Nonlocal Pair Research Articles

Aharonov-Bohm and Aharonov-Casher effects for local and nonlocal Cooper pairs

We study combined interference effects due to the Aharonov-Bohm (AB) and Aharonov-Casher (AC) phases in a Josephson supercurrent of local and nonlocal (split) Cooper pairs. We analyze a junction between two superconductors interconnected through a normal-state nanostructure with either (i) a ring, where single-electron interference is possible, or (ii) two parallel nanowires, where the single-electron interference can be absent, but the cross Andreev reflection can occur. In the low-transmission regime in both geometries the AB and AC effects can be related to only local or nonlocal Cooper pair transport, respectively.

Tunable hybridization of Majorana bound states at the quantum spin Hall edge

Confinement at the helical edge of a topological insulator is possible in the presence of proximity-induced magnetic (F) or superconducting (S) order. The interplay of both phenomena leads to the formation of localized Majorana bound states (MBS) or likewise (under certain resonance conditions) the formation of ordinary Andreev bound states (ABS). We investigate the properties of bound states in junctions composed of alternating regions of F or S barriers. Interestingly, the direction of magnetization in F regions and the relative superconducting phase between S regions can be exploited to hybridize MBS or ABS at will. We show that the local properties of MBS translate into a particular nonlocal superconducting pairing amplitude. Remarkably, the symmetry of the pairing amplitude contains information about the nature of the bound state that it stems from. Hence, this symmetry can in principle be used to distinguish MBS from ABS, owing to the strong connection between local density of states and nonlocal pairing in our setup.

Creation of Spin-Triplet Cooper Pairs in the Absence of Magnetic Ordering.

In superconducting spintronics, it is essential to generate spin-triplet Cooper pairs on demand. Up to now, proposals to do so concentrate on hybrid structures in which a superconductor (SC) is combined with a magnetically ordered material (or an external magnetic field). We, instead, identify a novel way to create and isolate spin-triplet Cooper pairs in the absence of any magnetic ordering. This achievement is only possible because we drive a system with strong spin-orbit interaction-the Dirac surface states of a strong topological insulator (TI)-out of equilibrium. In particular, we consider a bipolar TI-SC-TI junction, where the electrochemical potentials in the outer leads differ in their overall sign. As a result, we find that nonlocal singlet pairing across the junction is completely suppressed for any excitation energy. Hence, this junction acts as a perfect spin-triplet filter across the SC, generating equal-spin Cooper pairs via crossed Andreev reflection.

Amplification of Cooper pair splitting current in a graphene-based Cooper pair beam splitter geometry

Motivated by the recent experiments [Scientific Reports 6, 23051 (2016); Phys. Rev. Lett. 114, 096602 (2015)], we theoretically investigate Cooper pair splitting current in a graphene-based Cooper pair beam splitter geometry. By considering the graphene-based superconductor as an entangler device, instead of normal [two-dimensional (2D)] BCS superconductor, we show that the Cooper pair splitting current mediated by the crossed Andreev process is amplified compared to its normal superconductor counterpart. This amplification is attributed to the strong suppression of the local normal Andreev reflection process (arising from the Cooper pair splitting) from the graphene-based superconductor to lead via the same quantum dot, in comparison to the usual 2D superconductor. Due to the vanishing density of states at the Dirac point of undoped graphene, a doped graphene-based superconductor is considered here and it is observed that Cooper pair splitting current is very insensitive to the doping level in comparison to the usual 2D superconductor. The transport process of nonlocal spin-entangled electrons also depends on the type of pairing, i.e., whether the electron-hole pairing is onsite, intersublattice or the combination of both. The intersublattice pairing of graphene causes the maximum nonlocal Cooper pair splitting current, whereas the presence of both pairings reduces the Cooper pair splitting current.

Efficient image decolorization with a multimodal contrast-preserving measure

Decolorization is widely used in monotonic displaying, black-and-white printing, single-channel image processing, and many computer vision applications. The conversion of a color image into a grayscale one suffers from data loss. This paper presents a novel parallel decolorization method which effectively preserves not only the spatially local color contrast but also the dominant non-local color contrast. A new multimodal contrast-preserving measure with a multimodal Gaussian distribution is proposed to relax the constraint of color contrast. The dominant non-local color pair set is constructed by taking advantage of a linear bounding volume hierarchy while the local color pair set is produced by removing duplicate instances of local color pairs. The whole pipeline design is highly parallel, allowing for a real-time GPU-based implementation. Experimental results and comparisons show that the proposed method can produce plausible decolorized images. A number of single-channel image processing applications, including edge detection, image segmentation, color augmentation, and image stylization, are demonstrated to verify the feasibility of the proposed decolorization method.

Modeling opinion dynamics: Theoretical analysis and continuous approximation

Frequently we revise our first opinions after talking over with other individuals because we get convinced. Argumentation is a verbal and social process aimed at convincing. It includes conversation and persuasion and the agreement is reached because the new arguments are incorporated. Given the wide range of opinion formation mathematical approaches, there are however no models of opinion dynamics with nonlocal pair interactions analytically solvable. In this paper we present a novel analytical framework developed to solve the master equations with non-local kernels. For this we used a simple model of opinion formation where individuals tend to get more similar after each interactions, no matter their opinion differences, giving rise to nonlinear differential master equation with non-local terms. Simulation results show an excellent agreement with results obtained by the theoretical estimation.

