Search

Soft defects caused by flux quanta not captured by moats during superconductor integrated circuit cooldown are known to degrade circuit performance. However, haphazard or random moat placement does not necessarily improve circuit performance and may even degrade it. Under the IARPA SuperTools program we have both developed numerical simulation tools to extract simulation models of circuit structures in the presence of trapped fluxons and designed experiments to measure the probability of flux trapping in moats and the coupling of such trapped flux to circuit structures. Depending on moat structure, the coupling from a few moat-captured fluxons is shown to reduce the critical current for a SQUID by 20% or more, which justifies a thorough analysis. We present results for this very important aspect of magnetic rule checking and show how controlled flux trapping experiments in designated moats yield measurement results that fit simulated predictions very well. With the simulation tools validated, we show how flux trapping is incorporated into compact simulation models and we detail the extraction of magnetic coupling and the calculation of the compact models for both branch and loop-type simulations. We also show how phase-based simulation with the circuit simulator JoSIM allows arbitrary fluxon insertion in moats during transient circuit simulation and conclude with some recommended design rules for moat geometry, size, and placement.

Reversible logic gates were previously implemented in superconducting circuits as adiabatic-reversible gates, which are powered with a sufficiently slow clock. In contrast, we are studying ballistic-reversible gates, where fluxons serve to both encode the information and power the gates. No power is applied to the gate apart from the energy of the input fluxons, and the two possible flux polarities represent the bit states. Undamped long Josephson junctions (LJJs), where fluxons move at practically constant speed from inertia, form the input and output channels of the gates. LJJs are connected in the gates by circuit interfaces, which are designed to allow the ballistic scattering from input to output fluxon states, using the temporary excitation of a localized mode. The duration of the resonant scattering determines the operation time of the gate, approximately a few Josephson plasma periods. Due to the coherent conversions between fluxon and localized modes the ballistic gates can be very efficient: in our simulations only a few percent of the fluxon's energy are dissipated in the gate operation. Ballistic-reversible gates can be combined with other, non-ballistic gate circuits to extend the range of gate functionalities. Here we describe how the CNOT can be built as a structure that includes the IDSN (Identity-else-Same-gives-NOT) and Store-and-Launch (SNL) gates. The IDSN is a 2-bit ballistic gate, which we describe and analyze in terms of equivalent 1-bit circuits. The SNL is a clocking gate, that allows the storage of a bit and the clocked launch of a fluxon on a bit-state dependent output path. In the CNOT the SNL gates provide the necessary routing and fluxon synchronization for the input to the IDSN gate., 13 pages, 8 figures, 4 tables. Accepted for publication in IEEE - Transactions on Applied Superconductivity

Intermodulation distortion (IMD) of microwave signals incident upon a superconducting YBa2Cu3O7 thin film sample on a LaAlO3 substrate is shown to relax as the sample magnetization also relaxes, revealing the signature of fluxon decay in the microwave distortion. The sample contained a microchannel of columnar defects that was introduced using heavy ion beam irradiation. After exposure to and then removal of a low strength static magnetic field, IMD relaxed due to thermal activation of fluxons over the surface barrier. This process influenced second and third order IMD differently, visible in the differing functional form of the IMD in time and the temperature dependence of the relaxation function. The presence of columnar defects in the test sample suppressed thermal activation by pinning of fluxons, notably with complete suppression of relaxation in third order IMD at low temperatures. Higher order IMD was found to relax with the same functional form as the second and third order IMD of the same parity., Comment: 8 figures, 7 pages

For more than four decades, mass of Abrikosov vortices defied experimental observations. We demonstrate a method of its detection in high-temperature superconductors. Similarly to electrons, fluxons circulate in the direction given by the magnetic field, causing circular dichroism. We report the magneto-transmittance of a nearly optimally doped thin YBa$$_2$$ 2 Cu$$_3$$ 3 O$$_{7-\delta }$$ 7 - δ film, measured using circularly polarized submillimeter waves. The circular dichroism emerges in the superconducting state and increases with dropping temperature. Our results confirm the dominant role of quasiparticle states in the vortex core and yield the diagonal fluxon mass of $$2.2 \times 10^8$$ 2.2 × 10 8 electron masses per centimeter at 45 K and zero-frequency limit, and even larger off-diagonal mass of $$4.9 \times 10^8 m_e$$ 4.9 × 10 8 m e /cm.

In a previous paper, we described a new abstract circuit model for reversible computation called asynchronous ballistic reversible computing (ABRC), in which localized information-bearing pulses propagate ballistically along signal paths between stateful abstract devices and elastically scatter off those devices serially, while updating the device state in a logically-reversible and deterministic fashion. The ABRC model has been shown to be capable of universal computation. In the research reported here, we begin exploring how the ABRC model might be realized in practice using single flux quantum solitons (fluxons) in superconducting Josephson junction (JJ) circuits. One natural family of realizations could utilize fluxon polarity to represent binary data in individual pulses propagating near-ballistically, along discrete or continuous long Josephson junctions or microstrip passive transmission lines, and utilize the flux charge (-1, 0, +1) of a JJ-containing superconducting loop with Φ 0

As superconducting quantum processors increase in size and complexity, the scalability of standard techniques for qubit control and readout becomes a limiting factor. Replacing room temperature analog components with cryogenic digital components could allow for the realization of systems well beyond the current state-of-the-art qubit arrays with tens of qubits. The standard technique for performing a qubit measurement with heterodyne readout uses a quantum-limited cryogenic amplifier chain and requires bulky microwave components inside the refrigerator with multiple control lines and pump signals. Additionally, the result is only accessible in software at room temperature. An alternative method for measuring qubits involves mapping the qubit state onto the photon occupation in a microwave cavity, followed by subsequent photon detection using a Josephson photomultiplier (JPM). The JPM measures the qubit and stores the result in a classical circulating current. To make use of this result, we can leverage existing single flux quantum (SFQ) circuitry. An underdamped Josephson transmission line (JTL) can be coupled to the JPM and fluxons traveling along the JTL are accelerated or delayed, depending on the circulating current state of the JPM. This fluxon delay can then be converted to an SFQ logic signal resulting in a digital qubit readout with a proximal microfabricated device, paving the way for cryogenic digital feedback necessary for error-correcting codes.

