Josephson Junction Model Research Articles

Simulation of the Magnetization Reversal Effect Depending on the Current Pulse Duration within the φ0 Josephson Junction Model Using MPI and OpenMP Parallel Computing Techniques

Simulation of the Magnetization Reversal Effect Depending on the Current Pulse Duration within the φ0 Josephson Junction Model Using MPI and OpenMP Parallel Computing Techniques

Reproduced neuron-like excitability and bursting synchronization of memristive Josephson junctions loaded inductor

Employing electronic component including memristor and Josephson junction to mimic biological neuron or synapse has elicited intense research in recent years. Neurons described by nonlinear oscillators can exhibit complex electrical activities. Josephson junctions are excellent candidates for neuron-inspired components because of their physical properties with low energy costs and high efficiency. In this paper, we revisit a prior work on memristive Josephson junction (MJJ) to identify the dynamical mechanisms to mimic neuron-like excitability and spiking. The inductive memristive Josephson junction (L-MJJ) model is further developed by adding an inductor with internal resistor. It is found that the L-MJJ model can reproduce square-wave bursting of the classical neuronal model from the neurodynamics point of view. The coupling L-MJJ oscillators can achieve in-phase and antiphase bursting synchronization similar with nonlinear coupling neurons. From the framework of nonlinear dynamics theory, this work aspires to build effective bridge between superconducting physics and theoretical neuroscience. Obtained results confirm the potential feasibility of this junction in designing a neuron-inspired computation to explore dynamics of larger-scale neuromorphic network.

Variation Aware Optimization vs Classical Margin Optimization of Superconducting Electronics

We have developed a Superconducting Electronics Circuit Design Optimizer in conjunction with a Statistical Process Variation Josephson Junction Model and formal method of Logic Verification as a means to optimize circuits and mitigate their susceptibility to factors of yield loss. In this paper we will contrast the Yield improvement provided by direct yield optimization against classical methods of margin centering.

Superconducting-Oscillatory Neural Network With Pixel Error Detection for Image Recognition

Brain-inspired oscillatory neural networks (ONNs) utilize coupled oscillators to emulate biological neuronal dynamics. ONNs are naturally suitable for image/pattern recognition. Many hardware implementations of ONNs have been explored recently by using analog or digital CMOS systems, which can be limited by Moore's law. In this work, we used one of the advanced superconducting technologies for coupled oscillator networks to further improve the energy efficiency and processing speed. Inductively coupled ring oscillators using rapid single flux quantum (RSFQ) technology were designed and simulated. These Josephson junction (JJ) based oscillators can operate as fast as tens of GHz but only consume a energy of several aJ per operation. Excluding cryo-cooling factors, the estimated power consumption of our RSFQ oscillator is hundreds of nW at a frequency of 12.5 GHz, which is multiple times smaller than a typical CMOS ring oscillator. Furthermore, a system for pattern recognition with error detection was designed based on these oscillators. Synchronization dynamics in a pair of coupled oscillators were used to identify whether a test pixel matches a reference pixel. A network comprised of 16 pairs of oscillators were wired together, along with synchronization detectors and a fluxon integrator to demonstrate pattern recognition function. This work was performed using standard JJ models and demonstrated through WRspice and JoSIM software simulations. The circuits and systems proposed in this work aim to provide insights into the use of superconducting technology for implementing ONNs and may serve as basic building blocks for the design of more complex oscillatory computational networks in image processing and beyond. Single oscillator modeling and systematic network function exploration will be performed in future work.

Medical image encryption based on RNG with an autonomous piecewise damping Josephson junction jerk oscillator embedded in FPGA

This paper explore the dynamics, Field Programmable Gate Array (FPGA) validation of an autonomous piecewise damping Josephson junction jerk oscillator (APDJJJO) and uses it to protect medical images based on random number generator (RNG). APDJJJO is derived from a piecewise damping Josephson junction (JJ) model and has either no equilibrium points or two unstable equilibrium points. One-scroll chaotic hidden attractor, one-scroll sovereign complex attractor, periodic and one-scroll complex self-driven attractors coexisting, and bistable limit cycles are found in APDJJJO during the investigation based on numerical simulations. Additionally, the FPGA validation of the APDJJJO shows similar complex characteristics to those obtained during the investigation via numerical simulations. Lastly, the chaotic characteristics depicted by the APDJJJO are used to design a RNG for the encryption of medical images. The generated random bits are validated successfully by standard statistical tool set by the National Institute of Standards and Technology (NIST-800-22). Encryption algorithm is developed to secure a medical image by exploring the unpredicted bits generated. The safety and performances analysis are done to prove the robustness and efficiency of the image encryption algorithm.

