Degree Of Nonlocality Research Articles

(2 + 1) dimensional all-optical logical gates based on soliton interaction in bulk nonlocal nonlinear media

We propose the (2 + 1) dimensional all-optical logical gates based on the interaction between two components of vector solitons in nonlocal nonlinear media. The input logical states are controlled by tilting the input beams or not, and the output logical states are decided by integrated power on the photodetector. We design these logical gates in a theoretical model of liquid crystal E7 with only two input beams that are tilted in 2 dimensions, and this model is suitable to other nonlocal nonlinear media. With the degrees of nonlocality and the locations of two input beams properly preset, we achieve the logical AND, NAND, OR, NOR, XOR and NXOR gates. Expecting the logical OR gate, the logical gates are based on the attractive interaction.

Machine Learning the Physical Nonlocal Exchange-Correlation Functional of Density-Functional Theory.

We train a neural network as the universal exchange-correlation functional of density-functional theory that simultaneously reproduces both the exact exchange-correlation energy and the potential. This functional is extremely nonlocal but retains the computational scaling of traditional local or semilocal approximations. It therefore holds the promise of solving some of the delocalization problems that plague density-functional theory, while maintaining the computational efficiency that characterizes the Kohn-Sham equations. Furthermore, by using automatic differentiation, a capability present in modern machine-learning frameworks, we impose the exact mathematical relation between the exchange-correlation energy and the potential, leading to a fully consistent method. We demonstrate the feasibility of our approach by looking at one-dimensional systems with two strongly correlated electrons, where density-functional methods are known to fail, and investigate the behavior and performance of our functional by varying the degree of nonlocality.

Generation of bright spatial quasi-solitons by arbitrary initial beam profiles in local and nonlocal (1+1)-Dimensional nonlinear media

In this paper we demonstrate numerically that it is possible to generate bright spatial quasi-solitons, in media that are described by the (1+1)-Dimensional local and nonlocal Nonlinear Schrodinger Equation, using initial condition field distributions that are distinct from the analytical solution. In the local case different initial conditions were considered and in the nonlocal case different response functions and degrees of nonlocality were considered, obtaining the same behavior: at the beginning the initial profile is reshaped and after some distance, the beam propagates almost without change or in an small oscillatory way. The propagated intensity profile in the local case evolves to hyperbolic secant and in the nonlocal case to Gaussian, regardless of the degree of nonlocality. Analytical formulas for the propagated intensity profile are given.

Dynamics of Multipole Solitons and Vortex Solitons in PT-Symmetric Triangular Lattices with Nonlocal Nonlinearity

We investigate the evolution dynamics of solitons with complex structures in the PT-symmetric triangular lattices with nonlocal nonlinearity, including dipole solitons, six-pole solitons, and vortex solitons. Dipole solitons can be linearly stable with a small degree of gain/loss, while six-pole solitons can only be stable when both the degree of gain/loss and the degree of nonlocality are small. For unstable solitons, some humps will decay quickly or new hotspots will appear during propagation. According to the existence range of dipole solitons, the multipole solitons tend to exist in PT-symmetric triangular lattices whose nonlocal nonlinearity is intermediate. We also consider the vortex solitons with high topological charges in the same triangular lattices and find that their profiles are codetermined by the propagation constant, degree of nonlocality, and topological charge.

Neutron Star Matter and Baryonic Interactions

The properties of neutron-star matter up to the appearance of hyperons are calculated with the aid of Skyrme potentials. The conditions for the appearance of Λ hyperons in matter and values of the density at the point of their appearance are analyzed for various parametrizations of nucleon-nucleon and hyperon-nucleon interactions. The dependence of the results on the magnitude of density-dependent forces, the degree of nonlocality, the behavior of the symmetry energy, and incompressibility of nuclear matter is examined.

Nonlocality distillation and quantum voids

Via nonlocality distillation, a number of copies of a given nonlocal correlation can be turned into a new correlation displaying a higher degree of nonlocality. Apart from its clear relevance in situations where nonlocality is a resource, distillation protocols also play an important role in the understanding of information-theoretical principles for quantum theory. Here, we derive a necessary condition for nonlocality distillation from two copies and apply it, among other results, to show that $1$D and $2$D quantum voids --faces of the nonlocal simplex set with no quantum realization-- can be distilled up to PR-boxes. With that, we generalize previous results in the literature. For instance, showing a broad class of post-quantum correlations that make communication complexity trivial and violate the information causality principle.