We demonstrate a method for manipulating small ensembles of vortices in multiply-connected superconducting structures. A micron-size magnetic particle attached to the tip of a silicon cantilever is used to locally apply magnetic flux through the superconducting structure. By scanning the tip over the surface of the device, and by utilizing the dynamical coupling between the vortices and the cantilever, a high-resolution spatial map of the different vortex configurations is obtained. Moving the tip to a particular location in the map stabilizes a distinct multi-vortex configuration. Thus, the scanning of the tip over a particular trajectory in space permits non-trivial operations to be performed, such as braiding of individual vortices within a larger vortex ensemble -- a key capability required by many proposals for topological quantum computing., Comment: 14 pages, 9 figures

Interaction of the fluxon with the finite size dipole impurity in the long Josephson junction is investigated. The impurity has polarity and will be referred to as a {\it dipole} impurity because it also has a direction and, consequently, changes its sign under the space inversion transform $x \to -x$. Such a model is used to describe the inductively coupled to the Josephson transmission line qubit and the misaligned Abrikosov vortex that penetrates into the long Josephson junction. We derive the approximate equations of motion for the fluxon center of mass and its velocity. With the help of these equations we demonstrate that pinning and scattering of the fluxon on the impurity differs significantly from the case of the point impurity which is modelled by the derivative of the Dirac's $\delta$-function, Comment: 7 figures; Phys. Lett. A (in press)

The problem of speeding up quantum computations through controlling the states of qubits by short large-amplitude unipolar pulses is discussed. A new method is proposed to describe the dynamics of qubits that is based on the Magnus representation for the evolution operator (propagator) of qubits, which allows one to find a solution to the quantum control problem outside the framework of perturbation theory. The evolution of the states of a multiqubit system is represented as a motion on a special unitary group SU(N), similar to the rotation of the Bloch vector on the group SU(2) in the case of a single qubit. As an example, unitary transformations of single-qubit states under different excitation modes are considered. A general formula is found that establishes a relation between the shape of a pulse and the result of its action, similar to the well-known “area theorem” for Rabi pulses. The effect of unipolar pulses on a two-qubit system is analyzed in detail. Two situations are considered: first, a symmetric configuration, when the parameters of qubits do not differ and are acted upon by the same magnetic field from a fluxon, and second, when the configuration of levels arises in which, for one of the qubits, a transition to the nearest level becomes possible under perturbation. The general case of two interacting qubits—a four-level system—is considered analytically. A direct numerical simulation of the dynamics of a multiqubit system is performed to estimate the accuracy of approximation, and fidelity is used as a criterion of accuracy of operations. It is shown that the expressions obtained for the propagator allow one to formulate conditions for the pulse parameters that are necessary to perform logical operations.

We report a detailed theoretical study of a coherent macroscopic quantum-mechanical phenomenon - quantum beats of a single magnetic fluxon trapped in a two-cell SQUID of high kinetic inductance. We calculate numerically and analytically the low-lying energy levels of the fluxon, and explore their dependence on externally applied magnetic fields. The quantum dynamics of the fluxon shows quantum beats originating from its coherent quantum tunneling between the SQUID cells. We analyze the experimental setup based on a three-cell SQUID, allowing for time-resolved measurements of quantum beats of the fluxon., Comment: 11 pages, 12 figures

In the present work, the current-voltage (I-V) characteristics in a coupled long Josephson junction based on magnesium diboride are studied by establishing a system of equations of phase differences of various inter- and intra-band channels starting from the microscopic Hamiltonian of the junction system and simplifying it through the phenomenological procedures such as action, partition function, Hubbard-Stratonovich transformation (bosonization), Grassmann integral, saddle-point approximation, Goldstone mode, phase dependent effective Lagrangian and, finally, Euler-Lagrange equation of motion. The system of equations are solved using finite difference approximation for which the solution of unperturbed sine-Gordon equation is taken as the initial condition. Neumann boundary condition is maintained at both the ends so that the fluxon is capable of reflecting from the end of the system. The phase dependent current is calculated for different tunnel voltage and averaged out over space and time. The current-voltage characteristics are almost linear at low voltage and non-linear at higher voltage which indicates that the more complicated physical phenomena at this situation may occur. At some region of the characteristics, there exist a negative resistance which means that the junction system can be used in specific electronic devices such as oscillators, switches, memories etc. The non-linearity is also sensitive to the layer as well as to the junction thicknesses. Non-linearity occurs for lower voltage and for higher junction and layer thicknesses., Comment: 17 pages, 7 figures

