Symmetric Superposition Research Articles

Qubit analog with polariton superfluid in an annular trap.

We report on the experimental realization and characterization of a qubit analog with semiconductor exciton-polaritons. In our system, a polaritonic condensate is confined by a spatially patterned pump laser in an annular trap that supports energy-degenerate vortex states of the polariton superfluid. Using temporal interference measurements, we observe coherent oscillations between a pair of counter-circulating vortex states coupled by elastic scattering of polaritons off the laser-imprinted potential. The qubit basis states correspond to the symmetric and antisymmetric superpositions of the two vortex states. By engineering the potential, we tune the coupling and coherent oscillations between the two circulating current states, control the energies of the qubit basis states, and initialize the qubit in the desired state. The dynamics of the system is accurately reproduced by our theoretical two-state model, and we discuss potential avenues to implement quantum gates and algorithms with polaritonic qubits analogous to quantum computation with standard qubits.

Two-unitary complex Hadamard matrices of order 36

Abstract A family of two-unitary complex Hadamard matrices (CHMs) of size 36 stemming from a particular matrix is constructed. Every matrix in this orbit remains unitary after operations of partial transpose and reshuffling which makes it a distinguished subset of CHM. It provides a novel solution to the quantum version of the Euler problem, in which each field of the Graeco-Latin square of size six contains a symmetric superposition of all 36 officers with phases being multiples of sixth root of unity. This simplifies previously known solutions as all amplitudes of the superposition are equal and the set of phases consists of six elements only. Multidimensional parameterization allows for more flexibility in a potential experimental realization.

An Investigation of Harmonic Oscillation of an Ion Particle in a Non-uniform Electrostatic Field

In this study, we investigate the possibility to trap an ion particle in a non-uniform electrostatic field generated by two ionic rings, with the aim to obtain and verify general results regarding our proposition. To develop the equation of motion, we first derive the electric field generated by each ring, based on the multipole expansion technique under the azimuthally symmetrical charge distribution speculation and superposition principle. Then, we establish the equation of motion regarding the Lagrangian formalism. From the results, we observe that an ion particle can exhibit harmonic motion, if the stability condition is satisfied by an appropriate parametric setting. The results are confirmed by displacement responses and phase trajectory plots, which validate our belief in the prospect to trap an ion in an electrostatic field. Furthermore, the velocity amplitude is significantly influenced by both the charge concentration of each ring and its size.

Quantum Pattern Classification in a Three-Qubit System

The problem of pattern classification in quantum data has been of great importance over the past few years. This study investigates the effect of deploying Grover’s, the partial diffusion, and the fixed-phase algorithms separately to amplify the amplitudes of a desired pattern in an unstructured dataset. These quantum search operators were applied to symmetric and antisymmetric input superpositions on a three-qubit system for 20 iterations each. After each iteration, different probabilities of classification were calculated in order to determine the accuracy of classification for each of the three quantum search operators. The results indicated that, in the case of applying the three quantum search operators to incomplete superposition input states, the partial diffusion operator outperformed the other operators with a probability of correct classification that reached 100% in certain iterations. It also showed that the classification accuracy of the fixed-phase operator exceeded the accuracy of the other two operators by 40% in most cases when the input state was a uniform superposition, and some of the basis states were phase-inverted.

Dynamics of an excitation-transfer trimer: Interference, coherence, Berry's phase development, and vibrational control of non-adiabaticity.