Transition between self-focusing and self-defocusing in a nonlocally nonlinear system

We reveal the relevance between the nonlocality and the focusing/defocusing states in nonlocally nonlinear media, and predict a novel phenomenon that the self-focusing/self-defocusing property of the optical beam in the nonlocally nonlinear medium with a sine-oscillation response function depends on its degree of nonlocality. The transition from the focusing nonlinearity to the defocusing nonlinearity of the nonlinear refractive index will happen when the degree of nonlocality of the system goes cross a critical value, and vise verse. Bright and dark soliton solutions are obtained, respectively, in the focusing state and in the defocusing state, and their stabilities are also discussed. It is mentioned that such a phenomenon might be experimentally realized in the nematic liquid crystal with negative dielectric anisotropy or in the quadratic nonlinear medium.

Soliton dynamics in finite nonlocal media with cylindrical symmetry

The effect of finite boundaries in the propagation of spatial nonlocal solitons in media with cylindrical symmetry is analyzed. Using Ehrenfest's theorem together with the Green's function of the nonlinear refractive index equation, we derive an analytical expression for the force exerted on the soliton by the boundaries, verifying its validity by full numerical propagation. We show that the dynamics of the soliton are determined not only by the degree of nonlocality, but also by the boundary conditions for the refractive index. In particular, we report that a supercritical pitchfork bifurcation appears when the boundary condition exceed a certain threshold value.

Generation of solitons in media with arbitrary degree of nonlocality using an optimization procedure

Using a recently developed technique based on the Rayleigh-Ritz optimization principle, we generate solitons for media with an arbitrary degree of nonlocality. We demonstrate that it is possible to obtain a plethora of complex self-trapped beams using known solutions to the harmonic oscillator for one-dimensional (1D), 2D, and 3D systems, but working directly with a generalized nonlinear nonlocal Schr\odinger equation. We compare the parameters obtained variationally between the phenomenological Gaussian response and other more realistic nonlocal responses. We report that, for both kinds of nonlocal models, our approach obtains variational solutions that can remain self-trapped for certain conditions. We corroborate that, in general, the soliton dynamics can be different between the Gaussian response and the more realistic media for an arbitrary degree of nonlocality.

Intrinsic Relations of Bipartite Quantum Resources in Tripartite Systems

AbstractQuantum resources play crucial roles for displaying superiority in many quantum communication and computation tasks. To reveal the intrinsic relations hidden in these quantum resources, many efforts have been made in recent years. In this work, the correlations of the tripartite W‐type states based on bipartite quantum resources are investigated. The inter‐relations among the degree of coherence, concurrence, Bell nonlocality, and purity are presented. Considering Bell nonlocal and Bell local (satisfied the Clauser–Horne–Shimony–Holt inequality) states for the two‐qubit subsystems derived from the tripartite W‐type states, exact lower and upper boundaries of the degree of coherence versus concurrence are obtained. Interestingly, exact relation among the degree of coherence, concurrence, and purity is obtained. Moreover, coherence is also closely related to entanglement in two specific scenarios: the tripartite W‐type state under decoherence and a practical system for a renormalized spin‐1/2 Heisenberg model.

Concentration phenomena in the geometry of Bell correlations

Bell's theorem shows that local measurements on entangled states give rise to correlations incompatible with local hidden variable models. The degree of quantum nonlocality is not maximal though, as there are even more nonlocal theories beyond quantum theory still compatible with the nonsignalling principle. In spite of decades of research, we still have a very fragmented picture of the whole geometry of these different sets of correlations. Here we employ both analytical and numerical tools to ameliorate that. First, we identify two different classes of Bell scenarios where the nonsignalling correlations can behave very differently: in one case, the correlations are generically quantum and nonlocal while on the other quite the opposite happens as the correlations are generically classical and local. Second, by randomly sampling over nonsignalling correlations, we compute the distribution of a nonlocality quantifier based on the trace distance to the local set. With that, we conclude that the nonlocal correlations can show concentration phenomena: their distribution is peaked at a distance from the local set that increases both with the number of parts or measurements being performed.

Quantifying wave-function overlaps in inhomogeneous Majorana nanowires

A key property of Majorana zero modes is their protection against local perturbations. In the standard picture, this protection is guaranteed by a high degree of spatial nonlocality of the Majoranas, namely a suppressed wave-function overlap, in the topological phase. However, a careful characterisation of resilience to local noise goes beyond mere spatial separation, and must also take into account the projection of wave-function spin. By considering the susceptibility of a given zero mode to different local perturbations, we find the relevant forms of spin-resolved wave-function overlaps that measure its resilience. We quantify these overlaps and study their dependence with nanowire parameters in several classes of experimentally relevant configurations. These include nanowires with inhomogeneous depletion and induced pairing, barriers and quantum dots. Smooth inhomogeneities have been shown to produce near-zero modes, so-called pseudo-Majoranas, below the critical Zeeman field in the bulk. Surprisingly, their resilience is found to be comparable or better than that of topological Majoranas in realistic systems. We further study how accurately their overlaps can be estimated using a purely local measurement on one end of the nanowire, accessible through conventional transport experiments. In uniform nanowires this local estimator is remarkably accurate. In inhomogeneous cases it is less accurate but can still provide reasonable estimates for potential inhomogeneities of the order of the superconducting gap. We further analyse the zero mode wave-function structure, spin texture and spectral features associated with each type of inhomogeneity. All our results highlight the strong connection between internal wave-function degrees of freedom, nonlocality and protection in smoothly inhomogeneous nanowires.

