Degree Of Nonlocality Research Articles

Thermal quantum memory, Bell-non-locality, and entanglement behaviors in a two-spin Heisenberg chain model

This paper explores thermal quantum memory-assisted entropic uncertainty, Bell-non-locality, and entanglement in a two-qubit Heisenberg XXX chain with x-directional Dzyaloshinskii-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions in thermal equilibrium. We find this crucial that the initial degree of nonlocality and entanglement in the two-qubit state entirely depends upon the temperature, orientation, and strength of the DM and KSEA interaction of the magnetic field. Among many other situations, the magnetic field characterized by DM interaction with minimal temperature, exchange coupling strength, and KSEA interaction is the most reliable for generating and maintaining maximal nonlocality and entanglement while completely suppressing entropic uncertainty. On the other hand, repeated revivals and non-Markovian dynamics have been observed when the magnetic field is characterized by exchange coupling constant, DM and KSEA interaction with a higher temperature limit. Except for temperature-based magnetic fields, we show that maximal entanglement and nonlocality are generated and preserved in the two qubits with zero-order entropic uncertainty, which we believe is a better result than previous studies.

Long-time protection of thermal correlations in a hybrid-spin system under random telegraph noise.

The engineering features of transmitting mediums and their impact on different characteristics of a quantum system play a significant role in the efficient performance of nonlocal protocols. For this purpose, the dynamics of open quantum systems and coupling mediums remain a pathway. In this work, we investigate the dynamics of quantum correlations using negativity, uncertainty-induced nonlocality, and local quantum Fisher information in a hybrid qubit-qutrit thermal state when coupled with a magnetic field and influenced by random telegraph noise. Different features of the system parameters are taken into account while designing longer preservation of qubit-qutrit correlations. We show that the temperature has an inverse impact on the initial values of negativity, uncertainty-induced nonlocality, and local quantum Fisher information. When the magnetic field is characterized by different features, the entanglement, nonlocality, and Fisher information show a variety of dynamical maps, assuring their distinct nature. In addition, the qubit-qutrit correlations undergo repeated revivals when the configuration is restricted to the non-Markovian regime. On the other hand, an exponential drop with a single minimum is observed in the Markovian regime of the coupled field. Most importantly, our findings reveal that the present coupled fields have several advantages that can be leveraged to generate the optimal degree of entanglement, nonlocality, and local quantum Fisher information preservation in quantum dynamical maps.

Nonlocal quantum correlations in a bipartite quantum system coupled to a bosonic non-Markovian reservoir

In this paper, we explore the dynamics of nonlocal correlations in a two-qubit system, that is, first prepared in a Gisin state and then interacts with a bosonic non-Markovian environment. We employ uncertainty-induced nonlocality (UIN) and the Horodecki measure (Bell function) to characterize the degree of nonclassical correlations and quantum nonlocality in the system, taking into account the influence of the non-Markovian reservoir. The dynamics of the UIN and the Bell nonlocality are next examined using the various parameters that define the non-Markovian reservoir and the initial Gisin state. Our results show that the amount of nonlocal correlations and the degree of violation of Bell’s inequality can be modulated by varying the physical parameters characterizing the non-Markovian reservoir and the initial Gisin state. We also show that in some specific cases, the system exhibits nonclassical correlations while the evolved Gisin state does not violate Bell’s inequality. Our results also confirm that UIN is robust than Bell’s nonlocality in the presence of decoherence induced by the interaction with the non-Markovian reservoir.

Stable High‐Dimensional Weak‐Light Soliton Molecules and Their Active Control

AbstractBound states of solitons, alias soliton molecules (SMs), are well known in 1D systems, while making stable bound states of multidimensional solitons is a challenging problem because of the underlying instabilities. Here, a scheme for the creation of stable (2+1)D and (3+1)D optical SMs in a gas of cold Rydberg atoms is proposed, in which electromagnetically induced transparency (EIT) is induced by a control laser field. It is shown that, through the interplay of the EIT and the strong long‐range interaction between the Rydberg atoms, the system gives rise to giant nonlocal Kerr nonlinearity, which in turn supports stable (2+1)D spatial optical SMs, as well as ring‐shaped soliton necklaces, including rotating ones. They feature a large size, low generation power, and can be efficiently manipulated by tuning the nonlocality degree of the Kerr nonlinearity. Stable (3+1)D spatiotemporal optical SMs, composed of fundamental or vortex solitons, with low power and ultraslow propagation velocity, can also be generated in the system. These SMs can be stored and retrieved through the switching off and on of the control laser field. The findings reported here suggest applications to data processing and transmission in optical systems.

