariant with respect to substitution $t$ by $-t$. However examples considered in the paper demonstrate that these processes are irreversible. Numerical simulations show that presented theory describes the evolution of temperature field at short and large time scales with high accuracy.

Imaging of locally rough surfaces from intensity-only far-field or near-field data

Abstract: This paper is concerned with a nonlinear imaging problem, which aims to reconstruct a locally perturbed, perfectly reflecting, infinite plane from intensity-only (or phaseless) far-field or near-field data. A recursive Newton iteration algorithm in frequencies is developed to reconstruct the locally rough surface from multi-frequency intensity-only far-field or near-field data, where the fast integral equation solver developed by Zhang and Zhang (2013 SIAM J. Appl. Math. 73 1811?29) is used to solve the direct scattering problem in each iteration. For the case with far-field data, a main feature of our work is that the incident field is taken as a superposition of two plane waves with different directions rather than one plane wave, so the location and shape of the local perturbation of the infinite plane can be reconstructed simultaneously from intensity-only far-field data with multiple wave numbers. This is different from previous work on inverse scattering from phaseless far-field data, where only the shape reconstruction was considered due to the translation invariance property of the phaseless far-field pattern corresponding to one plane wave as the incident field. Finally, numerical examples are presented to demonstrate that our reconstruction algorithm is stable and accurate even for the case of multiple-scale profiles.

A uniqueness result for the decomposition of vector fields in Rd

Abstract: Given a vector field ρ(1,b) ∈ Lloc(R +×R,R) such that divt,x(ρ(1,b)) is a measure, we consider the problem of uniqueness of the representation η of ρ(1,b)L as a superposition of characteristics γ : (t − γ, t + γ) → R, γ̇(t) = b(t, γ(t)). We give conditions in terms of a local structure of the representation η on suitable sets in order to prove that there is a partition of R into disjoint trajectories ℘a, a ∈ A, such that the PDE divt,x ( uρ(1,b) ) ∈M(R), u ∈ L∞(R +×R), (1) can be disintegrated into a family of ODEs along ℘a with measure r.h.s.. The decomposition ℘a is essentially unique. We finally show that b ∈ Lt (BVx)loc satisfies this local structural assumption and this yields, in particular, the renormalization property for nearly incompressible BV vector fields.

Measuring the complex orbital angular momentum spectrum of light with a mode-matching method

Abstract: The relative phase shift among different components in the superposition of orbital angular momentum (OAM) states contains significant information. However, with existing methods of measuring the OAM spectrum, the phase term of the spectrum coefficient is hard to obtain. In this Letter, a mode-matching method is proposed to identify the complex OAM spectrum with a Mach-Zehnder interferometer and a charge-coupled device camera. It has the potential to extend the applications of OAM in scenarios sensitive to the phase factor, for instance, in imaging and quantum manipulation. The method is experimentally demonstrated with the superposition of two or three OAM states, while the maximum deviation of the energy ratio and the relative phase shift is 8.4% and 5.5% of 2π, respectively.