Showing papers on "Superposition principle published in 2016"

Vector Vortex Beam Generation with a Single Plasmonic Metasurface

Abstract: Despite a plethora of applications ranging from quantum memories to high-resolution lithography, the current technologies to generate vector vortex beams (VVBs) suffer from less efficient energy use, poor resolution, low damage threshold, and bulky size, preventing further practical applications. We propose and experimentally demonstrate an approach to generate VVBs with a single metasurface by locally tailoring phase and transverse polarization distribution. This method features the spin–orbit coupling and the superposition of the converted part with an additional phase pickup and the residual part without a phase change. By maintaining the equal components for the converted part and the residual part, the cylindrically polarized vortex beams carrying orbital angular momentum are experimentally demonstrated based on a single metasurface at subwavelength scale. The proposed approach provides unprecedented freedom in engineering the properties of optical waves with high-efficiency light utilization and a m...

Macroscopic Quantum Superposition in Cavity Optomechanics

Abstract: Quantum superposition in mechanical systems is not only key evidence for macroscopic quantum coherence, but can also be utilized in modern quantum technology. Here we propose an efficient approach for creating macroscopically distinct mechanical superposition states in a two-mode optomechanical system. Photon hopping between the two cavity modes is modulated sinusoidally. The modulated photon tunneling enables an ultrastrong radiation-pressure force acting on the mechanical resonator, and hence significantly increases the mechanical displacement induced by a single photon. We study systematically the generation of the Yurke-Stoler-like states in the presence of system dissipations. We also discuss the experimental implementation of this scheme.

Resonant behavior of multiple wave solutions to a Hirota bilinear equation

Abstract: For the exponential traveling wave solutions to the Hirota bilinear equations, a sufficient and necessary criterion for the existence of linear superposition principle has been given. Motivated by this criterion, we propose a new Hirota bilinear equation via using a multivariate polynomial. Applying the linear superposition principle to this new Hirota bilinear equation, we finally find two types of resonant multiple wave solutions, among which, the resonant three-wave solutions are illustrated with three-dimensional plots.

Ramsey Interference with Single Photons.

Abstract: Interferometry using discrete energy levels of nuclear, atomic, or molecular systems is the foundation for a wide range of physical phenomena and enables powerful techniques such as nuclear magnetic resonance, electron spin resonance, Ramsey-based spectroscopy, and laser or maser technology. It also plays a unique role in quantum information processing as qubits may be implemented as energy superposition states of simple quantum systems. Here, we demonstrate quantum interference involving energy states of single quanta of light. In full analogy to the energy levels of atoms or nuclear spins, we implement a Ramsey interferometer with single photons. We experimentally generate energy superposition states of a single photon and manipulate them with unitary transformations to realize arbitrary projective measurements. Our approach opens the path for frequency-encoded photonic qubits in quantum information processing and quantum communication.

Free Nano-Object Ramsey Interferometry for Large Quantum Superpositions

Abstract: We propose an interferometric scheme based on an untrapped nano-object subjected to gravity. The motion of the center of mass (c.m.) of the free object is coupled to its internal spin system magnetically, and a free flight scheme is developed based on coherent spin control. The wave packet of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during our scheme. We find a remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling), and also a dynamical decoupling nature of the scheme itself. Together they secure a high visibility of the resulting Ramsey fringes. The mass independence of our scheme makes it viable for a nano-object selected from an ensemble with a high mass variability. Given these advantages, a quantum superposition with a 100 nm spatial separation for a massive object of 10^{9} amu is achievable experimentally, providing a route to test postulated modifications of quantum theory such as continuous spontaneous localization.

FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory

Abstract: We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation—the locality of the dark matter equations and the scale invariance of the problem—as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theory and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm. The code, along with a user manual and example implementations, is available at https://github.com/JoeMcEwen/FAST-PT.

Macroscopic Quantum Superposition in Cavity Optomechanics

Abstract: Quantum superposition in mechanical systems is not only key evidence for macroscopic quantum coherence, but can also be utilized in modern quantum technology. Here we propose an efficient approach for creating macroscopically distinct mechanical superposition states in a two-mode optomechanical system. Photon hopping between the two cavity modes is modulated sinusoidally. The modulated photon tunneling enables an ultrastrong radiation-pressure force acting on the mechanical resonator, and hence significantly increases the mechanical displacement induced by a single photon. We study systematically the generation of the Yurke-Stoler-like states in the presence of system dissipations. We also discuss the experimental implementation of this scheme.