We present a theoretical study of coherent quantum dynamics of a single magnetic fluxon (MF) trapped in Josephson junction parallel arrays (JJPAs) with large kinetic inductances. The MF is the topological excitation carrying one quantum of magnetic flux, $\Phi_0$. The MF is quantitatively described as the $2\pi$-kink in the distribution of Josephson phases, and for JJPAs with high kinetic inductances the characteristic length of such distribution ("the size" of MF) is drastically reduced. Characterizing such MFs by the Josephson phases of three consecutive Josephson junctions we analyse the various coherent macroscopic quantum effects in the MF quantum dynamics. In particular, we obtain the MF energy band originating from the coherent quantum tunnelling of a single MF between adjacent cells of JJPAs. The dependencies of the band width $\Delta$ on the Josephson coupling energy $E_J$, charging energy $E_C$ and the inductive energy of a cell $E_L$, are studied in detail. In long linear JJPAs the coherent quantum dynamics of MF demonstrates decaying quantum oscillations with characteristic frequency $f_{qb}=\Delta/h$. In short annular JJPAs the coherent quantum dynamics of MF displays complex oscillations controlled by the Aharonov-Casher phase $\chi \propto V_g$, where $V_g$ is an externally applied gate voltage. In the presence of externally applied dc bias, $I$, a weakly incoherent dynamics of quantum MF is realized in the form of macroscopic Bloch oscillations leading to a typical "nose" current-voltage characteristics of JJPAs. As ac current with frequency $f$ is applied the current-voltage characteristics displays a set of equidistant current steps at $I_n=2en f$., Comment: 9 pages, 9 fugures

We investigate analytically and numerically the stability of bubble-like fluxons in disk-shaped heterogeneous Josephson junctions. Using ring solitons as a model of bubble fluxons in the two-dimensional sine-Gordon equation, we show that the insertion of coaxial dipole currents prevents their collapse. We characterize the onset of instability by introducing a single parameter that couples the radius of the bubble fluxon with the properties of the injected current. For different combination of parameters, we report the formation of stable oscillating bubbles, the emergence of internal modes, and bubble breakup due to internal mode instability. We show that the critical germ depends on the ratio between its radius and the steepness of the wall separating the different phases in the system. If the steepness of the wall is increased (decreased), the critical radius decreases (increases). Our theoretical findings are in good agreement with numerical simulations. We discuss applications in quantum information technologies., 21 pages, 13 figures

The basis for superconducting electronics can broadly be divided between two technologies: the Josephson junction and the superconducting nanowire. While the Josephson junction (JJ) remains the dominant technology due to its high speed and low power dissipation, recently proposed nanowire devices offer improvements such as gain, high fanout, and compatibility with CMOS circuits. Despite these benefits, nanowire-based electronics have largely been limited to binary operations, with devices switching between the superconducting state and a high-impedance resistive state dominated by uncontrolled hotspot dynamics. Unlike the JJ, they cannot increment an output through successive switching and their operation speeds are limited by their slow thermal-reset times. Thus, there is a need for an intermediate device with the interfacing capabilities of a nanowire but a faster, moderated response allowing for modulation of the output. We present a nanowire device based on controlled fluxon transport. We show that the device is capable of responding proportionally to the strength of its input, unlike other nanowire technologies. The device can be operated to produce a multilevel output with distinguishable states, the number of which can be tuned by circuit parameters. Agreement between experimental results and electrothermal circuit simulations demonstrates that the device is classical and may be readily engineered for applications including use as a multilevel memory.

We show that infrared radiation impinging onto a one-dimensional array of grooves drilled in the superconductor electrode of a long overlap junction can improve matching between fluxon oscillations at THz frequencies and a spoof plasmon of comparable wavelength. This example proves that metamaterials can be very helpful in integrating superconductive and subwavelength optical circuits with optimized matching, bridging the gap between infrared and microwave radiation.

Josephson fluxonic diode (JFD) has been studied and applied for gigahertz (GHz) imaging using the principle of generation of fluxons by an irradiated standing wave at gigahertz frequencies. In this device, the creation, movement, and dynamics of fluxon and anti-fluxon pairs as the magnetic field carriers in JFD have been examined in two separate modes of operation including forward and reverse bias. In both modes, the high nonlinearity feature is used for electromagnetic radiation detection. To verify this capability, an experimentally fabricated JFD based on Nb/AlOx/Nb trilayer technology has been deployed without being coupled to any patterned antenna or frontal optics. Also, the junction design parameters and DC biasing values have accordingly been chosen to achieve the best sensitivity to gigahertz radiations. As a result, the device well respond to the specified frequency, and an image is acquired at 71 GHz which proves the potential application of JFD as a pixel of the millimeter wave imaging systems with the direct detection mechanism.

Confocal Annular Josephson Tunnel Junctions (CAJTJs) which are the natural generalization of the circular annular Josephson tunnel junctions, have a rich nonlinear phenomenology due to the intrinsic non-uniformity of their planar tunnel barrier delimited by two closely spaced confocal ellipses. In the presence of a uniform magnetic field in the barrier plane, the periodically changing width of the elliptical annulus generates a asymmetric double-well for a Josephson vortex trapped in a long and narrow CAJTJ. The preparation and readout of the vortex pinned in one of the two potential minima, which are important for the possible realization of a vortex qubit, have been numerically and experimentally investigated for CAJTJs with the moderate aspect ratio 2:1. In this work we focus on the impact of the annulus eccentricity on the properties of the vortex potential profile and study the depinning mechanism of a fluxon in more eccentric samples with aspect ratio 4:1. We also discuss the effects of the temperature-dependent losses as well as the influence of the current and magnetic noise., Comment: arXiv admin note: text overlap with arXiv:1707.01672