Parameters controlling of vortex solitons in nonlocal nonlinear medium with gradually characteristic length

This paper discusses the dynamics of vortex beam in nematic liquid crystals with the tunable characteristic length (CL) of response function. It is found that the transition of the soliton states with different widths during propagations can be controlled by changing the CL under the condition that the nonlocal degree is constant. Furthermore, the transitions propagation of different soliton state is stable and can resist noise. In addition, the numerical results prove that the parameters of vortex solitons, such as rotating periods of angles, orbital angular momentum (OAM), gradient force upon micro-particles all can be controlled conveniently at the desired positions. The controllable density of OAM and gradient force have important academic value and application prospect in the field of optical tweezers and spanner.

Linear and nonlinear Bragg diffraction by electromagnetically induced gratings with PT symmetry and their active control in a Rydberg atomic gas

Due to its myriad applications in many fields of science and technology, novel light diffraction from specially designed optical gratings is a subject of great interest. Here, we propose a scheme to realize the linear and nonlinear Bragg diffractions from an electromagnetically induced grating (EIG) with parity-time $(\mathcal{PT})$ symmetry in a cold Rydberg atomic gas, where the Rydberg-Rydberg interaction between atoms are mapped to strong and long-range interaction between photons, characterized by a giant nonlocal Kerr nonlinearity. We show that a probe laser beam with very low light intensity incident upon the $\mathcal{PT}$-symmetric EIG can display distinctive asymmetric diffraction patterns, which can be actively manipulated through tuning the gain-absorption coefficient of the EIG and the input power of the laser beam. We also show that the intensity distribution among different diffraction orders depends significantly on the $\mathcal{PT}$-symmetry property of the EIG and on the magnitude and nonlocality degree of the Kerr nonlinearity. In addition, we demonstrate that such Bragg diffraction patterns can be controlled by an external gradient magnetic field, which provides a different way of diffraction control. The research results reported here are not only useful for understanding the unique properties of linear and nonlinear Bragg diffractions by $\mathcal{PT}$-symmetric gratings but may also be promising for designing optical devices applicable in optical information processing and transmission.

Fractional Entropy of Multichannel Kondo Systems from Conductance-Charge Relations.

Fractional entropy is a signature of nonlocal degrees of freedom, such as Majorana zero modes or more exotic non-Abelian anyons. Although direct experimental measurements remain challenging, Maxwell relations provide an indirect route to the entropy through charge measurements. Here we consider multichannel charge-Kondo systems, which are predicted to host exotic quasiparticles due to a frustration of Kondo screening at low temperatures. In the absence of experimental data for the charge occupation, we derive relations connecting the latter to the conductance, for which experimental results have recently been obtained. Our analysis indicates that Majorana and Fibonacci anyon quasiparticles are well developed in existing two- and three-channel charge-Kondo devices, and that their characteristic k_{B}logsqrt[2] and k_{B}log[(1+sqrt[5])/2] entropies are experimentally measurable.

Vector Spatiotemporal Solitons and Their Memory Features in Cold Rydberg Gases

We propose a scheme to generate stable vector spatiotemporal solitons through a Rydberg electromagnetically induced transparency (Rydberg-EIT) system. Three-dimensional vector monopole and vortex solitons have been found under three nonlocal degrees. The numerical calculation and analytical solutions indicate that these solitons are generated with low energy and can stably propagate along the axes. The behavior of vector spatiotemporal solitons can be manipulated by the local and nonlocal nonlinearities. The results show a memory feature as these solitons can be stored and retrieved effectively by tuning the control field.

Multi-peak solitons in nonlocal nonlinear system with sine-oscillation response

The multi-peak solitons and their stability are investigated for the nonlocal nonlinear system with the sine-oscillation response, including both the cases of positive and negative Kerr coefficients. The Hermite–Gaussian-type multi-peak solitons and the ranges of the degree of nonlocality within which the solitons exist are analytically obtained by the variational approach. This is the first time, to our knowledge at least, to discuss the solution existence range of the multi-peak solitons analytically, although approximately. The variational analytical results are confirmed by the numerical ones. The stability of the multi-peak solitons are addressed by the linear stability analysis. It is found that the upper thresholds of the peak-number of the stable solitons are five and four for the system with negative and positive Kerr coefficients, respectively.

