Long-range nonlocal flow of vortices in narrow superconducting channels

We report a new nonlocal effect in vortex matter, where an electric current confined to a small region of a long and sufficiently narrow superconducting wire causes vortex flow at distances hundreds of intervortex separations away. The observed remote traffic of vortices is attributed to a very efficient transfer of a local strain through the one-dimensional vortex lattice (VL), even in the presence of disorder. We also observe mesoscopic fluctuations in the nonlocal vortex flow, which arise due to "traffic jams" when vortex arrangements do not match a local geometry of a superconducting channel.     

Polarization effects in nanoaggregates of silver caused by local and nonlocal nonlinear-optical responses

A theoretical and experimental study is made into the combined manifestation of local and nonlocal optical responses in a cubic nonlinear isotropic medium such as an aggregated colloidal silver solution. The phenomenological treatment of polarization effects is performed for the general case with due regard for the frequency dispersion of both local and nonlocal nonlinearities and for the noncollinear propagation of pump and probe light waves. The inverse Faraday effect, the optical Kerr effect, and the self-rotation of the polarization ellipse in a fractal-disordered nonlinear medium are observed for the first time. The tensor components of the local and nonlocal cubic nonlinearities of colloidal silver solutions are measured for different degrees of aggregation. It is demonstrated that, as the size of silver aggregate increases, the nonlocal nonlinear response increases much more strongly than the local one. An inference is made that the mechanical motion of metal nanoparticles because of their dynamic interaction with the light wave field can contribute to the nonlinear polarization effects.     

Single photon transport properties in coupled cavity arrays nonlocally coupled to a two-level atom in the presence of dissipation

We discuss the effects of dissipation on the behavior of single photon transport in a system of coupled cavity arrays,with the two nearest cavities nonlocally coupled to a two-level atom.The single photon transmission amplitude is solved exactly by employing the quasi-boson picture.We investigate two different situations of local and nonlocal couplings,respectively.Comparing the dissipative case with the nondissipative one reveals that the dissipation of the system increases the middle dip and lowers the peak of the single photon transmission amplitudes,broadening the line width of the transport spectrum.It should be noted that the influence of the cavity dissipation to the single photon transport spectrum is asymmetric.By comparing the nonlocal coupling with the local one,one can find that the enhancement of the middle dip of single photon transmission amplitudes is mostly caused by the atom dissipation and that the reduced peak is mainly caused by the cavity dissipation,no matter whether it is a nonlocal or local coupling case.Whereas in the nonlocal coupling case,when the coupling strength gets stronger,the cavity dissipation has a greater effect on the single photon transport spectrum and the atom dissipation affection becomes weak,so it can be ignored.     

Identification and separation of local and nonlocal optical nonlinear refraction effects: theory and experiment

Understanding the nonlinear optical effect of novel materials plays a crucial role in the fields of photonics and optoelectronics. Herein, we theoretically and experimentally investigate the simultaneous presence of third-order locally refractive nonlinearity and thermally induced nonlocal nonlinearity saturation. We present analytical expressions for the closed-aperture Z-scan trace and the number of spatial self-phase modulation(SSPM) rings,which allows one to unambiguously and conveniently separate the contributions of local and nonlocal nonlinear refraction in the case that both effects occur simultaneously. As a test, we study both the local and thermally induced nonlocal nonlinear refraction in fullerene/toluene solution by performing continuous-wave Z-scan and SSPM measurements at two different wavelengths. This work enriches the understanding of the physical mechanism of the optical nonlinear refraction effect in solution dispersions of nanomaterials, which can be exploited for nonlinear photonic devices.     