This comprehensive study attempts to find out the evaluation of magnetoresistivity performance and flux pinning centers in the Bi-2223 superconductor with nickel impurities and diffusion annealing temperature interval 650 °C–850 °C by means of magnetotransport measurements (0–5T). It is found that the cooper-pair probabilities as well as pinning of thermal fluxon motions of two-dimensional (2D) pancake vortices and interlayer Josephson coupling between the isolated grains considerably improve with the annealing temperature up to 700 °C as a result of enhancement in the effective flux pinning regions. However, from 700 °C onwards the potential energy barriers decrease significantly due to the increment of permanent structural problems in the crystal system. Namely, the presence of excess Ni impurities develops the recoupling linelike/discrete pancakelike nature. In this respect, the bulk sample exposed to the diffusion annealing temperature of 850 °C exhibits the worst magnetic performance characteristics. The flux lines in the material more easily jump to neighboring states due to the cooper pair-breaking mechanism, and thus the thermal fluxon motions of 2D pancake vortices lead to the energy dissipation. We also discuss the differentiation of vortex lattice elasticity for the materials with the aid of the theoretically calculated quantities such as the thermodynamic critical field (μ0Hc), irreversibility field (μ0Hirr), lower critical field (μ0Hc1), upper critical field (μ0Hc2), penetration depth (λ), coherence length (ξ) and Ginzburg Landau parameter ( κ ). According to the computational values, the optimum annealing temperature of 700 °C strengthens the pinning of 2D pancake vortices, vortex lattice period and elasticity as a result of the decrease in the inter-plane interaction energy. To sum up, 700 °C favors the applications of bulk Ni surface-layered Bi-2223 compounds in rather higher magnetic fields for a major innovation.

This study reports the variations of magnetoresistivity performance and pinning ability for the bulk Bi 1.8 Pb 0.4 Sr 2 (MgB 2 ) x Ca 2.2 Cu 3.0 O y ceramic materials with the MgB 2 addition (0 ≤ x ≤ 0.5) in the crystal structure by magnetotransport measurements performed in the applied magnetic fields (0–7T). According to the results, the maximum critical transition temperature values ( T c offset and T c onset ) are about 114.1 K and 121.3 K for the best sample exposed to x = 0.05 content level of MgB 2 addition while the minimum T c offset and T c onset are obtained to be 109.4 K and 118.6 K for the pure sample at zero applied magnetic field, respectively. Besides, the highest T c offset value of 69.6 K is observed for the former sample at 7 T external field strength. This is attributed to the fact that the existence of optimum MgB 2 in the Bi-2223 crystal structure results in the increased nucleation center formations so that the binding between the dopants and adjacent layers can pin the fluxon motions of two-dimensional (2D) pancake vortices at higher magnetic field such a value of 7 T. On the other hand, the main reason of decrement in the T c offset parameters stems from the pair-breaking mechanism based on the changed spin states of cooper-pair electrons. Moreover, the flux pinning energy parameters estimated from thermally activated flux creep model tend to augment considerably with the increment of MgB 2 content level up to x = 0.05. Additionally, the coherence length and penetration depth parameters as well as the irreversibility and upper critical fields confirm the positive effect of optimum MgB 2 addition on the elastic moduli of vortex lattice, Josephson coupling length, magnetic performance and especially pinning ability throughout the Bi-2223 crystal structure.

In this paper we solve the double sine-Gordon (sG) equation with constant coefficients using the Hirota bilinearization method and generalize the result with the director dynamics of antiferroelectric liquid crystal and fluxon excitation in the Josephson junction. The obtained one and two soliton solutions are consistently described for the above two systems with real physical parameters.

Purpose: The purpose of this report is to present the similarities and differences between modified sine-Gordon models used in description of the curved Josephson junctions. The leading dynamical variable in this system is a gauge invariant phase difference of the macroscopic wave functions of the superconducting electrodes that form the junction. Findings: The main finding of this article is the observation that in the model used in description of junctions with quickly varying curvatures the significant part of the kink energy is confined in the curved regions of the junction. Research limitations/implications: The paper is limited to the description of the dynamics of fluxions in the long Josephson junctions. These junctions due to small transverse sizes (smaller than the Josephson penetration depth) can be considered as a one dimensional systems. Practical implications: It seems that junctions with appropriate geometry will find applications in future electronic devices. It is expected that curved Josephson junctions can be used in order to store a binary data. Originality/value: The main idea of the paper is to use a Riemann geometry in order to describe the influence of the curvature on the kink motion in the junction.

Braiding of anyons such as Majoranas or parafermions provides only Clifford gates which do not form a universal set of quantum gates. We propose a robust and resource-efficient scheme to perform a non-Clifford gate on a logical qudit encoded in parafermionic zero modes via the Aharonov-Casher effect. This gate can be implemented by moving a half flux quantum around the pair of parafermionic zero modes. The parafermion modes can be realized in a two-dimensional set-up using existing proposals and a half fluxon carrying half flux quantum can be created as a part of a half fluxon/anti-half fluxon pair in a spin-triplet Josephson junction with a dipole defect. With an appropriate bias current pulse, the half fluxon can be braided around the parafermions. Supplementing this gate with the braiding of parafermions provides the avenue for universal quantum computing with parafermions without magic state distillation., Comment: 9+7 pages, 3+1 figures, longer version with appendix and more details

The dynamics of the fluxon in the Josephson junction is studied. The dielectric layer of the junction has a variable thickness. It is shown that the modified area of the junction acts on the fluxon as a potential barrier. The relation between the critical bias current and the thickness of the dielectric layer is analytically and numerically determined.

