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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 study the Wegner-Wilson loops in the string-net model of Levin and Wen in the presence of a string tension. The latter is responsible for a phase transition from a topological deconfined phase (weak tension) to a trivial confined phase (strong tension). We analyze the behavior of all Wegner-Wilson loops in both limiting cases for an arbitrary input theory of the string-net model. Using a fluxon picture, we compute perturbatively the first contributions to a perimeter law in the topological phase as a function of the quantum dimensions. In the trivial phase, we find that Wegner-Wilson loops obey a modified area law, in agreement with a recent mean-field approach., 5 pages, 3 figures, published version

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.

A Josephson junction is a device made of two superconducting electrodes separated by a very thin layer of isolator or normal metal. This relatively simple device has found a variety of technical applications in the form of Superconducting Quantum Interference Devices (SQUIDs) and Single Electron Transistors (SETs). One can expect that in the near future the Josephson junction will find applications in digital electronics technology RSFQ (Rapid Single Flux Quantum) and in the more distant future in construction of quantum computers. Here we concentrate on the relation of the curvature of the Josephson junction with its inductance. We apply a simple Capacitively Shunted Junction (CSJ) model in order to find condition which guarantees consistency of this model with prediction based on the Maxwell and London equations with Landau-Ginzburg current of Cooper pairs. This condition can find direct experimental verification. Keywords: Josephson junction, CSJ model, Fluxon

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.

The appearance and origin of resonance phenomena are studied in an annular system of underdamped Josephson junctions. If no fluxon is trapped in the system, the dynamics is governed by the motion of fluxon-antifluxon pairs. If, on the other hand, trapped fluxons are present, in addition to their motion, the system can also exhibit the simultaneous motion of trapped fluxons and fluxon-antifluxon pairs. Locking between the rotating excitations (fluxons and antifluxons) and the Josephson frequency leads to the appearance of zero-field steps in the current-voltage characteristics, whose number is determined by the number of junctions and the total number of excitations present in the system. The obtained results clearly show that the branching of zero-field steps due to resonance between the rotating excitations and plasma oscillations in their tails appears only at the lower steps and completely disappears at the higher steps. A comparative analysis between systems without and those with trapped fluxons shows a correlation between their current-voltage characteristics. From a high-resolution analysis some special features of zero-field steps emerge such as an additional branch due to resonance between the pulsating fluxon and the Josephson frequency. Examination of systems with the same number but different types of excitations further reveals that their dynamics is determined not only by the number, but also by the type of excitations, i.e., systems with the same number but different types of excitations have different current-voltage characteristics. © 2020 American Physical Society.

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