We have investigated the phase dynamics and IV-characteristics of shunted Josephson junctions coupled to an $LC$ circuit. When the Josephson frequency $ω_J$ is close to the eigen frequency $ω_{rc}$ of the coupled resonance circuit, the IV-characteristic demonstrates an additional $rc$-branch. We have investigated the features of the $rc$-branch and of the superconducting current component for different values of the resonance frequency. It has been found that the maximal value of the superconducting current depends on the resonance frequency and that it increases when the end point of the $rc$-branch approaches the critical current. The dependence of the maximal superconducting current on the resonance frequency at different values of the dissipation parameter is peculiar, for the optimized maximum appears to be independent of the system parameters within $1\%$.
We investigate the dynamics of a resistively shunted Josephson junction. We compute the Josephson frequency and the generalized impedances for a variety of the parameters, particularly with relevance to predicting the measurable effects of zero-temperature current noise in the resistor.
We have studied both theoretically and experimentally how an LC series circuit connected in parallel to a Josephson junction influences the Josephson dynamics. The presence of the shell circuit introduces two energy scales, which in specific cases can strongly differ from the plasma frequency of the isolated junction. Josephson junctions were manufactured using Nb/Al-AlOx/Nb fabrication technology with various on-chip LC shunt circuits. Spectroscopic measurements in the quantum limit show an excellent agreement with theory taking into account the shunt inductance and capacitance in the Resisti…
The intrinsic nonlinearity of Josephson junctions converts Gaussian current noise in the input into non-Gaussian voltage noise in the output. For a resistively shunted Josephson junction with white input noise we determine numerically exactly the properties of the few lowest cumulants of the voltage fluctuations, and we derive analytical expressions for these cumulants in several important limits. The statistics of the voltage fluctuations is found to be Gaussian at bias currents well above the Josephson critical current, but Poissonian at currents below the critical value. In the transition r…
In this Chapter, we present our latest experimental results (along with their theoretical interpretation) related to some unusual magnetic properties of artificially prepared ordered two-dimensional Josephson junction arrays (of both shunted and unshunted Nb-AlO_x-Nb tunnel junctions). Namely, we address the following topics: (i) influence of non-uniform critical current density profile on magnetic field behavior of AC susceptibility, (ii) origin of the so-called dynamic reentrance phenomenon, and (iii) manifestation of novel geometric quantization effects in temperature behavior of AC magneti…
This is a detailed derivation of the equation for the voltage noise of a resistively shunted Josephson junction with non-sinusoidal current-phase relation, which was presented in Sov. Phys. JETP {\bf 67}, 579 (1988).
We are developing a superconductor electronics fabrication process with up to nine planarized superconducting layers, stackable stud vias, self-shunted Nb/AlOx-Al/Nb Josephson junctions, and one layer of MoNx kinetic inductors. The minimum feature size of resistors and inductors in the process is 250 nm. We present data on the mutual inductance of Nb stripline and microstrip inductors with linewidth and spacing from 250 nm to 1 μm made on the same or adjacent Nb layers, as well as the data on the linewidth and resistance uniformity.
We present a cluster algorithm for resistively shunted Josephson junctions and similar physical systems, which dramatically improves sampling efficiency. The algorithm combines local updates in Fourier space with rejection-free cluster updates which exploit the symmetries of the Josephson coupling energy. As an application, we consider the localization transition of a single junction at intermediate Josephson coupling and determine the temperature dependence of the zero bias resistance as a function of dissipation strength.