Today's industrial digital logic gates are reaching a technological limit and meanwhile, superconducting circuits produce fundamentally different technologies for the future of digital computing. The standard logic is irreversible and yet superconducting circuits allow digital reversible logic with a much higher energy efficiency per gate operation. Previous reversible gate circuits were “adiabatic,” meaning that they used adiabatic-clocking waveforms for their operation power. However, we are studying logic starting from a ballistic model, where ftuxons enable gates using only energy from their inertia. Our ftuxons are defined in Long Josephson Junctions (LJJs) and may travel ballistically, similar to a particle with negligible damping. Once a ftuxon's energy approaches close enough to the gate, a resonance is induced at the gate and the ftuxon loses its definite topology. Gates are comprised of the (few Josephson-penetration-depth long) ends of LJJs and a connecting circuit interface. Only after the resonance does a ftuxon get formed and yield the gate result without external power: a ftuxon for bit-state 0 or an antiftuxon for bit-state 1. Through earlier analysis of the numerically discovered phenomena we find that dynamics can be described with ftuxon- and antiftuxon-like excitations at the ends of LJJs within the gate. The bit-switching action in our gates is resonant indicating fundamentally different dynamics than the classic model of adiabatic reversible circuits. Our ballistic Reversible Fluxon Logic (RFL) gates have no added damping and calculated energy efficiencies of over 97%. Thus in our dynamical process the “bit energy” is preserved. However, irreversible logic completely dissipates this at each operation (e.g., charging energy in CMOS or SFQ energy in irreversible SFQ logic). An RFL gate can achieve a fast gate operation since its resonance is only few JJ plasma periods. We also describe the CNOT in our technology. It is enabled by a couple of vital gates: A IDSN logic gate, similar to our other ballistic gates, and a Store-aNd-Launch (SNL) timing gate to ensure proper synchronization of the bits. The latter allows bit storage followed by launching of a data ftuxon using an adiabatic pulse from a clock ftuxon with lower energy than the data ftuxon for good CNOT efficiency.

Compared to irreversible gate operations, reversible digital logic gates can provide a fundamental advantage in energy efficiency. Here we discuss previously discovered 1-bit ballistic reversible logic gates and new experimental plans to measure it. The gates consist of long Josephson junctions (LJJs) connected by a circuit interface. The gate dynamics evanescently extends into the LJJs to realize the physically resonant gate operation. It differs from known adiabatic superconducting gates because it does not work in the adiabatic limit. Depending on the gate type, that is the Identity or NOT gate, the polarity of the outgoing fluxon should be preserved or inverted, respectively. The dynamics of the scattering process, originally discovered in full numerical simulation, is understood using collective coordinate analysis. We plan to experimentally study how well a fluxon can travel ballistically towards the interface, and scatter with the designed gate operation. Here we present gate and SQUID-sensing layout designs for a NOT gate. The LJJ circuit layout uses niobium trilayer short junctions with connecting wiring for inductors. Part of the design includes the shunting capacitors at the gate interface which is key for the resonant dynamics in the gates.

The physics of Josephson tunnel junctions drastically depends on their geometrical configurations and here we show that also tiny geometrical details play a determinant role. More specifically, we develop the theory of short and long confocal annular Josephson tunnel junctions in the presence of an in-plane magnetic field of arbitrary orientations. The behavior of a circular annular Josephson tunnel junction is then seen to be simply a special case of the above result. For junctions having a normalized perimeter less than one the threshold curves are derived and computed even in the case with trapped Josephson vortices. For longer junctions a numerical analysis is carried out after the derivation of the appropriate motion equation for the Josephson phase. We found that the system is modeled by a modified and perturbed sine-Gordon equation with a space dependent effective Josephson penetration length inversely proportional to the local junction width. Both the fluxon statics and dynamics are deeply affected by the non-uniform annulus width. Static zero-field multiple-fluxon solutions exist even in presence of a large bias current. The tangential velocity of a traveling fluxon is not determined by the balance between the driving and drag forces due to the dissipative losses. Furthermore, the fluxon motion is characterized by a strong radial inward acceleration which causes electromagnetic radiation concentrated at the ellipse equatorial points., 21 pages, 5 figures

In Levin-Wen (LW) models, a wide class of exactly solvable discrete models, for two-dimensional topological phases, it is relatively easy to describe only single-fluxon excitations, but not the charge and dyonic as well as many-fluxon excitations. To incorporate charged and dyonic excitations in (doubled) topological phases, an extension of the LW models is proposed in this paper. We first enlarge the Hilbert space with adding a tail on one of the edges of each trivalent vertex to describe the internal charge degrees of freedom at the vertex. Then, we study the full dyon spectrum of the extended LW models, including both quantum numbers and wave functions for dyonic quasiparticle excitations. The local operators associated with the dyonic excitations are shown to form the so-called tube algebra, whose representations (modules) form the quantum double (categoric center) of the input data (unitary fusion category). In physically relevant cases, the input data are from a finite or quantum group (with braiding R matrices), and we find that the elementary excitations (or dyon species), as well as any localized/isolated excited states, are characterized by three quantum numbers: charge, fluxon type, and twist. They provide a “complete basis” for many-body states in the enlarged Hilbert space. Concrete examples are presented and the relevance of our results to the electric-magnetic duality existing in the models is addressed.