Dispersion of dilatation wave propagation in single-wall carbon nanotubes using nonlocal scale effects

Nonlocal continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with micro- or nano-structures. This paper investigates a model of wave propagation in single-wall carbon nanotubes (SWCNTs) with small scale effects are studied. The equation of motion of the dilatation wave is obtained using the nonlocal elastic theory. We show that a dispersive wave equation is obtained from a nonlocal elastic constitutive law, based on a mixture of a local and a nonlocal strain. The SWCNTs structures are treated within the multilayer thin shell approximation with the elastic properties taken to be those of the graphene sheet. The SWCNT was the (40,0) zigzag tube with an effective diameter of 3.13 nm. Nonlinear frequency equations of wave propagation in SWCNTs are described through the effect of small scale. The phase velocity and the group velocity are derived, respectively. The nonlinear dispersion relation is analyzed with different wave numbers versus scale coefficient. It can be observed from the results that the dispersion properties of the dilatation wave are induced by the small scale effects, which will disappear in local continuous models. The dispersion degree can be strengthened by increasing the scale coefficient and the wave number. Furthermore, the characteristics for the group velocity of the dilatation wave in carbon nanotubes can also be tuned by these factors.     

Local renormalizable gauge theories from nonlocal operators

The possibility that nonlocal operators might be added to the Yang-Mills action is investigated. We point out that there exists a class of nonlocal operators which lead to renormalizable gauge theories. These operators turn out to be localizable by means of the introduction of auxiliary fields. The renormalizability is thus ensured by the symmetry content exhibited by the resulting local theory. The example of the nonlocal operator is analyzed in detail. A few remarks on the possible role that these operators might have for confining theories are outlined.     

Transformation-optics description of nonlocal effects in plasmonic nanostructures

We develop an insightful transformation-optics approach to investigate the impact that nonlocality has on the optical properties of plasmonic nanostructures. The light-harvesting performance of a dimer of touching nanowires is studied by using the hydrodynamical Drude model, which reveals nonlocal resonances not predicted by previous local calculations. Our method clarifies the interplay between radiative and nonlocal effects in this nanoparticle configuration, which enables us to elucidate the optimum size that maximizes its absorption and field enhancement capabilities.     

Quantum nonlocality and beyond: limits from nonlocal computation

We address the problem of "nonlocal computation," in which separated parties must compute a function without any individual learning anything about the inputs. Surprisingly, entanglement provides no benefit over local classical strategies for such tasks, yet stronger nonlocal correlations allow perfect success. This provides intriguing insights into the limits of quantum information processing, the nature of quantum nonlocality, and the differences between quantum and stronger-than-quantum nonlocal correlations.     

Implementing a Nonlocal Toffoli Gate Using Partially Entangled Qubit Pairs

We investigate the local implementation of a nonlocal quantum Toffoli gate via partially entangled states. Firstly, we show how the nonlocal Toffoli gate can be implemented with unit fidelity and a certain probability by employing two partially entangled qubit pairs as quantum channels. The quantum circuit that does this proposed implementation is built entirely of local single-level and two-level gates if the target node harness a three-level qudit as a catalyser. This enables the construction of this key nonlocal quantum gate with existing technology. Then, we put forward a scheme to realize deterministic and exact implementation of this nonlocal gate via more partially entangled pairs. In this scheme, the control nodes’ local positive operator valued measurements (POVMs) lies at the heart. We construct the required POVMs. The fact that the deterministic and exact implementation of a nonlocal multi-qubit gate could be realized by using partially entangled qubit pairs and comparatively fewer resources cost is notable.     

Phase structure of a 3D nonlocal U(1) gauge theory: deconfinement by gapless matter fields

In this paper, we study a 3D compact U(1) lattice gauge theory with a variety of nonlocal interactions that simulates the effects of gapless/gapful matter fields. We restrict the nonlocal interactions among gauge variables only to those along the temporal direction and adjust their coupling constants optimally to simulate the isotropic nonlocal couplings of the original model. This theory is quite important to investigate the phase structures of QED₃ and strongly-correlated electron systems like the 2D quantum spin models, the fractional quantum Hall effect, the $t\text{–}J$ model of high-temperature superconductivity. We perform numerical studies of this theory to find that, for a certain class of power-decaying couplings, there appears a second-order phase transition to the deconfinement phase as the gauge coupling constant is decreased. On the other hand, for the exponentially-decaying coupling, there are no signals for second-order phase transition. These results indicate the possibility that introduction of sufficient number of massless matter fields destabilizes the permanent confinement in the 3D compact U(1) pure gauge theory due to instantons.     