Quantum optical circulator controlled by a single chirally coupled atom

Abstract: We demonstrate a fiber-integrated quantum optical circulator that is operated by a single atom and that relies on the chiral interaction between emitters and transversally confined light. Like its counterparts in classical optics, our circulator exhibits an inherent asymmetry between light propagation in the forward and the backward direction. However, rather than a magnetic field or a temporal modulation, it is the internal quantum state of the atom that controls the operation direction of the circulator. This working principle is compatible with preparing the circulator in a coherent superposition of its operational states. Such a quantum circulator may thus become a key element for routing and processing quantum information in scalable integrated optical circuits. Moreover, it features a strongly nonlinear response at the single-photon level, thereby enabling, e.g., photon number-dependent routing and novel quantum simulation protocols.

Interference at the Single Photon Level Along Satellite-Ground Channels.

Abstract: Quantum interference arising from the superposition of states is striking evidence of the validity of quantum mechanics, confirmed in many experiments and also exploited in applications. However, as for any scientific theory, quantum mechanics is valid within the limits in which it has been experimentally verified. In order to extend such limits, it is necessary to observe quantum interference in unexplored conditions such as moving terminals at large distances in space. Here, we experimentally demonstrate single photon interference at a ground station due to the coherent superposition of two temporal modes reflected by a rapidly moving satellite a thousand kilometers away. The relative speed of the satellite induces a varying modulation in the interference pattern. The measurement of the satellite distance in real time by laser ranging allows us to precisely predict the instantaneous value of the interference phase. We then observed the interference patterns with a visibility up to 67% with three different satellites and with a path length up to 5000 km. Our results attest to the viability of photon temporal modes for fundamental tests of physics and quantum communication in space.

Observation of Quantum Interference between Separated Mechanical Oscillator Wave Packets.

Abstract: A trapped ion is produced in a superposition of motional wave packets, which are shown to interfere despite being separated by 240 nanometers.

Super-resolution radar

Abstract: In this paper, we study the identification of a time-varying linear system from its response to a known input signal. More specifically, we consider systems whose response to the input signal is given by a weighted superposition of delayed and Doppler-shifted versions of the input. This problem arises in a multitude of applications such as wireless communications and radar imaging. Due to practical constraints, the input signal has finite bandwidth $B$ , and the received signal is observed over a finite time interval of length $T$ only. This gives rise to a delay and Doppler resolution of $1/B$ and $1/T$ . We show that this resolution limit can be overcome, i.e., we can exactly recover the continuous delay–Doppler pairs and the corresponding attenuation factors, by solving a convex optimization problem. This result holds provided that the distance between the delay–Doppler pairs is at least $2.37/B$ in time or $2.37/T$ in frequency. Furthermore, this result allows the total number of delay–Doppler pairs to be linear up to a log-factor in $BT$ , the dimensionality of the response of the system, and thereby the limit for identifiability. Stated differently, we show that we can estimate the time–frequency components of a signal that is $S$ -sparse in the continuous dictionary of time–frequency shifts of a random window function, from a number of measurements that is linear up to a log-factor in $S$ .

Light Modes of Free Space

Abstract: A surprisingly large number of known distinct sets of light patterns propagate in free space essentially unchanged. These sets of light patterns (intensity distributions of the electric–magnetic fields) can be divided into two groups: light Waves and light Beams. Wave sets are solutions of the exact Helmholtz equation (HE). Beam sets are solutions of the paraxial HE. The sets of Waves and Beams can be further classified according to the coordinate system to which they belong. All sets are complete and orthogonal such that any square integrable input field can be decomposed into a linear superposition of the set's functions. We classify the patterns, present the solution equations and display sample patterns for each of 4 Wave sets and each of 14 Beam sets.

Exotic looped trajectories of photons in three-slit interference.