Coupled mode and novel soliton structure in fused coupler

In this paper, we investigate the characteristics of bright-like solitons, flat-topped solitons, and gray solitons in nonlocal nonlinear fused coupler. Firstly, the fundamental bright-like solitons with different parameters are obtained by the Newton iteration. It is found that the peak value and beam width of the ground state bright-like soliton increase with the enhancement of the nonlocality degree and nonlinear parameter, and they decrease with the propagation constant increasing. The power of the ground state bright-like soliton increases with the increase of the nonlocality degree and the width of coupling function, and it decreases with the propagation constant increasing. These numerical results can also be verified in the case of multipolar bright-like solitons. Secondly, by changing the coupled mode, the solutions of multipolar bright-like solitons, flat-topped soliton and grey solitons are obtained. The transmission stability of multipolar bright-like solitons, flat-topped soliton and grey solitons are studied. The stability of solitons is verified by means of linear stability analysis and fractional Fourier evolution. In the process of long-distance propagation, the propagation of bright-like solitons, gray solitons, and flat-topped soliton with one to three-pole symmetric peaks are stable, and the tripolar bright-like solitons with different soliton peaks and tripolar gray solitons are unable to transmit steadily. At the same time, it is found that the gray soliton with three poles or more is not easy to maintain its transmission stability. It is also found that the higher the grey scale of the gray soliton, the easier it is to realize stable transmission. Finally, it is found that the coupling function width not only affects the power of the soliton, but also realize the conversion among different soliton structures by adjusting the coupling function width.

Deflection and manipulation of weak optical solitons by non-Hermitian electromagnetically induced gratings in Rydberg atoms

Based on a Rydberg-electromagnetically-induced-transparency (Rydberg-EIT) system, an electromagnetically induced grating (EIG) with parity-time (<inline-formula><tex-math id="M1">\begin{document}${\cal{PT}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20220456_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20220456_M1.png"/></alternatives></inline-formula>) symmetry is realized. The formation of solitons before the probe laser field reaching the EIG as well as its deflection when passing through the EIG are both investigated. It is found that due to the enhanced nonlinear optical effect of the Rydberg-EIT system, stable optical soliton can be formed with a very weak input light energy. In addition, it is found that by changing the gain/absorption coefficient of EIG, the period of EIG, and the nonlocality degree of optical Kerr nonlinear of the system, the deflection degree of the optical soliton can be effectively changed and manipulated. The research results of this work can provide a theoretical basis for the future applications of <inline-formula><tex-math id="M2">\begin{document}${\cal{PT}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20220456_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20220456_M2.png"/></alternatives></inline-formula>-symmetric EIG and may be useful in the fields of all-optical manipulation and optical information processing.

Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom

In the tensorial group field theory approach to quantum gravity, the theory is based on discrete building blocks and continuum spacetime is expected to emerge from their collective dynamics, possibly at criticality, via a phase transition. On a compact group of fixed volume this can be expected to be only possible in a large-volume or thermodynamic limit. Here we show how phase transitions are possible in TGFTs in two cases: a) considering the non-local group degrees of freedom on a non-compact Lie group instead of a compact one (or taking a large-volume limit of a compact group); b) in models including ℝ-valued local degrees of freedom (that can be interpreted as discrete scalar fields, often used in this context to provide a matter reference frame). After adapting the Landau-Ginzburg approach to this setting of mixed local/non-local degrees of freedom, we determine the critical dimension beyond which there is a Gaussian fixed point and a continuous phase transition which can be described by mean-field theory. This is an important step towards the realization of a phase transition to continuum spacetime in realistic TGFT models for quantum gravity.

SpookyNet: Learning force fields with electronic degrees of freedom and nonlocal effects

Machine-learned force fields combine the accuracy of ab initio methods with the efficiency of conventional force fields. However, current machine-learned force fields typically ignore electronic degrees of freedom, such as the total charge or spin state, and assume chemical locality, which is problematic when molecules have inconsistent electronic states, or when nonlocal effects play a significant role. This work introduces SpookyNet, a deep neural network for constructing machine-learned force fields with explicit treatment of electronic degrees of freedom and nonlocality, modeled via self-attention in a transformer architecture. Chemically meaningful inductive biases and analytical corrections built into the network architecture allow it to properly model physical limits. SpookyNet improves upon the current state-of-the-art (or achieves similar performance) on popular quantum chemistry data sets. Notably, it is able to generalize across chemical and conformational space and can leverage the learned chemical insights, e.g. by predicting unknown spin states, thus helping to close a further important remaining gap for today’s machine learning models in quantum chemistry.