We theoretically investigate the phase-dependent heat transport of a temperature-biased granular Josephson junction in the presence of a perpendicular magnetic field. We illustrate the influence of geometry of the junction on the thermal current. The use of granular Josephson junction rather than bulk one makes significant changes in the heat current behavior. The heat current diffraction pattern of the rectangular, circular and annular geometries with no trapped fluxons demonstrates similar to the current of s-wave superconducting junction. By increasing the number of trapped fluxon, the pattern of current behaves such as d-wave superconducting junction. The feasibility of using granular superconductors, with different geometries, controlled by the magnetic field provides an appropriate tool to obtain the desired result for a specific application.

The present study is devoted to development of a technique for numerical simulation of the wave function dynamics the single Josephson qubits and arrays of noninteracting qubits controlled by ultra-short pulses. We wish to demonstrate the feasibility of a new principle of basic logical operations on the picosecond timescale. The influence of the unipolar pulse (“fluxon”) form on the evolution of the state during the execution of the quantum one-qubit operations – “NOT”, “READ” and “ NOT ” – is investigated in the presence of decoherence. In the array of non interacting qubits, the question of the influence of the spread of their energy parameters (tunnel constants) is studied. It is shown that a single unipolar pulse can control a huge array of artificial atoms with 10% spread of geometric parameters in the array.

New computing technologies are being sought near the end of CMOS transistor scaling, meanwhile superconducting digital, i.e., single-flux quantum (SFQ), logic allows incredibly efficient gates which are relevant to the impending transition. In this work we present a proposed reversible logic, including gate simulations and schematics under the name of Reversible Fluxon Logic (RFL). In the widest sense it is related to SFQ-logic, however it relies on (some approximately) reversible gate dynamics and promises higher efficiency than conventional SFQ which is logically irreversible. Our gates use fluxons, a type of SFQ which has topological-particle characteristics in an undamped Long Josephson junction (LJJ). The collective dynamics of the component Josephson junctions (JJs) enable ballistic fluxon motion within LJJs as well as good energy preservation of the fluxon for JJ-circuit gates. For state changes, the gates induce switching of fluxon polarity during resonant scattering at an interface between different LJJs. Related to the ballistic nature of fluxons in LJJ, the gates are powered, almost ideally, only by data fluxon momentum in stark contrast to conventionally damped logic gates which are powered continuously with a bias. At first the fundamental Identity and NOT gates are introduced. Then 2-bit gates are discussed, including the IDSN gate which actually allows low fluxon-number inputs for more than 4 input states. A digital CNOT, an important milestone for 2-bit reversible superconducting gates, is planned as a central result. It uses a store and launch gate to stop and then later route a fluxon. This use of the store and launch gate allows a clocked CNOT gate and synchronization within. The digital CNOT gate could enable high efficiency relative to conventional irreversible gates and shows the utility of the IDSN as a reversible gate primitive.

This work presents a study of the detection principles for weak magnetic signals in the presence of thermal fluctuations using a superconductor ballistic detector based on Josephson transmission lines. The importance of taking the relativistic aspect into account both in calculating the dynamics of the interaction between a fluxon and current inhomogeneity and in analyzing the influence of thermal fluctuations on this dynamics, is shown. Optimization of detector parameters such as the bias current and energy dissipation is presented to maximize the signal-to-noise ratio.

The Aharonov–Bohm oscillations of the energy gap and the persistent current in carbon nanotube rings (CNTRs) are investigated theoretically. By considering the rotational symmetry about the axis of CNTRs, we construct a tight-binding model for CNTRs under a magnetic flux (MF) Φ. The Φ-dependent energy gap and persistent current are calculated when the bond lengths are different between the outer atoms and inner atoms. We find that all CNTRs are semiconductors and that zigzag CNTRs exhibit paramagnetism at small magnetic flux Φ in contrast with the diamagnetism of armchair CNTRs. In addition, the effect of the vortex magnetic flux (VMF) on CNTRs is studied. The persistent current is periodic in a VMF Φθ with the same period fluxon Φ0 as in a MF Φ. Furthermore, the VMF is more effective at tuning the energy gaps of the CNTRs than the MF.

We have considered the quantum dynamics of an array of nSQUIDs -- two-junction SQUIDs with negative mutual inductance between their two arms. Effective dual-rail structure of the array creates additional internal degree of freedom for the fluxons in the array, which can be used to encode and transport quantum information. Physically, this degree of freedom is represented by electromagnetic excitations localized on the fluxon. We have calculated the spatial profile and frequency spectrum of these excitations. Their dynamics can be reduced to two quantum states, so that each fluxons moving through the array carries with it a qubit of information. Coherence properties of such a propagating qubits in the nSQUID array are characterized by the dynamic suppression of the low-frequency decoherence due to the motion-induced spreading of the noise spectral density to a larger frequency interval., Comment: 10 pages, 3 figures

The kink solution in the long Josephson junction is studied. The perturbation scheme of constructing the fluxon solution in curved junction is formulated. The prediction from the perturbation scheme is compared with the prediction that follows from the numerical studies of the complete field model.