Abstract: The validity of the superposition principle and of Born's rule are well-accepted tenants of quantum mechanics Surprisingly, it has been predicted that the intensity pattern formed in a three-slit experiment is seemingly in contradiction with the most conventional form of the superposition principle when exotic looped trajectories are taken into account However, the probability of observing such paths is typically very small, thus rendering them extremely difficult to measure Here we confirm the validity of Born's rule and present the first experimental observation of exotic trajectories as additional paths for the light by directly measuring their contribution to the formation of optical interference fringes We accomplish this by enhancing the electromagnetic near-fields in the vicinity of the slits through the excitation of surface plasmons This process increases the probability of occurrence of these exotic trajectories, demonstrating that they are related to the near-field component of the photon's wavefunction

The mutual information in random linear estimation

Abstract: We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections, a problem relevant in compressed sensing, sparse superposition codes or code division multiple access just to cite few. There has been a number of works considering the mutual information for this problem using the heuristic replica method from statistical physics. Here we put these considerations on a firm rigorous basis. First, we show, using a Guerra-type interpolation, that the replica formula yields an upper bound to the exact mutual information. Secondly, for many relevant practical cases, we present a converse lower bound via a method that uses spatial coupling, state evolution analysis and the I-MMSE theorem. This yields, in particular, a single letter formula for the mutual information and the minimal-mean-square error for random Gaussian linear estimation of all discrete bounded signals.

Dissipative Optomechanical Preparation of Macroscopic Quantum Superposition States.

Abstract: The transition from quantum to classical physics remains an intensely debated question even though it has been investigated for more than a century. Further clarifications could be obtained by preparing macroscopic objects in spatial quantum superpositions and proposals for generating such states for nanomechanical devices either in a transient or a probabilistic fashion have been put forward. Here, we introduce a method to deterministically obtain spatial superpositions of arbitrary lifetime via dissipative state preparation. In our approach, we engineer a double-well potential for the motion of the mechanical element and drive it towards the ground state, which shows the desired spatial superposition, via optomechanical sideband cooling. We propose a specific implementation based on a superconducting circuit coupled to the mechanical motion of a lithium-decorated monolayer graphene sheet, introduce a method to verify the mechanical state by coupling it to a superconducting qubit, and discuss its prospects for testing collapse models for the quantum to classical transition.

Parsimonious, Simulation Based Verification of Linear Systems

Abstract: We present a technique to verify safety properties of linear systems (possibly time varying) using very few simulations. For a linear system of dimension n, our technique needs \(n+1\) simulation runs. This is in contrast to current simulation based approaches, where the number of simulations either depends upon the number of vertices in the convex polyhedral initial set, or on the proximity of the unsafe set to the set of reachable states. At its core, our algorithm exploits the superposition principle of linear systems. Our algorithm computes both an over and an under approximation of the set of reachable states.

FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory

Abstract: We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation -- the locality of the dark matter equations and the scale invariance of the problem -- as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theory and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm, including the applications described here.

Moving load-induced response of damaged beam and its application in damage localization:

Abstract: The dynamic response of a beam under a moving load is a superposition of two components, namely, the moving-frequency component corresponding to the moving load and the natural-frequency component of the beam. This study investigates the closed-form solution of the dynamic response of a damaged simply supported beam subjected to a moving load and examines the effects of the loss of local stiffness on these two components. The study provides deep insights into beam damage detection based on moving load-induced response. Consequently, a simple and intuitive method for damage localization is developed. First, the closed-form solution is derived based on the modal perturbation and modal superposition method. The closed-form solution enables the individual examination of damage-induced changes in moving- and natural-frequency components. The results show that the moving-frequency component is preferred in damage localization. Then, multi-scale discrete wavelet transform is employed to separate the moving-frequ...

High-order rogue wave solutions for the coupled nonlinear Schrödinger equations-II

Abstract: We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schrodinger equations. Based on the generalized Darboux transformation and formal series method, we obtain the high-order rogue wave solution without the special limitation on the wave vectors. As an application, we exhibit the first, second-order rogue wave solutions and the superposition of them by computer plotting. We find the distribution patterns for vector rogue waves are much more abundant than the ones for scalar rogue waves, and also different from the ones obtained with the constrain conditions on background fields. The results further enrich and deepen our realization on rogue wave excitation dynamics in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids.

Superposition of polytropes in the inner heliosheath

Abstract: This paper presents a possible generalization of the equation of state and Bernoulli's integral when a superposition of polytropic processes applies in space and astrophysical plasmas. The theory of polytropic thermodynamic processes for a fixed polytropic index is extended for a superposition of polytropic indices. In general, the superposition may be described by any distribution of polytropic indices, but emphasis is placed on a Gaussian distribution. The polytropic density–temperature relation has been used in numerous analyses of space plasma data. This linear relation on a log–log scale is now generalized to a concave-downward parabola that is able to describe the observations better. The model of the Gaussian superposition of polytropes is successfully applied in the proton plasma of the inner heliosheath. The estimated mean polytropic index is near zero, indicating the dominance of isobaric thermodynamic processes in the sheath, similar to other previously published analyses. By computing Bernoulli's integral and applying its conservation along the equator of the inner heliosheath, the magnetic field in the inner heliosheath is estimated, B ~ 2.29 ± 0.16 μG. The constructed normalized histogram of the values of the magnetic field is similar to that derived from a different method that uses the concept of large-scale quantization, bringing incredible insights to this novel theory.