Propagation dynamics of finite-energy Airy beams in competing nonlocal nonlinear media

We investigate the propagation dynamics of Airy beams in competing nonlocal nonlinear media featuring focusing cubic and defocusing quintic nonlocal optical nonlinearities. By means of numerical methods, it has been shown that the solitons shedding from Airy beams and their interaction are strongly dependent on the strength of nonlinearity and degree of nonlocality. In a highly nonlocal regime, anomalous interaction of two Airy solitons with high intensity leads to the formation of stable bound states in both in-phase and out-of-phase cases.

Majorana oscillations modulated by Fano interference and degree of nonlocality in a topological superconducting-nanowire–quantum-dot system

We explore theoretically the influence of Fano interference in the so-called Majorana oscillations in a T-shaped hybrid setup formed by a quantum dot (QD) placed between conducting leads and side-coupled to a topological superconducting nanowire (TSNW) hosting zero-energy Majorana bound states (MBSs) at the ends. Differential conductance as a function of the external magnetic field reveals oscillatory behavior. Both the shape and amplitude of the oscillations depend on the bias-voltage, degree of MBSs non-locality and Fano parameter of the system determining the regime of interference. When the latter is such that direct lead-lead path dominates over lead-QD-lead path and the bias is tuned in resonance with QD zero-energy, pronounced fractional Fano-like resonances are observed around zero-bias for highly non-local geometries. Further, the conductance profiles as a function of both bias-voltage and QD energy level display "bowtie" and "diamond" shapes, in qualitative agreement with both previous theoretical and experimental works. These findings ensure that our proposal can be used to estimate the degree of MBS non-locality, thus allowing to investigate their topological properties.

Nonlocality of Majorana modes in hybrid nanowires

Spatial separation of Majorana zero modes distinguishes trivial from topological midgap states and is key to topological protection in quantum computing applications. Although signatures of Majorana zero modes in tunneling spectroscopy have been reported in numerous studies, a quantitative measure of the degree of separation, or nonlocality, of the emergent zero modes has not been reported. Here, we present results of an experimental study of nonlocality of emergent zero modes in superconductor-semiconductor hybrid nanowire devices. The approach takes advantage of recent theory showing that nonlocality can be measured from splitting due to hybridization of the zero mode in resonance with a quantum dot state at one end of the nanowire. From these splittings as well as anticrossing of the dot states, measured for even and odd occupied quantum dot states, we extract both the degree of nonlocality of the emergent zero mode, as well as the spin canting angles of the nonlocal zero mode. Depending on the device measured, we obtain either a moderate degree of nonlocality, suggesting a partially separated Andreev subgap state, or a highly nonlocal state consistent with a well-developed Majorana mode.

Generation, transport and detection of valley-locked spin photocurrent in WSe2-graphene-Bi2Se3 heterostructures.

Quantum optoelectronic devices capable of isolating a target degree of freedom (DoF) from other DoFs have allowed for new applications in modern information technology. Many works on solid-state spintronics have focused on methods to disentangle the spin DoF from the charge DoF1, yet many related issues remain unresolved. Although the recent advent of atomically thin transition metal dichalcogenides (TMDs) has enabled the use of valley pseudospin as an alternative DoF2,3, it is nontrivial to separate the spin DoF from the valley DoF since the time-reversal valley DoF is intrinsically locked with the spin DoF4. Here, we demonstrate lateral TMD-graphene-topological insulator hetero-devices with the possibility of such a DoF-selective measurement. We generate the valley-locked spin DoF via a circular photogalvanic effect in an electric-double-layer WSe2 transistor. The valley-locked spin photocarriers then diffuse in a submicrometre-long graphene layer, and the spin DoF is measured separately in the topological insulator via non-local electrical detection using the characteristic spin-momentum locking. Operating at room temperature, our integrated devices exhibit a non-local spin polarization degree of higher than 0.5, providing the potential for coupled opto-spin-valleytronic applications that independently exploit the valley and spin DoFs.