We detail several interesting features in the dynamics of an equilaterally shaped electronic excitation-transfer (EET) trimer with distance-dependent intermonomer excitation-transfer couplings. In the absence of electronic-vibrational coupling, symmetric and antisymmetric superpositions of two single-monomer excitations are shown to exhibit purely constructive, oscillatory, and purely destructive interference in the EET to the third monomer, respectively. In the former case, the transfer is modulated by motion in the symmetrical framework-expansion vibration induced by the Franck-Condon excitation. Distortions in the shape of the triangular framework degrade that coherent EET while activating excitation transfer in the latter case of an antisymmetric initial state. In its symmetrical configuration, two of the three single-exciton states of the trimer are degenerate. This degeneracy is broken by the Jahn-Teller-active framework distortions. The calculations illustrate closed, approximately circular pseudo-rotational wave-packet dynamics on both the lower and the upper adiabatic potential energy surfaces of the degenerate manifold, which lead to the acquisition after one cycle of physically meaningful geometric (Berry) phases of π. Another manifestation of Berry-phase development is seen in the evolution of the vibrational probability density of a wave packet on the lower Jahn-Teller adiabatic potential comprising a superposition of clockwise and counterclockwise circular motions. The circular pseudo-rotation on the upper cone is shown to stabilize the adiabatic electronic state against non-adiabatic internal conversion via the conical intersection, a dynamical process analogous to Slonczewski resonance. Strategies for initiating and monitoring these various dynamical processes experimentally using pre-resonant impulsive Raman excitation, short-pulse absorption, and multi-dimensional wave-packet interferometry are outlined in brief.

Optical Vortex Beams with a Symmetric OAM Spectrum beyond a Sector Aperture

In this work, we theoretically and numerically show that in the superposition of optical Gaussian vortices with a symmetric OAM spectrum, the normalized orbital angular momentum (OAM) carried by the beam and the topological charge (TC) equal TC of the middle constituent vortex. We also show that after passing a sector-shaped aperture, the symmetric superposition preserves the OAM carried, with the TC becoming fractional and proportional to the angle of the sector aperture. As it further propagates in free space after the sector aperture, the TC of the superposition becomes an integer, albeit indefinite, thanks to the aperture edges generating a multitude of extra optical vortices with positive and negative unit TC, irregularly arranged across the beam.

Research on the traceability method based on half symmetric superposition

In order to achieve high-accuracy self-calibration and traceability of electromagnetic standard voltage transformers, a measurement method that can be used for voltage ratio standard error voltage coefficients is proposed. Using two auxiliary standard voltage transformers, the error variation of the voltage transformer under different voltages can be obtained through three-step measurement. Compared with the traditional error voltage coefficient measurement method and international comparison, the feasibility of the method and the rationality of the uncertainty evaluation of the measurement results are verified. The self-calibration ratio difference measurement uncertainty of the 110 kV standard voltage transformer is better than 5 × 10−6, and the angular difference measurement uncertainty is better than 5 µrad. The method can be used to trace the source of standard devices up to 1000 kV power frequency voltage ratio, which have characteristics such as high accuracy and good stability.

Integrable high-efficiency generation of three-photon entangled states by a single incident photon

Generation of multi-photon entangled states with high efficiency in integrated photonic quantum systems is still a big challenge. The usual three-photon generation efficiency based on the third-order nonlinear effect is extremely low. Here, we propose a scheme to generate three-photon correlated states, which are entangled states in frequency space and bound states in real space, with high efficiency. This method relies on two crucial processes. On one hand, by employing a Sagnac interferometer, an incident photon can be transformed into a symmetric superposition of the clockwise and counterclockwise modes of the Sagnac loop, which can then be perfectly absorbed by the emitter. On the other hand, the coupling strengths of the two transition paths of the emitter to the Sagnac loop are set to be equal, under which the absorbed photon can be emitted completely from the cascaded transition path due to quantum interference. By adjusting the coupling strengths among the three transition paths of the emitter and the waveguide modes, we can control the spectral entanglement and spatial separation among the three photons. Our proposal can be used to generate three-photon entangled states on demand, and the efficiency can be higher than 90% with some practical parameters, which can find important applications in integrated quantum information processing.

Method for Tunnel Displacements Calculation Based on Mobile Tunnel Monitoring System.