Control, synchronisation and antisynchronisation of chaos in two non-identical Josephson junction models via sliding mode control and its FPGA implementation

Control, synchronisation and antisynchronisation of chaos in two non-identical Josephson junction models via sliding mode control and its FPGA implementation

Supercurrent in Bi4Te3 Topological Material-Based Three-Terminal Junctions

In this paper, in an in situ prepared three-terminal Josephson junction based on the topological insulator Bi4Te3 and the superconductor Nb the transport properties are studied. The differential resistance maps as a function of two bias currents reveal extended areas of Josephson supercurrent, including coupling effects between adjacent superconducting electrodes. The observed dynamics for the coupling of the junctions is interpreted using a numerical simulation of a similar geometry based on a resistively and capacitively shunted Josephson junction model. The temperature dependency indicates that the device behaves similar to prior experiments with single Josephson junctions comprising topological insulators' weak links. Irradiating radio frequencies to the junction, we find a spectrum of integer Shapiro steps and an additional fractional step, which is interpreted with a skewed current-phase relationship. In a perpendicular magnetic field, we observe Fraunhofer-like interference patterns in the switching currents.

Dynamics and comparative study of the synchronization of some Josephson junction models

In this work, the chaotic dynamics of some Josephson junction models and their synchronization are studied. First, the dynamics of the different junctions have been studied through bifurcation diagrams and corresponding Lyapunov exponents. As the case of junctions based on high temperature superconductors, the dynamics of RCLSJ and fractal junctions have been studied by taking into account the non-harmonicity parameter of the super current of the junction. Then, the identical synchronization between two RCLSJ models is realized for the null and non-null values of the non-harmonic parameter. We then showed that the reduced-order synchronization of the RCLSJ model with three other models can be achieved using both feedback constants and Lyapunov’s stability theory for different values of the non-harmonic constant taken in the chaotic domain.

Identical and reduced-order synchronizations of some Josephson junctions model

Identical and reduced-order synchronizations of some Josephson junctions model

Ac Josephson effect in Corbino-geometry Josephson junctions constructed on Bi2Te3 surface

Recently, a Corbino-geometry type of Josephson junction constructed on the surface of topological insulators has been proposed for hosting and braiding Majorana zero modes. As a first step to test this proposal, we successfully fabricated Corbino-geometry Josephson junctions (JJs) on the surface of Bi2Te3 flakes. Ac Josephson effect with fractional Shapiro steps was observed in the Corbino-geometry JJs while the flux in the junction area was quantized. By analyzing the experimental data using the resistively shunted Josephson junction model, we found that the Corbino-geometry JJs exhibit a skewed current–phase relation due to its high transparency. The results suggest that Corbino-geometry JJs constructed on the surface of topological insulators may provide a promising platform for studying Majorana-related physics.

Simulation of switching to voltage state in an intrinsic Josephson junction

When a current applied to an intrinsic Josephson junction (IJJ) in a copper oxide high-temperature superconductor is increased, the IJJ enters a voltage state and then the voltage increases stepwise. After these voltage states, when the current is lowered, THz oscillation occurs. The voltage state is described as a running state of a particle in a washboard potential, using the RCSJ model of the Josephson junction (JJ). In this study, we investigate these running states in the IJJ, using a coupled layered JJ model with the finite element method. Especially, we focus on time evolution of phase differences in all JJs in the IJJ under weak external current.

Self-Field Effects in a Josephson Junction Model for ${J_\text{c}}$ in REBCO Tapes

Self-Field Effects in a Josephson Junction Model for ${J_\text{c}}$ in REBCO Tapes

Image encryption with a Josephson junction model embedded in FPGA

Image encryption with a Josephson junction model embedded in FPGA

Diagnosing flux penetration condition of the Mo/Au bilayer transition-edge sensor

The magnetic-field-dependence critical current Ic(Ha) is measured for the Mo/Au bilayer transition-edge sensors. A model based on a surface barrier delaying the first penetration of magnetic flux into a flat superconducting strip, including both the geometrical and Bean–Livingston barrier, in combination with two Josephson junction models with different characteristic lengths, is found to ubiquitously fit the Ic(Ha) curves of devices with various geometry designs. The bulk penetration depth, London depairing current density, Josephson junction critical current, self-field coupling coefficient, and conditions of the first vortex entry are investigated throughout the superconducting transition. The evidences of Josephson effect are observed in both Fraunhofer interference pattern and Shapiro steps.

