Josephson Junction System Research Articles

Self-heating effects and switching dynamics in graphene multiterminal Josephson junctions

We experimentally investigate the electronic transport properties of a three-terminal graphene Josephson junction. We find that self-heating effects strongly influence the behavior of this multiterminal Josephson junction (MTJJ) system. We show that existing simulation methods based on resistively and capacitively shunted Josephson junction networks can be significantly improved by taking into account these heating effects. We also investigate the phase dynamics in our MTJJ by measuring its switching current distribution and find correlated switching events in different junctions. We show that the switching dynamics is governed by phase diffusion at low temperatures. Furthermore, we find that self-heating introduces additional damping that results in overdamped I−V characteristics when normal and supercurrents coexist in the device. Published by the American Physical Society 2024

Half-integer Shapiro steps in MgB2 focused He ion beam Josephson junctions

Abstract Half-integer microwave induced steps (Shapiro steps) have been observed in many different Josephson junction systems, which have attracted a lot of attention because they signify the deviation of current phase relation (CPR) and uncover many unconventional physical properties. In this article, we first report the discovery of half-integer Shapiro steps in MgB2 focused He ion beam (He-FIB) Josephson junctions. The half-integer steps’ dependence on microwave frequency, temperature, microwave power, and magnetic field is also analyzed. We find that the existence of half-integer steps can be controlled by the magnetic field periodically, which is similar to that of high temperature superconductor (HTS) grain boundary junctions, and the similarity of the microstructures between gain boundary junctions and He-FIB junctions is discussed. As a consequence, we mainly attribute the physical origin of half-integer steps in MgB2 He-FIB junctions to the model that a He-FIB junction is analogous to a parallel junctions’ array. Our results show that He-FIB technology is a promising platform for researching CPR in junctions made of different superconductors.

Schrödinger cat state formation in small bosonic Josephson junctions at finite temperatures and dissipation

In this work, we consider the feasibility of Schrödinger cat (SC) and states formation by a convenient bosonic Josephson junction system in two-mode approximation. Starting with purely quantum description of two-mode Bose–Einstein condensate we investigate the effective potential approach that provides an accurate analytical description for the system with a large number of particles. We show that in the zero temperature limit SC states result from a quantum phase transition that occurs when the nonlinear strength becomes comparable with the Josephson coupling parameter. The Wigner function approach demonstrates the growth of the SC state halves separation and formation of -like states (a Fock state superposition) with the particle number increase. We examine the possibility to attain the SC state at finite temperatures and a weak dissipation leading to appearing of some critical temperature; it defines the second-order phase transition from classical activation process to the SC state formation through the quantum tunneling phenomenon. Numerical estimations demonstrate that the critical temperature is sufficiently below the temperature of atomic condensation. The results obtained may be useful for experimental observation of SC states with small condensate Josephson junctions.

Anomalous metals: From “failed superconductor” to “failed insulator”

Resistivity saturation is found on both superconducting and insulating sides of an "avoided" magnetic-field-tuned superconductor-to-insulator transition (H-SIT) in a two-dimensional In/InOx composite, where the anomalous metallic behavior cuts off conductivity or resistivity divergence in the zero-temperature limit. The granular morphology of the material implies a system of Josephson junctions (JJs) with a broad distribution of Josephson coupling EJ and charging energy EC, with an H-SIT determined by the competition between EJ and EC. By virtue of self-duality across the true H-SIT, we invoke macroscopic quantum tunneling effects to explain the temperature-independent resistance where the "failed superconductor" side is a consequence of phase fluctuations and the "failed insulator" side results from charge fluctuations. While true self-duality is lost in the avoided transition, its vestiges are argued to persist, owing to the incipient duality of the percolative nature of the dissipative path in the underlying random JJ system.

Enhanced nonlinear quantum metrology with weakly coupled solitons in the presence of particle losses

The estimation of physical parameters with Heisenberg sensitivity and beyond is one of the crucial problems for current quantum metrology. However, unavoidable lossy effect is commonly believed to be the main obstacle when applying fragile quantum states. To utilize the lossy quantum metrology, we offer an interferometric procedure for phase parameters estimation at the Heisenberg (up to 1/N) and super-Heisenberg (up to 1/N^3) scaling levels in the framework of the linear and nonlinear metrology approaches, respectively. The heart of our setup is the novel soliton Josephson Junction (SJJ) system providing the formation of the quantum probe, i.e, the entangled Fock (N00N-like) state, beyond the superfluid-Mott insulator quantum phase transition point. We illustrate that such states are close to the optimal ones even with moderate losses. The enhancement of phase estimation accuracy remains feasible both for the linear and nonlinear metrologies with the SJJs, and allows further improvement for the current experiments performed with atomic condensate solitons with a mesoscopic number of particles.