Efficient, high-precision, and automatic measurement of tunnel structural changes is the key to ensuring the safe operation of subways. Conventional manual, static, and discrete measurements cannot meet the requirements of rapid and full-section detection in subway construction and operation. Mobile laser scanning technology is the primary method for tunnel detection. Herein, we propose a method to calculate shield tunnel displacements of a full cross-section tunnel. The point cloud data, obtained via a mobile tunnel deformation detection system, were fitted, projected, and interpolated to generate an orthophoto image. Combined with the cumulative characteristics of the tunnel gray gradient, the longitudinal ring seam of the tunnel was identified, while the Canny algorithm and Hough line detection algorithm identified the transverse seam. The symmetrical vertical foot method and cross-section superposition analysis were used to calculate the circumferential and radial displacements, respectively. The proposed displacement calculation method achieves automatic recognition of a ring seam, reduces human–computer interaction, and is fast, intelligent, and accurate. Furthermore, the description of the tunnel deformation location and deformation amount is more quantitative and specific. These results confirm the significance of shield tunnel displacement monitoring based on mobile monitoring systems in tunnel disease monitoring.

Dynamics of field nonclassicality in the Jaynes–Cummings model

Employing an informational quantifier for nonclassicality of bosonic field based on the Wigner–Yanase skew information, we investigate the dynamics of field nonclassicality in the Jaynes–Cummings model evolving from several typical initial atom–field states: coherent states, Fock states, and thermal states for the field, and ground state, excited state, symmetric superposition state, and maximally mixed state for the atom. We reveal some intriguing features of the field dynamics and their sensitivity on the initial states from an informational perspective. The results show that field nonclassicality can be generated in most cases and exhibits complex dynamic patterns involving collapses and revivals. A remarkable observation is that the initial coherent field states, assisted by the atom, can be converted to almost maximally nonclassical field states constrained by the average photon number, even though all coherent states are the most classical and possess the same minimal nonclassicality among pure states. The field dynamics may be exploited to estimate the initial atom as well as the field states, prepare desired evolving states and process quantum information.

On BER for M-User NOMA with Symmetric SC

In non-orthogonal multiple access (NOMA), the ideal perfect successive interference cancellation (SIC) is validated theoretically by the random channel coding, practically such as low-density parity-check (LDPC) codes or turbo codes. Recently, symmetric superposition coding (SSC) has been shown to achieve the ideal perfect SIC bit-error rate (BER) performance by simulations with as many as three users, while the authors of this letter derived the analytical expression for BER, only for to a two-user scenario. In this letter, the derivation of the closed-form BER expression for M users is reported. It is shown that the SSC NOMA achieves near-perfect SIC BER performance. This is possible for with two reasons; one is the power allocation of the user fairness, and the other is the optimal maximum-likelihood (ML) detection.

How Can Near-Perfect SIC NOMA Be Implemented? (Part II): Complement Superposition Coding for 4-Ary Pulse Amplitude Modulation

In non-orthogonal multiple access (NOMA), the successive interference cancellation (SIC) implementation is very important, because the performance of the stronger channel user with the low power allocation is greatly affected by the SIC performance. Up to now, in order to achieve the perfect SIC performance, two techniques for the single level modulation, such as binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK), have been reported in the literature; one way is the dynamic superposition coding (DSC), which is the combination of the normal superposition coding (NSC) and symmetric superposition coding (SSC). The other way is the orthogonal NOMA with polar on-off keying (POOK). As an extended research, this paper challenges the perfect SIC NOMA performance for the 4-ary pulse amplitude modulation (4PAM); the perfect SIC performance cannot be obtained by a simple combination of NSC and SSC, just as for BPSK. For 4PAM case, we need new superposition coding, i.e., the complement superposition coding (CSC). It is shown analytically that the combination of NSC, SSC, and CSC can achieve the near-perfect SIC performance. As a result, the DSC concept could be applied for the multilevel modulations, in order to achieve the near-perfect SIC performance in NOMA.