Time evolution of intrinsic alignments of galaxies

Intrinsic alignments (IA), correlations between the intrinsic shapes and orientations of galaxies on the sky, are both a significant systematic in weak lensing and a probe of the effect of large-scale structure on galactic structure and angular momentum. In the era of precision cosmology, it is thus especially important to model IA with high accuracy. Efforts to use cosmological perturbation theory to model the dependence of IA on the large-scale structure have thus far been relatively successful; however, extant models do not consistently account for time evolution. In particular, advection of galaxies due to peculiar velocities alters the impact of IA, because galaxy positions when observed are generally different from their positions at the epoch when IA is believed to be set. In this work, we evolve the galaxy IA from the time of galaxy formation to the time at which they are observed, including the effects of this advection, and show how this process naturally leads to a dependence of IA on the velocity shear. We calculate the galaxy-galaxy-IA bispectrum to tree level (in the linear matter density) in terms of the evolved IA coefficients. We then discuss the implications for weak lensing systematics as well as for studies of galaxy formation and evolution. We find that considering advection introduces nonlocality into the bispectrum, and that the degree of nonlocality represents the memory of a galaxy's path from the time of its formation to the time of observation. We discuss how this result can be used to constrain the redshift at which IA is determined and provide Fisher estimation for the relevant measurements using the example of SDSS-BOSS.

Nonlocal logarithmic nonlinear optical soliton

The propagation of optical beam in (1 + 2)-dimensional nonlocal logarithmic nonlinear media is studied. The numerical simulation shows that the intensity profiles of solitons undergo a gradual and continuous transition from a Gaussian-shaped function in the general nonlocal media to an approximately hyperbolic secant function in the local case. Due to the nonlocal effect, the stability of solitons increases with the increase of nonlocality degree. Concretely speaking, the quasi-stable solitons can be formed in local and weakly nonlocal (nonlocality degree α < 0.5) logarithmic nonlinear media. In general nonlocal case (0.5 ≤ α≤1), the completely stable solitons can be formed. In special case (α = 1), even the initial power increase largely, the solitons can still exist even the initial power has large change for the saturable nonlinear contract effect. However, when α = 1.1, the solitons cannot be formed at any initial power because nonlinear effect is too small to balance diffraction effect.

Multi-pole dark solitons in nonlocal and cubic-quintic nonlinear medium

In this paper, we mainly simulate the characteristics of the ground state dark soliton and the multipole dark soliton in the nonlocal and cubic-quintic nonlinear medium. Firstly, the influences of the degree of nonlocality on the amplitude and the width of the dark soliton in the self-defocusing cubic-and self-focusing quantic-nonlinear medium are studied. Secondly, we find the nonlinear parameters affecting the amplitude values of solitons, but the refractive index induced by the light beam is always a fixed value. The numerical results show that the ground state dark soliton can be propagated stably alone the z axis, and the stable states of the dipole soliton and the dark tri-pole and quadru-pole solitons are stable. However, some quadru-pole dark soliton is unstable after propagating the remote distance. Furthermore, we also discuss the characteristics of the ground state dark soliton and the dark dipole soliton in the local cubic-nonlinear and nonlocal quantic nonlinear media. Both the amplitude and the beam width of the dark ground state soliton and dark dipole soliton are also affected by the degree of nonlocality and nonlinearity. Two boundary values of the induced refractive index change with the variations of the three nonlinear parameters. The dark soliton and the dipole dark soliton are more stable in the self-focusing cubic nonlinear and the nonlocal self-defocusing quantic nonlinear medium than those in the self defocusing cubic nonlinear and nonlocal self-focusing quantic nonlinear medium. The powers of single dark soliton and dark tri-pole soliton decrease monotonically with the increase of propagation constant when the cubic-quintic nonlinearities are certain values and these degrees of nonlocalities are taken different values. Furthermore, we also analyze linear stabilities of various nonlocal spatial dark solitons. And we find that the dipole dark soliton is unstable when the propagation constant is in the region[-0.9,-1.0]. These properties of linear stabilities of other multi-pole dark solitons are the same as their propagation properties.

How Does Nonlocal Dispersal Affect the Selection and Stability of Periodic Traveling Waves?

In ecology a number of spatiotemporal datasets on cyclic populations reveal periodic traveling waves of abundance. This calls for studies of periodic traveling wave solutions of ecologically realistic mathematical models. For many species, such models must include long-range dispersal. However, mathematical theory on periodic traveling waves is almost entirely restricted to reaction-diffusion equations, which assume purely local dispersal. I study integrodifferential equation models in which dispersal is represented via a convolution. The dispersal kernel is assumed to be of either Gaussian or Laplace form; in either case it contains a parameter scaling the width of the kernel. I show that as this parameter tends to zero, the integrodifferential equation asymptotically approaches a reaction-diffusion model. I exploit this limit to determine the effect of a small degree of nonlocality in dispersal on periodic traveling wave properties and on the selection of a periodic traveling wave solution by localized perturbation of an unstable steady state. My analysis concerns equations of “$\lambda$--$\omega$” type, which are the normal form of a large class of oscillatory systems close to a Hopf bifurcation point. I finish the paper by showing how my results can be used to determine the effect of nonlocal dispersal on spatiotemporal dynamics in a predator-prey system.