Efficient Nonlocal <Emphasis Type="Italic">M</Emphasis>-Control and <Emphasis Type="Italic">N</Emphasis>-Target Controlled Unitary Gate Using Non-symmetric GHZ States

Efficient local implementation of a nonlocal M-control and N-target controlled unitary gate is considered. We first show that with the assistance of two non-symmetric qubit⁽¹⁾-qutrit^(N) Greenberger-Horne-Zeilinger (GHZ) states, a nonlocal 2-control and N-target controlled unitary gate can be constructed from 2 local two-qubit CNOT gates, 2N local two-qutrit conditional SWAP gates, N local qutrit-qubit controlled unitary gates, and 2N single-qutrit gates. At each target node, the two third levels of the two GHZ target qutrits are used to expose one and only one initial computational state to the local qutrit-qubit controlled unitary gate, instead of being used to hide certain states from the conditional dynamics. This scheme can be generalized straightforwardly to implement a higher-order nonlocal M-control and N-target controlled unitary gate by using M non-symmetric qubit⁽¹⁾-qutrit^(N) GHZ states as quantum channels. Neither the number of the additional levels of each GHZ target particle nor that of single-qutrit gates needs to increase with M. For certain realistic physical systems, the total gate time may be reduced compared with that required in previous schemes.     

Entangled Fields in Multiple Cavities as a Testing Ground for Quantum Mechanics

Entangled states provide the necessary tools for conceptual tests of quantum mechanics and other alternative theories. These tests include local hidden variables theories, pre- and postselective quantum mechanics, QND measurements, complementarity, and tests of quantum mechanics itself against, e.g., the so-called causal communication constraint. We show how to produce various nonlocal entangled states of multiple cavity fields that are useful for these tests, using cavity QED techniques. First, we discuss the generation of the Bell basis states in two entangled cavities, when there is at most one photon in either of the cavities, and then a straightforward generalization to similar N-cavity states. We then show how to produce a nonlocal entangled state when there is precisely one photon hiding in three cavities. These states can be produced by sending appropriately prepared atoms through the cavities. As applications we briefly review two proposals: one to test quantum mechanics against the causal communication constraint using a two-cavity entangled state and the other to test pre- and postselective quantum mechanics using a three-cavity entangled state. The outcome of the latter experiment can be discussed from the viewpoint of the consistent histories interpretation of quantum mechanics and therefore provides an opportunity to subject quantum cosmological ideas to laboratory tests. Finally, we point out the relation between these schemes and the schemes suggested for quantum computing, teleportation, and quantum copying.     

Nonlocal response of electric and magnetic modes in a silver cuboid dimer

The nonlocal effect on the spontaneous emission of a silver cuboid dimer is investigated using a local analog model. Magnetic as well as electric dipole excitations are introduced to excite different gap modes. The nonlocal response of electric and magnetic modes on various parameters of gap(width and refractive index) are investigated. Unidirectional radiation is achieved by the interaction between electric and magnetic modes in both local and nonlocal models. Compared to local simulations, the resonant wavelength is blue shifted and the spontaneous emission enhancement is weakened in the nonlocal model. The relative shifts of the resonant wavelengths get larger in smaller gaps with a higher refractive index.     

The Integrals of Motion for the Deformed W-Algebra $${W_{q,t}(\widehat{gl_N})}$$. II. Proof of the Commutation Relations

We explicitly construct two classes of infinitely many commutative operators in terms of the deformed W-algebra , and give proofs of the commutation relations of these operators. We call one of them local integrals of motion and the other nonlocal, since they can be regarded as elliptic deformations of local and nonlocal integrals of motion for the Virasoro algebra and the W ₃ algebra [1,2]. Dedicated to Professor Tetsuji Miwa on the occasion of the 60th birthday     