Resonance phenomena in an annular array of underdamped Josephson junctions

Appearance and origin of resonance phenomena have been studied in the annular system of underdamped Josephson junctions. If no fluxon is trapped in the system, dynamics is governed by the motion of fluxon-antifluxon pairs, while if trapped fluxons are present, they can move solely but also simultaneously with the 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, which can further exhibit branching due to resonance between the rotating excitations and plasma oscillations in their tale. The number of zero field steps and their branching are strongly determined by the total number of excitations present in the system. High resolution analysis further reveals not only some interesting properties of zero field steps, but also shows that the current-voltage characteristics is determined not only by the number, but also by the type of excitations, i.e., whether the dynamics is governed only by the motion of fluxon-antifluxon pairs or the trapped fluxons, or they move simultaneously in the system.

Noise-induced dynamics in a Josephson junction driven by trichotomous noises

Abstract Noise-induced dynamics is explored in a Josephson junction system driven by multiplicative and additive trichotomous noises in this paper. Under the adiabatic approximation, the analytical expression of average output current for the Josephson junction is obtained, which can be used to characterize stochastic resonance (SR). If only the additive trichotomous noise is considered, the large correlation time of additive noise can induce the suppression and the SR in the curve of average output current. When the effects of both multiplicative and additive trichotomous noises are considered, two pronounced peaks exist in the curves of average output current for large multiplicative noise amplitude and optimal additive noise intensity. That is, the stochastic multi-resonance phenomenon is observed in this system. Moreover, the curve of average output current appears a single peak as a function of multiplicative noise intensity, which disappears for the case of small fixed additive noise amplitude. Especially, the mean first-passage time (MFPT) as the function of additive trichotomous noise intensity displays a non-monotonic behavior with a maximum for the large multiplicative noise amplitude, which is called the phenomenon of the noise enhanced stability (NES).

Ac-driven annular Josephson junctions: The missing Shapiro steps

Examination of an annular system of underdamped Josephson junctions in the presence of external radiation showed that the ability of the system to lock with some external radiation was determined not only by the number but also by the type of rotating excitations (fluxons or antifluxons). Shapiro steps can be observed in the current-voltage characteristics only in the system with trapped fluxons or in the system with fluxon-antifluxon pairs. If the trapped fluxons circulate simultaneously with fluxon-antifluxon pairs, there are no Shapiro steps regardless of the amplitude or frequency of the applied external radiation.

Effect of parameter mismatches on chaos synchronization between Josephson junctions coupled in series and driven by a central junction

Synchronization of chaos between Josephson junctions coupled in series and driven by a central junction is studied under the parameter mismatches condition. It is shown that in most cases high quality synchronization between the Josephson junctions with such a coupling topology is achievable even under significant parameter mismatches. It is also established that synchronization quality between the Josephson junctions is most sensitive to the parameter mismatches between the frequencies of the ac current driving the junctions. These results are of immense significance to obtain high power system of Josephson junctions, which can be a mobile, cost effective source of Terahertz radiation with a wide range of applications in different areas of science such as medicine, ecology, security, communication, etc.

Scaling theory of a quantum ratchet

The asymmetric responses of the system between the external force of right and left directions are called "nonreciprocal". There are many examples of nonreciprocal responses such as the rectification by p-n junction. However, the quantum mechanical wave does not distinguish between the right and left directions as long as the time-reversal symmetry is intact, and it is a highly nontrivial issue how the nonreciprocal nature originates in quantum systems. Here we demonstrate by the quantum ratchet model, i.e., a quantum particle in an asymmetric periodic potential, that the dissipation characterized by a dimensionless coupling constant $\alpha$ plays an essential role for nonlinear nonreciprocal response. The temperature ($T$) dependence of the second order nonlinear mobility $\mu_2$ is found to be $\mu_2 \sim T^{6/\alpha -4 }$ for $\alpha<1$, and $\mu_2 \sim T^{2(\alpha -1)}$ for $\alpha>1$, respectively, where $\alpha_c=1$ is the critical point of the localization-delocalization transition, i.e., Schmid transition. On the other hand, $\mu_2$ shows the behavior $\mu_2 \sim T^{-11/4}$ in the high temperature limit. Therefore, $\mu_2$ shows the nonmonotonous temperature dependence corresponding to the classical-quantum crossover. The generic scaling form of the velocity $v$ as a function of the external field $F$ and temperature $T$ is also discussed. These findings are relevant to the heavy atoms in metals, resistive superconductors with vortices and Josephson junction system, and will pave a way to control the nonreciprocal responses.