Controllable circular Airy beams via dynamic linear potential

Abstract: We investigate controllable spatial modulation of circular autofocusing Airy beams, under action of different dynamic linear potentials, both theoretically and numerically. We introduce a novel treatment method in which the circular Airy beam is represented as a superposition of narrow azimuthally-modulated one-dimensional Airy beams that can be analytically treated. The dynamic linear potentials are appropriately designed, so that the autofocusing effect can either be weakened or even eliminated when the linear potential exerts a "pulling" effect on the beam, or if the linear potential exerts a "pushing" effect, the autofocusing effect can be greatly strengthened. Numerical simulations agree with the theoretical results very well.

Controllable circular Airy beams via dynamic linear potential

Abstract: We investigate controllable spatial modulation of circular autofocusing Airy beams, under action of different dynamic linear potentials, both theoretically and numerically. We introduce a novel treatment method in which the circular Airy beam is represented as a superposition of narrow azimuthally-modulated one-dimensional Airy beams that can be analytically treated. The dynamic linear potentials are appropriately designed, so that the autofocusing effect can either be weakened or even eliminated when the linear potential exerts a “pulling” effect on the beam, or if the linear potential exerts a “pushing” effect, the autofocusing effect can be greatly strengthened. Numerical simulations agree with the theoretical results very well.

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.

Decomposition of Electromagnetic Interferences in the Time-Domain

Abstract: Electromagnetic interferences are potentially very complex signals formed by the superposition of transient (broadband) and continuous wave (narrowband) components with significant randomness in both amplitude and phase. Decomposing the electromagnetic interference measured in the time domain into a set of intrinsic mode functions is useful to gain insights of the process that generates the interference. Evaluating the intrinsic mode functions contributes to improving the measurement capabilities of the time-domain electromagnetic emissions measurement systems based on the general-purpose oscilloscopes. In this paper, a combination of techniques that includes empirical mode decomposition and transient mode decomposition is used to separate the main components of complex electromagnetic disturbances. This approach requires no prior information on the spectral content of the measured EMI and it does not perform a domain transformation. Examples of electromagnetic interference decomposition verify the effectiveness and the accuracy of the proposed approach. Finally, a discussion on the advantages, practical applications, limitations, and drawbacks of the described techniques is addressed.

Mesoscopic Superposition States Generated by Synthetic Spin-Orbit Interaction in Fock-State Lattices.

Abstract: Mesoscopic superposition states of photons can be prepared in three cavities interacting with the same two-level atom. By periodically modulating the three cavity frequencies around the transition frequency of the atom with a 2π/3 phase difference, the time reversal symmetry is broken and an optical circulator is generated with chiralities depending on the quantum state of the atom. A superposition of the atomic states can guide photons from one cavity to a mesoscopic superposition of the other two cavities. The physics can be understood in a finite spin-orbit-coupled Fock-state lattice where the atom and the cavities carry the spin and the orbit degrees of freedom, respectively. This scheme can be realized in circuit QED architectures and provides a new platform for exploring quantum information and topological physics in novel lattices.

Superposition Method for Cogging Torque Prediction in Permanent Magnet Machines With Rotor Eccentricity

Abstract: This paper proposes an analytical method that combines the superposition concept and the subdomain method to predict the cogging torque of permanent magnet (PM) machines with a rotor eccentricity. The original eccentric machine is first divided into several sections along the air-gap circumferential direction. Then, the equivalent air-gap lengths of all sections will be determined and individually used to build up a series of concentric models representing each section. By the superposition method, the air-gap flux density of the original eccentric machine can be synthesized from that of every concentric model predicted through the subdomain method. Consequently, the cogging torque can be predicted by the integral of Maxwell stress tensor based on the synthesized air-gap flux density. To prove the efficacy of the proposed method, two fractional-slot PM machines with different slot/pole number combinations are taken as examples, together with the validation of a finite-element analysis.