From Ising Model to Kitaev Chain

In this general article, we map the one-dimensional transverse field quantum Ising model of ferromagnetism to Kitaev's one-dimensional p-wave superconductor, which has its application in fault-tolerant topological quantum computing. Mapping Pauli's spin operators of transverse Ising chain to spinless fermionic creation and annihilation operators by Inverse Jordan-Wigner transformation leads to a Hamiltonian form closely related to Kitaev Chain, which exhibits topological phase transition where phases are characterized by different topological invariant that changes discontinuously at the transition point. Kitaev Chain supports two Majorana zero modes (MZMs) in the non-trivial topological phase, while none is in the trivial phase. The doubly degenerate ground state of the transverse Ising in ferromagnetic phase corresponds to non-local free fermion degree made from MZMs. The quasi-particle excitations of Ising chain, viz., domain wall formation in the ferromagnetic phase and spin-flip in paramagnetic phase maps to Bogoliubon excitations. The mapping suggests that a non-local order parameter can be defined for Kitaev Chain to work with the usual paradigm of Landau's theory.

Topological isoconductance signatures in Majorana nanowires

We consider transport properties of a hybrid device composed by a quantum dot placed between normal and superconducting reservoirs, and coupled to a Majorana nanowire: a topological superconducting segment hosting Majorana bound states (MBSs) at the opposite ends. It is demonstrated that if highly nonlocal and nonoverlapping MBSs are formed in the system, the zero-bias Andreev conductance through the dot exhibits characteristic isoconductance profiles with the shape depending on the spin asymmetry of the coupling between the dot and the topological superconductor. Otherwise, for overlapping MBSs with less degree of nonlocality, the conductance is insensitive to the spin polarization and the isoconductance signatures disappear. This allows to propose an alternative experimental protocol for probing the nonlocality of the MBSs in Majorana nanowires.

Self-organized structures of two-component laser fields and their active control in a cold Rydberg atomic gas

We investigate the formation and control of stationary optical patterns in a cold Rydberg atomic gas via double electromagnetically induced transparency. We show that, through the modulational instability of plane-wave state of a laser field with two polarization components, the system undergoes a spontaneous symmetry breaking and hence the emergence of plentiful self-organized spatial optical structures, which can be manipulated by the ratio between the cross- and self-Kerr nonlinearities, the nonlocality degree of the Kerr nonlinearities, and the populations initially prepared in the two atomic ground states. Interestingly, a crossover from mixture to separation in space (optical phase separation) of the two polarization components occurs when the ratio between the cross- and self-Kerr nonlinearities exceeds a critical value. We also show that the system supports nonlocal two-component spatial optical solitons and vortices when the parameters of the system are selected suitably. The rich diversity and active controllability of the self-organized optical structures reported here provide a way for realizing novel optical patterns and solitons and their structural phase transitions based on Rydberg atomic gases.

Propagations of Fresnel diffraction accelerating beam in Schrödinger equation with nonlocal nonlinearity* *Project supported by the National Natural Science Foundation of China (Grant Nos. 61805068, 61875053, and 62074127), China Postdoctoral Science Foundation (Grant No. 2017M620300), and the Fund from the Science and Technology Department of Henan Province, China (Grant No. 202102210111).

Accelerating beams have been the subject of extensive research in the last few decades because of their self-acceleration and diffraction-free propagation over several Rayleigh lengths. Here, we investigate the propagation dynamics of a Fresnel diffraction beam using the nonlocal nonlinear Schrödinger equation (NNLSE). When a nonlocal nonlinearity is introduced into the linear Schrödinger equation without invoking an external potential, the evolution behaviors of incident Fresnel diffraction beams are modulated regularly, and certain novel phenomena are observed. We show through numerical calculations, under varying degrees of nonlocality, that nonlocality significantly affects the evolution of Fresnel diffraction beams. Further, we briefly discuss the two-dimensional case as the equivalent of the product of two one-dimensional cases. At a critical point, the Airy-like intensity profile oscillates between the first and third quadrants, and the process repeats during propagation to yield an unusual oscillation. Our results are expected to contribute to the understanding of NNLSE and nonlinear optics.