Features of the Dynamics of a System of Coupled Josephson Junctions with Topologically Trivial and Nontrivial Barriers: Manifestation of the Majorana Mode

The appearance of parametric resonance and the excitation of a longitudinal plasma wave in a system of coupled Josephson junctions with topologically trivial and nontrivial barriers have been demonstrated. The voltage at resonance as a function of the dissipation parameter has a minimum at which the parametric resonance condition changes from ωJ = 2ωLPWtoωJ = ωLPW, where is the Josephson frequency and ωLPW is the frequency of the formed longitudinal plasma wave. The position of this minimum for the system with nontrivial barriers is shifted from that for the system with trivial barriers. This shift can be used to identify the appearance of Majorana states.

Chaos synchronization between Josephson junctions coupled in series and driven by a central junction

All-to-all chaos synchronization between Josephson junctions coupled in series and driven by a central junction is studied. It is demonstrated that high quality synchronization between the Josephson junctions with such a coupling topology is achievable. These results are important to obtain high power system of Josephson junctions, which can be a mobile, cost effective source of Terahertz radiation. Such systems are extremely important from the application point of view of Terahertz radiation in different areas of science such as medicine, ecology, security, communication, etc.

Trajectory Tracking between Josephson Junction and Classical Chaotic System via Iterative Learning Control

This article addresses trajectory tracking between two non-identical systems with chaotic properties. To study trajectory tracking, we used the Rossler chaotic and resistive-capacitive-inductance shunted Josephson junction (RCLs-JJ) model in a similar phase space. In order to achieve goal tracking, two stages were required to approximate target tracking. The first stage utilizes the active control technique to transfer the output signal from the RCLs-JJ system into a quasi-Rossler system. Next, the RCLs-JJ system employs the proposed iterative learning control scheme in which the control signals are from the drive system to trace the trajectory of the Rossler system. The numerical results demonstrate the validity of the proposed method and the tracking system is asymptotically stable.

Time-evolution of photon heat current through series coupled two mesoscopic Josephson junction devices

Photon heat current tunneling through a series coupled two mesoscopic Josephson junction (MJJ) system biased by dc voltages has been investigated by employing the nonequilibrium Green’s function approach. The time-oscillating photon heat current is contributed by the superposition of different current branches associated with the frequencies of MJJs ωj (j = 1, 2). Nonlinear behaviors are exhibited to be induced by the self-inductance, Coulomb interaction, and interference effect relating to the coherent transport of Cooper pairs in the MJJs. Time-oscillating pumping photon heat current is generated in the absence of temperature difference, while it becomes zero after time-average. The combination of ωj and Coulomb interactions in the MJJs determines the concrete heat current configuration. As the external and intrinsic frequencies ωj and ω0 of MJJs match some specific combinations, resonant photon heat current exhibits sinusoidal behaviors with large amplitudes. Symmetric and asymmetric evolutions versus time t with respect to ω1t and ω2t are controlled by the applied dc voltages of V1 and V2. The dc photon heat current formula is a special case of the general time-dependent heat current formula when the bias voltages are settled to zero. The Aharonov–Bohm effect has been investigated, and versatile oscillation structures of photon heat current can be achieved by tuning the magnetic fluxes threading through separating MJJs.

Shift of Shapiro Step in High Critical Temperature Superconductors

The influence of the charge imbalance effect on a system of intrinsic Josephson junctions of high temperature superconductors under external electromagnetic radiation is investigated. We find that the charge imbalance is responsible for the slope of the Shapiro step in the IV-characteristic. The nonperiodic boundary conditions shift the Shapiro step from the canonical position which is determined by the frequency of the external radiation. We also find how the system parameters influence the shift of the Shapiro step.