Improved Performance of NOMA: Multilevel Symmetric Superposition Coding under Rayleigh Fading Channel

The main principle of non-orthogonal multiple access (NOMA) recommends that low power is allocated to the strong channel user, in order to guarantee the user fairness. Recently, symmetric superposition coding (SSC) has been proposed to mitigate the effect of error propagation (EP) in NOMA with quadrature phase shift keying (QPSK) for visible light communication (VLC) networks. It has been verified analytically that SSC NOMA with binary phase shift keying (BPSK) achieves the performance of the perfect SIC for the power allocation factor range less than 50%. However, SSC for multilevel modulations has not been reported in the literature in NOMA. As continuing researches, we propose NOMA with the multilevel SSC for the 4-ary pulse amplitude modulation (4PAM). It is shown that the performance of 4PAM SSC NOMA achieves the perfect SIC performance for the power allocation factor range less than about 10 %, while the performance of 4PAM NOMA with the normal superposition coding (NSC) is the same as that of the perfect SIC NOMA for the power allocation factor range less than about 5 %. As a result, the promising feature of SSC, i.e., the improved performance on the low power allocation range, is still preserved for multilevel modulations.

Benefits from using two receivers for interpretation of low-strain integrity tests on pipe piles

The double-velocity symmetrical superposition method (DVSSM), which consists of superimposing and averaging two synchronization signals measured at two symmetrical points of the neutral plane of flexural vibration (in an angle of 90°), is proposed to eliminate the high-frequency interference at the pipe pile head without increasing the predominant period of impact pulse. An analytical solution is derived using the transfer matrix method. The calculated responses from the developed solution are compared with the experimental results for different receiving radius angles to evaluate the effectiveness of the developed solution. A parametric study is also conducted to investigate the suitability of the DVSSM. The findings demonstrate that the high-frequency interference is caused by a combination of the flexural behavior of the pile cross section and the wave propagation along the pipe pile head. The flexural vibration mode comprises the primary component of the high-frequency interference, which can be eliminated through the DVSSM without increasing the predominant period of impact pulse. The DVSSM can serve as an efficient method to detect defects near the pile head with much higher detection accuracy than the conventional method.

Two-dimensional magnetoexciton superposition states with Dirac cone dispersion law and quantum interference effects in optical transitions

The essential influence of the electron-hole (e-h) exchange Coulomb interaction on the properties of the two-dimensional magnetoexcitons was revealed. The main of them is the creation of two new symmetric and asymmetric superposition states formed by two bright magnetoexciton states with electron structure determined only by the direct Coulomb interaction and with the total angular momentum projections F=±1. The symmetric state due to the exchange e-h Coulomb interaction acquires a Dirac cone dispersion law in the range of small in-plane wave vectors with the group velocity proportional to the magnetic field strength B, with equal probabilities of the quantum transitions from the ground state of the crystal in both light circular polarizations but with maximum probability in the Faraday geometry of the light propagation and vanishing probability in the Voigt one. In difference on it, the asymmetric superposition state remains with the usual dispersion law inherited from the bare magnetoexciton states and has a dipole-active quantum transitions in both circular polarizations, indifferent on the direction of the light propagation. The both symmetric and asymmetric superposition states revealed the quantum interference effects in the case of the light with two linear polarizations, the vectors of which have different parities as regards the inversion of the light wave vector k→. The symmetric (asymmetric) state is allowed in the case of linear polarization vector with positive (negative) parity and is forbidden in the case of linear polarization vector with negative (positive) parity. The obtained optical results open the possibility to investigate the thermodynamic properties of the 2D Bose gas with Dirac cone dispersion law.

Variations of topological charge of vortex beam based on a diffraction plate with spiral transmission structures

The phenomenon of vortex beams passing through a diffraction plate with rotationally symmetric superposition of spiral pinholes array is investigated. The variations of the topological charges of vortex beams are theoretically analyzed, numerically simulated and experimentally observed. It proves that the obtained topological charge value (l) is a combination of that of incident beam (l0) and the number of the spiral structures (m). The relationship is l = Mm-l0, where M is an integer. With this study, we proved that spiral transmission structures can also achieve the variations of the topological charge of a vortex beam. And this method is simple and costless. With the advantages of this method, it might have important applications in optical communications and optical tweezers.