Spatial locality of electronic correlations in LiFeAs

We address the question of the degree of spatial non-locality of the self energy in the iron-based superconductors, a subject which is receiving considerable attention. Using LiFeAs as a prototypical example, we extract the self energy from angular-resolved photoemission spectroscopy (ARPES) data. We use two distinct electronic structure references: density functional theory in the local density approximation and linearized quasiparticle self consistent GW (LQSGW). We find that with the LQSGW reference, spatially local dynamical correlations provide a consistent description of the experimental data, and account for some surprising aspects of the data such as the substantial out of plan dispersion of the electron Fermi surface having dominant xz/yz character. Hence, correlations effects can be separated into static non-local contributions well described by LQSGW and dynamical local contributions. Hall effect and resistivity data are shown to be consistent with this description.

Experimentally Bounding Deviations From Quantum Theory in the Landscape of Generalized Probabilistic Theories

Many experiments in the field of quantum foundations seek to adjudicate between quantum theory and speculative alternatives to it. This requires one to analyze the experimental data in a manner that does not presume the correctness of the quantum formalism. The mathematical framework of generalized probabilistic theories (GPTs) provides a means of doing so. We present a scheme for determining which GPTs are consistent with a given set of experimental data. It proceeds by performing tomography on the preparations and measurements in a self-consistent manner, i.e., without presuming a prior characterization of either. We illustrate the scheme by analyzing experimental data for a large set of preparations and measurements on the polarization degree of freedom of a single photon. We first test various hypotheses for the dimension of the GPT vector space for this degree of freedom. Our analysis identifies the most plausible hypothesis to be dimension 4, which is the value predicted by quantum theory. Under this hypothesis, we can draw the following additional conclusions from our scheme: (i) that the smallest and largest GPT state spaces that could describe photon polarization are a pair of polytopes, each approximating the shape of the Bloch sphere and having a volume ratio of 0.977±0.001, which provides a quantitative bound on the scope for deviations from the state and effect spaces predicted by quantum theory, and (ii) that the maximal violation of the Clauser, Horne, Shimony, and Holt inequality can be at most 1.3%±0.1 greater than the maximum violation allowed by quantum theory, and the maximal violation of a particular inequality for universal noncontextuality can not differ from the quantum prediction by more than this factor on either side. The only possibility for a greater deviation from the quantum state and effect spaces or for greater degrees of supraquantum nonlocality or contextuality, according to our analysis, is if a future experiment (perhaps following the scheme developed here) discovers that additional dimensions of GPT vector space are required to describe photon polarization, in excess of the four dimensions predicted by quantum theory to be adequate to the task.4 MoreReceived 31 August 2020Accepted 1 March 2021DOI:https://doi.org/10.1103/PRXQuantum.2.020302Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasOptical tests of quantum theoryQuantum opticsQuantum InformationAtomic, Molecular & Optical

Inertial amplification induced band gaps in corrugated-core sandwich panels

Corrugated-core sandwich panels (CSPs) have numerous applications but suffer from poor vibration performance in low-frequency range. To address this issue, a type of four-bar inertial amplification (IA) mechanism, whose inertia is increased by amplifying the movement of small masses, is proposed here to enhance the low-frequency vibration reduction capability of CSPs. The proposed structure is modelled by using finite element method (FEM) with considering the in-plane and out-of-plane degrees of freedom of IA mechanisms simultaneously. After validating the proposed model by the commercial software from the perspective of the band-structure, the vibration characteristics of the IA-CSP are investigated numerically. The results show that the attachment of the IA mechanisms can obtain wide bandgaps in low-frequency range, which hence greatly enhancing the vibration suppression performance of typical CSPs. Compared with the local resonators attached CSP, the proposed IA-CSP achieves broader band attenuation in low-frequency range with the same additional mass. Considering spatial constraints, the parametric studies are performed, which reveals that the spans and local stiffness of the IA attached locations determine the degree of nonlocality and hence influence the edge frequencies of bandgaps. The concept of tunable bandgap knob is finally presented to realize the dynamic manipulation of bandgaps under the spatial constraints.