Long-lived fluxon excitations can be trapped inside a superinductor ring, which is divided into an array of loops by a periodic sequence of Josephson junctions in the quantum regime, thereby allowing fluxons to tunnel between neighboring sites. By tuning the Josephson couplings, and implicitly the fluxon tunneling probability amplitudes, a wide class of 1D tight-binding lattice models may be implemented and populated with a stable number of fluxons. We illustrate the use of this quantum simulation platform by discussing the Su-Schrieffer-Heeger model in the 1-fluxon subspace, which hosts a symmetry protected topological phase with fractionally charged bound states at the edges. This pair of localized edge states could be used to implement a superconducting qubit increasingly decoupled from decoherence mechanisms., Comment: 13 pages, 7 figures

We study a model of Josephson layered structure which is characterized by two peculiarities: (i) superconducting layers are thin; (ii) due to suppression of superconducting states in superconducting layers the current-phase relation is non-sinusoidal and is described by two sine harmonics. The governing equation is a nonlocal generalization of double sine-Gordon (NDSG) equation. We argue that the dynamics of fluxons in the NDSG model is unusual. Specifically, we show that there exists a set of particular velocities for non-radiating fluxon propagation. In dynamics the presence of these ``priveleged'' velocitied results in phenomenon of quantization of fluxon velocities: in our numerical experiments a travelling kink-like excitation radiates energy and slows down to one of these particular velocities, taking a shape of predicted 2-pi-kink. This situation differs from both, double sine-Gordon local model and the nonlocal sine-Gordon model, considered before. We conjecture that the set of these velocities is infinite and present an asymptotic formula for them., Comment: 18 pages, 6 figures; submitted to Physica D

The Josephson vortex (fluxon) interaction with the rectangular impurity of finite size in two-dimensional Josephson junction with dissipation is studied. The energy density radiated during the scattering of fluxon on inhomogeneity is found. The total radiation energy dependence as a function of the fluxon velocity and impurity size is obtained. The dependence has a resonant behavior that can be explaned by the interference of emitted waves. Keywords: fluxon, microshort, Josephson junction, sine-Gordon equation.

We describe a superconducting three-terminal device that uses a simple geometric effect known as current crowding to sense the flow of current and actuate a readout signal. The device consists of a "Y"-shaped current combiner, with two currents (sense and bias) entering separately through the top arms of the "Y", intersecting, and then exiting together through the bottom leg of the "Y". When current is added to or removed from one of the arms (e.g., the sense arm), the superconducting critical current in the other arm (i.e., the bias arm) is modulated. The current in the sense arm can thus be determined by measuring the critical current of the bias arm, or inversely, the sense current can be used to modulate the state of the bias arm. The dependence of the bias critical current on the sense current occurs due to the geometric current crowding effect, which causes the sense current to interact locally with the bias arm. Measurement of the critical current in the bias arm does not break the superconducting state of the sense arm or of the bottom leg, and thus, quantized currents trapped in a superconducting loop were able to be repeatedly measured without changing the state of the loop. Current crowding is a universal effect in nanoscale superconductors, and so this device has potential for applicability across a broad range of superconducting technologies and materials. More generally, any technology in which geometrically induced flow crowding exists in the presence of a strong nonlinearity might make use of this type of device.

Stochastic fluxon dynamics and spatial ordering are studied in a superconducting Nb film patterned with a periodic (3×3 micron) square array of holes. First, imaging of the film is performed using Scanning Hall Probe Microscope following application of the random noise magnetic drive. We observe formation of the fluxon stripe patterns oriented preferentially along the principal axes of the array. Next, ac magnetic field is applied as superposition of harmonic and random noise components and the local magnetic response is probed with the micron-sized Hall sensor at a single array site. We find that hopping of the fluxons becomes synchronized with the harmonic driving at certain amplitude of the random noise; the latter is found to be dependent upon the harmonic drive frequency. We attribute our observations to the phenomenon of stochastic resonance that is ubiquitous in non-linear multi-level systems with dynamic threshold and discuss a possibility of flux manipulation using stochastically-resonant periodic driving.

We report on the microwave surface resistance of melt-textured Y_1.6Ba_2.3Cu_3.3O_7-x samples, doped with different amount of B_2O_3 and, subsequently, irradiated by thermal neutrons at the fluence of 1.476 \times 10^17 cm^-2. The microwave surface resistance has been measured as a function of temperature and DC magnetic field. The experimental results are quantitatively discussed in the framework of the Coffey and Clem theory, properly adapted to take into account the d-wave nature of cuprate superconductors. By fitting the experimental data at zero DC field, we have highlighted the effects of the induced defects in the general properties of the samples, including the intergranular region. The analysis of the results obtained at high DC fields allowed us to investigate the fluxon dynamics and deduce the depinning frequency; in particular, we have shown that the addition of B_2O_3 up to 0.1 wt% increases the effectiveness of the defects to hinder the fluxon motion induced by the microwave current., Comment: 9 pages, 8 embedded figures, accepted for publication in Physica C

We have observed the effect of the Aharonov-Casher (AC) interference on the spectrum of a superconducting system containing a symmetric Cooper pair box (CPB) and a large inductance. By varying the charge $n_{g}$ induced on the CPB island, we observed oscillations of the device spectrum with the period $\Delta n_{g}=2e$. These oscillations are attributed to the charge-controlled AC interference between the fluxon tunneling processes in the CPB Josephson junctions. Total suppression of the tunneling (complete destructive interference) has been observed for the charge $n_{g}=e(2n+1)$. The CPB in this regime represents the $4\pi$-periodic Josephson element, which can be used for the development of the parity-protected superconducting qubits., Comment: 6 pages, 3 figures

We discuss the existence of fluxons in superconductor/ferromagnet/superconductor Josephson junction with external current described by an inhomogeneous double sine-Gordon equation. Based on an extended Feynman’s argument, we derived the corresponding current-phase relation from the nonlinear interaction of the macroscopic wavefunctions between the two superconductors. The result shows that the only solution that survive under the presence of external current are the bright and dark fluxons, while a new type of dark fluxon with peculiar shape is found.