Mixed Local-Nonlocal Vector Schrödinger Equations and Their Breather Solutions

To the best of our knowledge, all nonlinearities in the known nonlinear integrable systems are either local or nonlocal. A natural problem is whether there exist some nonlinear integrable systems with both local and nonlocal nonlinearities, and how to solve this kinds of spectral nonlinear integrable systems with both local and nonlocal nonlinearities. Recently, some novel mixed local-nonlocal vector Schrödinger equations are presented, which are different from the single local and nonlocal coupled Schrödinger equation. We investigate the Darboux transformation of mixed local-nonlocal vector Schrödinger equations with a spectral problem. Starting from a special Lax pairs, the mixed localnonlocal vector Schrödinger equations are constructed. We obtain the one- and two- and N-soliton solution formulas of the mixed local-nonlocal vector Schrödinger equations with N-fold Darboux transformation. Based on the obtained solutions, the propagation and interaction structures of these multi-solitons are shown, the evolution structures of the one-solitons are exhibited, the overtaking elastic interactions among the two-breather solitons are considered. We find that unlike the local and nonlocal cases, the mixed local-nonlocal vector Schrödinger equations have some novel results. The results in this paper might be helpful for understanding some physical phenomena described in plasmas.     

Demonstrating superior discrimination of locally prepared states using nonlocal measurements

We experimentally demonstrate the superior discrimination of separated, unentangled two-qubit correlated states using nonlocal measurements, when compared with measurements based on local operations and classical communications. When predicted theoretically, this phenomenon was dubbed "quantum nonlocality without entanglement." We characterize the performance of the nonlocal, or joint, measurement with a payoff function, for which we measure 0.72 +/- 0.02, compared with the maximum locally achievable value of 2/3 and the overall optimal value of 0.75.     

Nonlocal symmetries of Plebański’s second heavenly equation

We study nonlocal symmetries of Plebański’s second heavenly equation in an infinite-dimensional covering associated to a Lax pair with a non-removable spectral parameter. We show that all local symmetries of the equation admit lifts to full-fledged nonlocal symmetries in the infinite-dimensional covering. Also, we find two new infinite hierarchies of commuting nonlocal symmetries in this covering and describe the structure of the Lie algebra of the obtained nonlocal symmetries.     

Numerisch genaue Lösungen des nichtlokalen Schalenmodells

Nonlocal potentials can in general be transformed only approximately into local potentials with additional energy dependence. For the optical modelPerey andBuck did an exact nonlocal calculation with the Schrödinger-equation in integro-differential form and also a good local approximation. Certain systematic deviations in the results (concerning the wave-functions) of both processes are of special interest in the shell model. Therefore the eigenvalue problem has been solved now with the most successful nonlocal potential, also used byPerey andBuck, both exactly and approximately, that is with the potential, which is nondiagonal, and its approximation, which is diagonal in local space. The solution of this approximate nonlocal potential serves again as zero order starting value (E ₀,u ₀) for an iteration process, which now is twofold, in order to find that exact solution (E,u). Thus we get together with the exact solution also the deviation of the approximate nonlocal (local-equivalent) one.     

Cosmological perturbation theory in slow-roll spacetimes

We present a gauge-invariant argument that a nonlocal measure of second-order metric and matter perturbations dominates that of linear fluctuations in its effect on the gravitational field in "slow-rolling" spacetimes.     

A Simplified Quantum Logic Network for Unambiguous Discrimination of Two Nonlocal and Unknown Pure Qubit States

Two nonlocal and unknown pure qubit states can, with a certain probability of success, be discriminated unambiguously with the aid of local operations, classical communication, and shared entanglements (LOCCSE). We present a scheme for such kind of nonlocal unambiguous quantum state discrimination. This scheme consists of a nonlocal positive operator valued measurement (POVM). This nonlocal POVM can be realized by performing nonlocal unitary operations on initial system and ancillary qubits, and local von Neumann projective measurements on the ancilla plus initial system. By utilizing the degrees of freedom of the original system Hilbert space, we need far more simpler operations than those required by the original Neumark approach. We construct a quantum logic network to implement the required nonlocal POVM.