Nanoscale magnetization of a single vortex in d-wave superconductors

A finite-size scaling of the nanoscale magnetization m on size averaging R of a single vortex in d-wave bulk superconductor is developed using quasiclassical Eilenberger equations. Nanoscaling is anchoring around the linear London approximation for bulk superconductors. Comparing the results with those obtained in local nonlinear approach demonstrated the importance of the nonlocal contribution. Temperature dependences of two-point correlation function χ(T,R1,R2)=m(T,R2)/m(0,R2)−m(T,R1)/m(0,R1) with R2 > R1 and one-point function χ(T, R1 → ∞, R2) are calculated. It is found that χ(T, R1, R2), R2 > R1, is a nonmonotonous function of temperature and changes sign at high temperatures. This nonmonotonous temperature dependence can be understood as a result of competition between various effects i) Volovik effect and nonlocal corrections to superconducting electron density dominating in low temperature range, and ii) current-induced suppression of the order parameter dominating at high temperatures. The introduced nonmagnetic disorder greatly suppresses the low temperature nonlocal and nonlinear effects, leaving the order parameter effects to prevail in the whole temperature range. Nonlocal pairing and tunneling effects are investigated at the superconductor - normal metal border by considering a d-wave superconducting dot (d-dot) inside a normal diffusive metal. These effects result in a suppression of the supercurrent in the vortex core and are essential in nanodots with relatively small sizes. At sizes larger than a temperature dependent characteristic length the nanoscale physics transforms into bulk solution.

Signatures of nonlocal Cooper-pair transport and of a singlet-triplet transition in the critical current of a double-quantum-dot Josephson junction

We study the critical Josephson current flowing through a double quantum dot weakly coupled to two superconducting leads. We use analytical as well as numerical methods to investigate this setup in the limit of small and large bandwidth leads in all possible charging states, where we account for on-site interactions exactly. Our results provide clear signatures of nonlocal spin-entangled pairs, which support interpretations of recent experiments [Deacon, R. S. et al., Nat. Commun. 6, 7446 (2015)]. In addition, we find that the ground state with one electron on each quantum dot can undergo a tunable singlet-triplet phase transition in the regime where the superconducting gap in the leads is not too large, which gives rise to an additional new signature of nonlocal Cooper pair transport.

Statistics of Simulated and Observed Pair Separations in the Gulf of Mexico

AbstractPair-separation statistics of in situ and synthetic surface drifters deployed near the Deepwater Horizon site in the Gulf of Mexico are investigated. The synthetic trajectories derive from a 1-km-resolution data-assimilative Navy Coastal Ocean Model (NCOM) simulation. The in situ drifters were launched in the Grand Lagrangian Deployment (GLAD). Diverse measures of the dispersion are calculated and compared to theoretical predictions. For the NCOM pairs, the measures indicate nonlocal pair dispersion (in which pair separations grow exponentially in time) at the smallest sampled scales. At separations exceeding 100 km, pair motion is uncorrelated, indicating absolute rather than relative dispersion. With the GLAD drifters, however, the statistics are ambiguous, with some indicating local dispersion (in which pair separations exhibit power-law growth) and others suggesting nonlocal dispersion. The difference between the two datasets stems in part from inertial oscillations, which affect the energy levels at small scales without greatly altering pair dispersion. These were significant in GLAD but much weaker in the NCOM simulation. In addition, the GLAD drifters were launched over a limited geographical area, producing few independent realizations and hence lower statistical significance. Restricting the NCOM set to pairs launched at the same locations yields very similar results, suggesting the model is for the most part capturing the observed dispersion.

Bose-condensed atomic systems with nonlocal interaction potentials

The general approach for describing systems with a Bose–Einstein condensate, where atoms interact through nonlocal pair potentials, is presented. Special attention is paid to nonintegrable potentials, such as the dipolar interaction potential. The potentials that are not absolutely integrable can have not well-defined Fourier transforms. Using formally these not defined Fourier transforms leads to unphysical conclusions. To make the Fourier transform well defined, the interaction potential has to be regularised. This is illustrated by the example of dipolar interactions.

Odd-frequency triplet superconductivity at the helical edge of a topological insulator

Non-local pairing processes at the edge of a two-dimensional topological insulator in proximity to an $s$-wave superconductor are usually suppressed by helicity. However, additional proximity of a ferromagnetic insulator can substantially influence the helical constraint and therefore open a new conduction channel by allowing for crossed Andreev reflection (CAR) processes. We show a one-to-one correspondence between CAR and the emergence of odd-frequency triplet superconductivity. Hence, non-local transport experiments that identify CAR in helical liquids yield smoking-gun evidence for unconventional superconductivity. Interestingly, we identify a setup -- composed of a superconductor flanked by two ferromagnetic insulators -- that allows us to favor CAR over electron cotunneling which is known to be a difficult but essential task to be able to measure CAR.