We study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also high-frequency librational motion in the tails. Subject to suitable conditions of a general nature, we analyze the fluxon condensate solution approximating the given initial data for small time near points where the initial data crosses the separatrix of the phase portrait of the simple pendulum. We show that the solution is locally constructed as a universal curvilinear grid of superluminal kinks and grazing collisions thereof, with the grid curves being determined from rational solutions of the Painleve-II system.

Nonlinear eigenvalue problems for fluxons in long Josephson junctions with exponentially varying width are treated. Appropriate algorithms are created and realized numerically. The results obtained concern the stability of the fluxons, the centering both magnetic field and current for the magnetic flux quanta in the Josephson junction as well as the ascertaining of the impact of the geometric and physical parameters on these quantities. Each static solution of the nonlinear boundary-value problem is identified as stable or unstable in dependence on the eigenvalues of associated Sturm-Liouville problem. The above compound problem is linearized and solved by using of the reliable Continuous analogue of Newton method.

In order to study the fluxon behavior in a Josephson junction, a dielectric with variable thickness was inserted between two superconductors, which can be position-dependent. An analytical solution of the sine-Gordon equation is obtained. Subsequently, the relation between the kinetic and potential energy of a fluxon is obtained along with the analytic relationships between the velocity of the fluxon and the dielectric thickness. Finally, an exact topological soliton solution is obtained for the sine-Gordon equation with and without strong perturbations through the use of the ansatz method.

We consider a Josephson junction system installed with a finite length inhomogeneity, either of micro-resistor or micro-resonator type. The system can be modelled by a sine-Gordon equation with a piecewise-constant function to represent the varying Josephson tunneling critical current. The existence of pinned fluxons depends on the length of the inhomogeneity, the variation in the Josephson tunneling critical current and the applied bias current. We establish that a system may either not be able to sustain a pinned fluxon, or - for instance by varying the length of the inhomogeneity - may exhibit various different types of pinned fluxons. Our stability analysis shows that changes of stability can only occur at critical points of the length of the inhomogeneity as a function of the (Hamiltonian) energy density inside the inhomogeneity - a relation we determine explicitly. In combination with continuation arguments and Sturm-Liouville theory, we determine the stability of all constructed pinned fluxons. It follows that if a given system is able to sustain at least one pinned fluxon, a microresistor has exactly one pinned fluxon, i.e. the system selects one unique pinned stable pinned configuration, and a microresonator has at least one stable pinned configuration. Moreover, it is shown that both for micro-resistors and micro-resonators this stable pinned configuration may be non-monotonic - something which is not possible in the homogeneous case. Finally, it is shown that results in the literature on localised inhomogeneities can be recovered as limits of our results on micro-resonators. © 2011 Cambridge University Press.

We analyze a possible superconductivity in the hole-doped system of layered hydrogenized graphene by taking into account thermal fluctuations of the order parameter. In particular, we demonstrate that in the one-layer case the values of the high mean-field (MF) critical temperature $T_{c}^{MF}\sim 80-90K$, predicted recently by Savini et al \cite{Savini}, do not alter significantly due to the fluctuations, and the Berezinskii-Kosterlitz-Thouless (BKT) critical temperature of the vortex superconductivity is almost the same as the MF temperature at doping 0.01-0.1. We show that in the case of multilayer system, when the coupling between the layers stabilizes the superconducting phase in the form of fluxon superconductivity, the critical temperature $T_{c}$ can increase dramatically to the values $\sim 150K$, higher than the corresponding values in cuprates under ambient pressure.

We investigate the microwave surface resistance of an infinitely long type-II superconductor in the critical state carrying transport DC current, in the absence and in the presence of external magnetic fields. Calculations include both different cooling processes and various current and field arrangements. Theoretical results in field-cooled sample show that the microwave surface resistance exhibits an initial slow variation followed by a faster one above a threshold current value. This occurs when the current induced magnetic field generates fluxons of opposite directions on the two sample edges.

In previous papers (Mazzetti et al. in Phys. Rev. B 77:064516, 2008; Ponta et al. in Phys. Rev. B 79:134513, 2009) the mechanism of resistive transition of MgB 2 films has been investigated by the analysis of the non-stationary noise produced during the transition process. The developed model suggested that when the transition occurs very near to T C at low bias current, a mixed state, consisting of normal and superconductive domains, takes place. A different model based on fluxoids dynamics, generated by the current and/or by an external field, is appropriate when the transition occurs at strong bias currents and temperatures much lower than T C . The purpose of this paper is a further investigation of the transition process at low bias currents by analyzing the 1/f power spectra of the noise, taken in stationary conditions at different values of the specimen resistance. These spectra, when renormalized to represent the relative fluctuation of the specimen resistance, are practically coincident, a fact in agreement with the developed model.

The topic of fluxons in Josephson junctions appears often and in many contexts within superconductivity. The potential applications and the appearance of high-T c superconductivity are some of the reasons for this recently increased interest. Several comprehensive reviews of fluxons (solitons) in long Josephson junctions [8], [2], [10], [9] exist, of which particularly the most recent [9] gives an excellent overview of the state of the art for low- T c niobium-type long Josephson junctions. In recent years the properties of long Josephson junctions stacked on top of each other has been studied quite intensively. This is because such systems model existing low-T c superconducting multilayers. In addition these models have revealed surprising dynamical properties. The appearance of high-T c ceramic superconductors has also had quite an impact on the topic of fluxons in superconductors, in particular stacked long Josephson junctions. Here the fluxons play a very important role, for example, in the BSCCO type of material with a layered structure and big anisotropy. Dynamic properties of fluxons are also relevant for the material properties such as the bulk current density and the behaviour near the transition temperature. Some of these high-T c phenomena we will try to include in our description below.