Homoclinic and heteroclinic chaos in nonlinear systems driven by trichotomous noise**Project supported by the National Natural Science Foundation of China (Grant No. 11672231), the Natural Science Foundation of Shaanxi Province, China (Grant No. 2016JM1010), the Fundamental Research Funds for the Central Universities, China (Grant No. 3102015ZY073), and the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical

The homoclinic and heteroclinic chaos in nonlinear systems subjected to trichotomous noise excitation are studied. The Duffing system and the Josephson-junction system are taken for example to calculate the corresponding amplitude thresholds for the onset of chaos on the basis of the stochastic Melnikov process with the mean-square criterion. It is shown that the amplitude threshold for the onset of chaos can be adjusted by changing the internal parameters of trichotomous noise, thereby inducing or suppressing chaotic behaviors in the two systems driven by trichotomous noise. The effects of trichotomous noise on the systems are verified by vanishing the mean largest Lyapunov exponent and demonstrated by phase diagrams and time histories.

Effect of inductive and capacitive coupling on the current–voltage characteristic and electromagnetic radiation from a system of Josephson junctions

We have studied the current–voltage characteristic of a system of long Josephson junctions taking into account the inductive and capacitive coupling. The dependence of the average time derivative of the phase difference on the bias current and spatiotemporal dependences of the phase difference and magnetic field in each junction are considered. The possibility of branching of the current–voltage characteristic in the region of zero field step, which is associated with different numbers of fluxons in individual Josephson junctions, is demonstrated. The current–voltage characteristic of the system of Josephson junctions is compared with the case of a single junction, and it is shown that the observed branching is due to coupling between the junctions. The intensity of electromagnetic radiation associated with motion of fluxons is calculated, and the effect of coupling between junctions on the radiation power is analyzed.

Вычисление ВАХ для систем джозефсоновских переходов.О построении асимптотики вблизи точки излома

Solving the system of essentially nonlinear differential equations for different we obtain thecurrent-voltage characteristics (IVC) for a system of Josephson junctions (JJ) as a hysteresisloop. When the current approaches on the back way the breakpoint the voltage ()falls sharply to zero. In addition, in numerical modelling (non-periodic boundary conditions(NPBC)) IVC multiple branching is observed near . It is interesting to study this phenomenonanalytically developing asymptotic methods. There had been developed simple &ldquo;asymptotic&rdquo;formulas suitable for calculation of all IVC points except near to . A numerical-analyticalmethod allowing to shorten IVC calculation time essentially was proposed. This method showedgood results in IVC multiple branching calculation in particular. All calculations were performedusing the REDUCE system. We succeeded first to calculate analytically all points of IVC. Anapproximate solution at the breakpoint region (periodic boundary conditions (PBC)) has beendeveloped using the Bogolyubov-Krylov method.

Theory of Enhanced Interlayer Tunneling in Optically Driven High-T_{c} Superconductors.

Motivated by recent pump-probe experiments indicating enhanced coherent c-axis transport in underdoped YBCO, we study Josephson junctions periodically driven by optical pulses. We propose a mechanism for this observation by demonstrating that a parametrically driven Josephson junction shows an enhanced imaginary part of the low-frequency conductivity when the driving frequency is above the plasma frequency, implying an effectively enhanced Josephson coupling. We generalize this analysis to a bilayer system of Josephson junctions modeling YBCO. Again, the Josephson coupling is enhanced when the pump frequency is blue detuned to either of the two plasma frequencies of the material. We show that the emergent driven state is a genuine, nonequilibrium superconducting state, in which equilibrium relations between the Josephson coupling, current fluctuations, and the critical current no longer hold.

Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light

We review recent developments concerning non-equilibrium quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues. We start with quantum impurity models summarizing the effect of dissipation and of driving the system. We mention theoretical and experimental efforts to characterize these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect is characterized by a renormalized light-frequency and a peak in the Rayleigh elastic transmission of a photon. We also address the physics of hybrid systems comprising mesoscopic quantum dot devices coupled to an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing to engineer the Jaynes-Cummings lattice and Rabi lattice models. This opens the door to novel many-body physics with light out of equilibrium, in relation with the Mott-superfluid transition observed with ultra-cold atoms in optical lattices. Then, we summarize recent theoretical predictions for realizing topological phases with light. Synthetic gauge fields and spin-orbit couplings have been successfully implemented with ultra-cold atoms in optical lattices --- using time-dependent Floquet perturbations periodic in time, for example --- as well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose-Hubbard models in ladder and two-dimensional geometries. The Bose-Hubbard model is related to the Jaynes-Cummings lattice model in the large detuning limit between light and matter. In the presence of synthetic gauge fields, we show that Meissner currents subsist in an insulating Mott phase.