Detecting nonlocal Cooper pair entanglement by optical Bell inequality violation

Based on the Bardeen Cooper Schrieffer (BCS) theory of superconductivity, the coherent splitting of Cooper pairs from a superconductor to two spatially separated quantum dots has been predicted to generate nonlocal pairs of entangled electrons. In order to test this hypothesis, we propose a scheme to transfer the spin state of a split Cooper pair onto the polarization state of a pair of optical photons. We show that the produced photon pairs can be used to violate a Bell inequality, unambiguously demonstrating the entanglement of the split Cooper pairs.

The finiteness of the discrete spectrum of a model operator associated with a system of three particles on a lattice

We consider a model operator H associated with a system of three particles on a lattice interacting via nonlocal pair potentials. Under some natural conditions on the parameters specifying this model operator H, we prove the finiteness of its discrete spectrum.

Exact localized eigenstates for an extended Bose-Hubbard model with pair-correlated hopping

We show that a Bose-Hubbard model extended with pair-correlated hopping has exact eigenstates, quantum lattice compactons, with complete single-site localization. These appear at parameter values where the one-particle tunneling is exactly canceled by nonlocal pair correlations, and correspond in a classical limit to compact solutions of an extended discrete nonlinear Schr\"odinger model. Classical compactons at other parameter values, as well as multisite compactons, generically get delocalized by quantum effects, but strong localization appears asymptotically for increasing particle number.

Essential spectrum of a model operator associated with a three-particle system on a lattice

We consider a model operator H associated with the system of three particles interacting via nonlocal pair potentials on a ν-dimensional lattice. We identify channel operators and use their spectra to describe the position and structure of the essential spectrum of H. We obtain an analogue of the Faddeev equation for the eigenfunctions of H.

Competing pairing states for ultracold fermions in optical lattices with an artificial staggered magnetic field

We study fermionic superfluidity in an ultracold Bose-Fermi mixture loaded into a square optical lattice subjected to a staggered flux. While the bosons form a Bose-Einstein condensate at very low temperature and weak interaction, the interacting fermions experience an additional long-ranged attractive interaction mediated by phonons in the bosonic condensate. This leads us to consider a generalized Hubbard model with on-site and nearest-neighbor attractive interactions, which give rise to two competing pairing channels. We use the Bardeen-Cooper-Schrieffer theory to determine the regimes where distinct fermionic superfluids are stabilized and find that the nonlocal pairing channel favors a superfluid state which breaks both the gauge and the lattice symmetries, similar to unconventional superconductivity occurring in some strongly correlated systems. Furthermore, the particular structure of the single-particle spectrum leads to unexpected consequences, for example, a dome-shaped superfluid region in the temperature versus filing fraction phase diagram, with a normal phase that contains much richer physics than a Fermi liquid. Notably, the relevant temperature regime and coupling strength are readily accessible in state of the art experiments with ultracold trapped atoms.

Nonlocal pair correlations in the one-dimensional Bose gas at finite temperature

The behavior of the spatial two-particle correlation function is surveyed in detail for a uniform 1D Bose gas with repulsive contact interactions at finite temperatures. Both long-, medium-, and short-range effects are investigated. The results span the entire range of physical regimes, from ideal gas, to strongly interacting, and from zero temperature to high temperature. We present perturbative analytic methods, available at strong and weak coupling, and first-principle numerical results using imaginary time simulations with the gauge-P representation in regimes where perturbative methods are invalid. Nontrivial effects are observed from the interplay of thermally induced bunching behavior versus interaction induced antibunching.

Folding potential for nonlocal pair interaction

A general expression is obtained in the coordinate representation for the folding potential describing the interaction of an incoming structureless particle with the centre of mass of a composite nucleus in the case of nonlocal pair interactions. This expression is derived using the Fourier transform of the folding potential in the momentum representation, written as a sum of triangle Feynman diagrams. Two vertices of such a diagram describe the virtual decay of the nucleus into nucleons and the inverse synthesis process. The third vertex is the Fourier component of the pair potential of interaction of the incoming particle with a nucleon belonging to this nucleus. A similar approach was used to obtain the expression for the double-folding potential describing the interaction of two composite objects (nuclei).

Spatial Nonlocal Pair Correlations in a Repulsive 1D Bose Gas

We analytically calculate the spatial nonlocal pair correlation function for an interacting uniform 1D Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects.

On the number of eigenvalues of a model operator associated to a system of three-particles on lattices

A model operator H associated to a system of three particles on the threedimensional lattice ℤ3 that interact via nonlocal pair potentials is studied. The following results are established. (i) The operator H has infinitely many eigenvalues lying below the bottom of the essential spectrum and accumulating at this point if both the Friedrichs model operators $$h_{\mu _\alpha } $$ (0), α = 1, 2, have threshold resonances. (ii) The operator H has finitely many eigenvalues lying outside the essential spectrum if at least one of the operators $$h_{\mu _\alpha } $$ (0), α = 1, 2, has a threshold eigenvalue.