Zero-bias resistances of a single resistance-shunted Josephson junction are calculated as a function of the temperature by means of the path-integral Monte Carlo method in case a charging energy $E_{\rm C}$ is comparable with a Josephson energy $E_{\rm J}$. The low-temperature behavior of the zero-bias resistance changes around $α=R_{\rm Q}/R_{\rm S}=1$, where $R_{\rm S}$ is a shunt resistance and $R_{\rm Q}=h/(2e)^2$. The temperature dependence of the zero-bias resistance shows a power-law-like behavior whose exponent depends on $E_{\rm J}/E_{\rm C}$. These results are compared with the exper…
Conventional Josephson metal-insulator-metal devices are inherently underdamped and exhibit hysteretic current-voltage response due to a very high subgap resistance compared to that in the normal state. At the same time, overdamped junctions with single-valued characteristics are needed for most superconducting digital applications. The usual way to overcome the hysteretic behavior is to place an external low-resistance normal-metal shunt in parallel with each junction. Unfortunately, such solution results in a considerable complication of the circuitry design and introduces parasitic inductan…
Self-shunted aluminum Josephson junctions with high-transparency barriers were fabricated using the shadow-evaporation technique and measured at low temperatures, T=25 mK. Due to high junction transparency, the IV-characteristics were found to be of only small hysteresis with retrapping-to-switching current ratio of up to 80%. The observed critical currents were close to the Ambegaokar-Baratoff values (up to 80-100%). Good barrier quality was confirmed by the low subgap leakage currents in the quasiparticle branches, which makes the self-shunted Al junctions promising for application in integr…
Thermodynamics and transport properties of resistance-shunted Josephson junctions are studied theoretically in the tight-binding limit E_C/E_J<<1, where E_C and E_J are a charging energy and a Josephson coupling energy respectively. Based on a phenomenological harmonic-oscillator model, weak coupling region K=R_Q/R<<1 is analytically studied, where R and R_Q=h/(2e)^2 are a shunted resistance and the quantum resistance. In addition to the effective bandwidth, we find that this multi-level system genuinely has a novel crossover at lower energy below which the density of states becomes strongly d…
Within the framework of the microscopic model of tunneling, we modelled the behavior of the Josephson junction shunted by the Superconductor-Insulator-Normal metal (SIN) tunnel junction. We found that the electromagnetic impedance of the SIN junction yields both the frequency-dependent damping and dynamic reactance which leads to an increase in the effective capacitance of the circuit. We calculated the dc I-V curves and transient characteristics of these circuits and explained their quantitative differences to the curves obtained within the resistively shunted junction model. The correct oper…
We have studied the Josephson dynamics of resistively-shunted ballistic superconducting quantum point contacts at finite temperatures and arbitrary number of conducting modes. Compared to the classical Josephson dynamics of tunnel junctions, dynamics of quantum point contacts exhibits several new features associated with temporal fluctuations of the Josephson potential caused by fluctuations in the occupation of the current-carrying Andreev levels.
The choice of impedance used to shunt a Josephson junction determines if the charge transferred through the circuit is quantized: a capacitive shunt renders the charge discrete, whereas an inductive shunt leads to continuous charge. This discrepancy leads to a paradox in the limit of large inductances L. We show that while the energy spectra of the capacitively and inductively shunted junction are vastly different, their high-frequency responses become identical for large L. Inductive shunting thus opens the possibility to observe charging effects unimpeded by charge noise.
Recent progress in superconductor electronics fabrication has enabled single-flux-quantum (SFQ) digital circuits with close to one million Josephson junctions (JJs) on 1-cm$^2$ chips. Increasing the integration scale further is challenging because of the large area of SFQ logic cells, mainly determined by the area of resistively shunted Nb/AlO$_x$-Al/Nb JJs and geometrical inductors utilizing multiple layers of Nb. To overcome these challenges, we are developing a fabrication process with self-shunted high-J$_c$ JJs and compact thin-film MoN$_x$ kinetic inductors instead of geometrical inducto…
Superconducting weak-link (WL), behaving like a Josephson junction (JJ), is fundamental to many superconducting devices such as nanoSQUIDs, single-photon detectors, and bolometers. The interplay between unique nonlinear dynamics and inevitable Joule heating in a JJ leads to new characteristics. Here, we report a time-dependent model incorporating thermal effect in the AC Josephson regime for a Josephson WL shunted by a resistor together with an inductor to investigate the dynamics as well as the resulting current-voltage characteristics. We find that the dynamic regime where phase and temperat…