Multi-wavelength multi-focus Fresnel solar concentrator with square uniform irradiance: design and analysis.

In this paper, a two-step optical design method is proposed to build a superior Fresnel-based photovoltaic concentrator for enhancing light conversion efficiency with the multi-junction solar cell. In the first step, we orthogonally segment a traditional Fresnel concentrator and remove the two normal stripe bands around the horizontal and vertical axes, as well as recombine the resultant four quadrants again. By using such a specific Fresnel concentrator design, a square light pattern can be constructed owing to the off-axis non-rotational symmetric superposition of light. In the second step, as for the response wavelengths of a specific triple-junction solar cell, we further carry out a triple-wavelength and multi-focus design of the above Fresnel concentrator for improving the uniformity of light distribution on the solar cell. To show the validity of this novel design method, a solar concentrator, with typical design parameters including the geometrical concentration ratio of 800× and the F-number of 0.775, is designed and simulated. As a result, theoretical irradiance uniformity up to 87% is obtained. In addition, considering the fact that no second optical element is involved in the concentrator system, our design method inherently has the advantages of good compactness, high efficiency, low cost, and ease for mass-production. We believe that such a concentrator is of great significance to solar cells for high conversion efficiency of light in the concentrator photovoltaic system.

Quantifiable example of complementarity relation between optical orbital angular momentum and angular position

A light beam with phase singularity (PS) characterized with azimuthally symmetric angular positions (APs) can be constructed by the rotationally symmetric superposition of numerous fractional vortex light beams with identical charges. The profile of this light beam deforms after propagation owing to its orbital angular momentum (OAM) noneigenvalue, and the deformation degree can be evaluated by the degree of phase dislocation associated with the PS. The expectation value of the mean deviation of its OAM from its characteristic charge value and the variation of the degree of phase dislocation obey a proportionality relation. This light beam offers a quantifiable example of a complementarity relation between the observables of optical OAM and AP, which are the OAM noneigenvalue and intensity AP variation, respectively. This complementarity relation is significant for an existing experiment employing the quantum state of this light beam.

‘Near’-Cat States: Nonclassicality and Generation

We introduce new configurations of (anti-)symmetric superpositions of two ‘near’-coherent states, ∣α, δθ〉, shifted in phase by π, the latter being introduced by Othman et al. as a new class of quantum states attached to the simple harmonic oscillator and also generated via a Mach–Zehnder interferometer. To gain an insight into the effectiveness of these states in quantum information theory, we present a general analysis of nonclassical properties by evaluating the Mandel parameter, quadrature squeezing, amplitude-squared squeezing, and the Wigner distribution function. We show that the factor δθ plays an essential role in the nonclassical properties of these (anti-)symmetric superposed states. Finally, we propose a theoretical scheme to generate introduced states within a cavity QED framework.

Schwarzschild dynamical model of the Fornax dwarf spheroidal galaxy

We present a full dynamical model of the Fornax dwarf spheroidal galaxy obtained with the spherically symmetric Schwarzschild orbit superposition method applied to the largest kinematic data set presently available. We modelled the total mass content of the dwarf with the mass-to-light ratio $\Upsilon$ varying with radius and found that Fornax is with high probability embedded in a massive and extended dark matter halo. We estimated the total mass contained within 1$\,$kpc to be $M(<1\,$kpc$)=1.25^{+0.06}_{-0.13} \times 10^8\,$M$_{\odot}$. The data are consistent with the constant mass-to-light ratio, i.e. the mass-follows-light model, only at 3$\sigma$ level, but still require a high value of $\Upsilon \approx 11.2\,$M$_{\odot}/$L$_{\odot}$. Our results are in general agreement with previous estimates of the dynamical mass profile of Fornax. As the Schwarzschild method does not require any assumptions on the orbital anisotropy of the stars, we obtained a profile of the anisotropy parameter $\beta$ as an output of our modelling. The derived anisotropy is close to zero in the centre of the galaxy and decreases with radius, but remains consistent with isotropic orbits at all radii at 1$\sigma$ confidence level.