Josephson Junction Model: FPGA Implementation and Chaos-Based Encryption of sEMG Signal through Image Encryption Technique

The field programmable gate array (FPGA) implementation of the nonlinear resistor-capacitor-inductor shunted Josephson junction (NRCISJJ) model and its application to sEMG (Surface ElectroMyoGraphic) signal encryption through image encrypted technique are reported in this study. Thanks to the numerical simulations and FPGA implementation of the NRCISJJ model, different shapes of chaotic attractors are revealed by varying the parameters. The chaotic behaviour found in the NRCISJJ model is used to encrypt the sEMG signal through image encryption technique. The results obtained are interesting and open up many perspectives.

Dynamical Analysis and Microcontroller Implementation of Linear Resistor-Capacitor Shunted Josephson Junction Model

Theoretical analysis and microcontroller implementation of linear resistive-capacitive shunted Josephson junction (LRCSJJ) model are investigated in this paper. The rate-equations describing the LRCSJJ model has two or no equilibrium points relying on the external direct current (DC). One of the equilibrium points is a stable node and the other one is a saddle node. The hysteresis loop of current-voltage characteristics increases with the increasing of the capacitance of Josephson junction (JJ). Excitable mode, limit cycle, periodic and chaotic behaviors are found in LRCSJJ model with external alternative current thanks to the two modulation parameters largest Lyapunov exponents (LLE) diagram. LRCSJJ model exhibits two different shapes of chaotic attractors by varying the modulation amplitude. Finally, the existence of chaotic behaviors is confirmed by microcontroller results obtained from the microcontroller implementation of LRCSJJ model.

Josephson junction model with cosine interference term: Analysis, microcontroller implementation, and network analysis

The dynamical behavior of a single and network of Josephson junction (JJ) model with cosine interference term (CIT) is explored in this paper. The rate-equations describing a single JJ model with CIT have no or two equilibrium points as a function of direct current (DC). The stability of two equilibrium points reveals that one of the equilibrium points is stable node and other is saddle node. The presence of CIT leads to the change of regular spiking and intrinsic bursting to periodic bursting. JJ circuit model with CIT shows the existence of bistable periodic attractors, periodic attractors, hidden chaotic attractors, and coexisting attractors during the numerical simulations. By increasing the coherence parameter, the coexisting attractors are controlled to bistable limit cycles. The microcontroller implementation of the JJ model with CIT is implemented to ascertain the results of numerical simulations. To demonstrate the collective behavior of the JJ model with CIT, a lattice array of identical JJ models with CIT is constructed and studied. By considering the coupling constant as the control parameter, it is demonstrated that the existence of incoherent nodes for lower coupling values and formation of chimera states when the coupling strength is increased.

Suppressing Chaos in Josephson Junction Model with Coexisting Attractors and Investigating Its Collective Behavior in a Network

Suppressing Chaos in Josephson Junction Model with Coexisting Attractors and Investigating Its Collective Behavior in a Network

Chaos Synchronization in Josephson Junction Using a Nonlinear Model Predictive Controller Based on Particle Filter: Processor in the Loop Implementation

In this paper, a model predictive control approach based on a generic particle filter is proposed to synchronize two Josephson junction models with different parameters. For this purpose, an appropriate objective function is defined to assess the particles within the state space. This objective function minimizes simultaneously the tracking error, control effort, and control smoothness. The dynamic optimization problem is solved using a generic particle filter. Here, Josephson junction is described with Resistive Capacitive Inductive Shunted Josephson model, and the synchronization is obtained using the slave–master technique. Moreover, to verify the implementation capability of the proposed algorithm, a processor in loop experiment is performed. The results show that the open-loop system, without the controller, has a chaotic behavior. Numerical simulations are conducted to assess the performance of the proposed algorithm. The results show that the proposed approach can be implemented in a real-time application. Also, the performance of the suggested controller is compared with the proportional integral derivative controller and sliding mode controller.

Microcontroller Implementation, Chaos Control, Synchronization and Antisynchronization of Josephson Junction Model

The microcontroller implementation, chaos control, synchronization, and antisynchronization of the nonlinear resistive-capacitive-inductive shunted Josephson junction (NRCISJJ) model are reported in this paper. The dynamical behavior of the NRCISJJ model is performed using phase portraits, and time series. The numerical simulation results reveal that the NRCISJJ model exhibits different shapes of hidden chaotic attractors by varying the parameters. The existence of different shapes of hidden chaotic attractors is confirmed by microcontroller results obtained from the microcontroller implementation of the NRCISJJ model. It is theoretically demonstrated that the two designed single controllers can suppress the hidden chaotic attractors found in the NRCISJJ model. Finally, the synchronization and antisynchronization of unidirectional coupled NRCISJJ models are studied by using the feedback control method. Thanks to the Routh Hurwitz stability criterion, the controllers are designed in order to control chaos in JJ models and achieved synchronization and antisynchronization between coupled NRCISJJ models. Numerical simulations are shown to clarify and confirm the control, synchronization, and antisynchronization.