The dynamic critical exponent $z$ is determined numerically for the $d$-dimensional XY model ($d=2, 3$, and 4) subject to relaxational dynamics and resistively shunted junction dynamics. We investigate both the equilibrium fluctuation and the relaxation behavior from nonequilibrium towards equilibrium, using the finite-size scaling method. The resulting values of $z$ are shown to depend on the boundary conditions used, the periodic boundary condition, and fluctuating twist boundary condition (FTBC), which implies that the different treatments of the boundary in some cases give rise to differen…
Using a point (superconductor-constriction-superconductor, ScS) contact in a single-Josephson-junction superconducting quantum interference device (RF SQUID) provides stochastic resonance conditions at any arbitrary small value of loop inductance and contact critical current, unlike SQUIDs with more traditional tunnel (superconductor-insulator-superconductor, SIS) junctions. This is due to the unusual potential energy of the ScS RF SQUID which always has a barrier between two wells thus making the device bistable. This paper presents the results of a numerical simulation of the stochastic dyna…
We theoretically investigate the phase and voltage correlation dynamics, which includes both the deterministic contribution and stochastic fluctuations, under a current noise generated by a resistor including thermal and quantum fluctuations in a resistively and capacitively shunted Josephson junction. An external current is found to shift and intensify the deterministic contributions in phase and voltage. In addition to effects of external current, we observe the relaxation of autocorrelation functions of phase and voltage, which includes the variances due to the current noise, to finite valu…
We present an electronic circuit whose dynamical properties emulate those of a resistively and capacitively shunted Josephson junction (RCSJ). We show how it reproduces the switching properties of a shunted junction and its dependence on the quality factor. A thermal noise source is then used to characterize the temperature dependence of the phase dynamics. In the presence of an AC drive, phase locking is observed at integer and rational multiples of the drive frequency, and it competes with chaotic behavior when the quality factor of the junction exceeds unity. We characterize the stability o…
We investigated current-voltage characteristics of unshunted and externally shunted Josephson junctions (JJs) with high critical current densities, Jc, in order to extract their basic parameters and statistical characteristics for JJ modeling in superconducting integrated circuits and to assess their potential for future technology nodes. Nb/AlOx-Al/Nb JJs with diameters from 0.5 μm to 6 μm were fabricated using a fully planarized process with Mo or MoNx thin-film shunt resistors with sheet resistance Rsq = 2 Ω/sq and Rsq = 6 Ω/sq, respectively. We used our standard MIT LL process SFQ5ee to fa…
Using a new cluster Monte Carlo algorithm, we study the phase diagram and critical properties of an interacting pair of resistively shunted Josephson junctions. This system models tunneling between two electrodes through a small superconducting grain, and is described by a double sine-Gordon model. In accordance with theoretical predictions, we observe three different phases and crossover effects arising from an intermediate coupling fixed point. On the superconductor-to-metal phase boundary, the observed critical behavior is within error-bars the same as in a single junction, with identical v…
We introduce a new design concept for superconducting quantum bits (qubits) in which we explicitly separate the capacitive element from the Josephson tunnel junction for improved qubit performance. The number of two-level systems (TLS) that couple to the qubit is thereby reduced by an order of magnitude and the measurement fidelity improves to 90%. This improved design enables the first demonstration of quantum state tomography with superconducting qubits using single shot measurements.
We investigate theoretical aspects of the detection of Majorana bound states in Josephson junctions using the semiclassical RCSJ model of junction dynamics. The influence of a 4$π$-periodic supercurrent contribution can be detected through its effect on the width of the Shapiro steps and the Fourier spectrum of the voltage signal. We explain how the inclusion of a capacitance term results in a strong quenching of the odd steps when the junction is underdamped, and hence may be used to effectively detect Majorana bound states. Furthermore, in presence of capacitance the first and third steps ar…
Epitaxial NbN-junction-based self-shunted superconducting flux qubit with high anharmonicity
Tohoku University（东北大学）；RIKEN Center for Quantum Computing（理化学研究所量子计算中心）；The University of Tokyo（东京大学）；Inamori Research Institute for Science (InaRIS)（稻盛科学研究所）；National Institute of Information and Communications Technology (NICT)（信息通信研究机构）
We report on anomalous conductance in a resistively and capacitively shunted Josephson junction which is simultaneously driven by ac and dc currents. The dependence of the voltage across the junction on the frequency of the ac current shows windows of absolute negative conductance regimes, i.e. for a positive (negative) dc current, the voltage is negative (positive).
Recently transport measurements have been carried out in resistively shunted long superconducting nanowires [M. W. Brenner {\it et. al.}, Phys. Rev. B {\bf{85}}, 224507 (2012)]. The measured voltage-current ($V$-$I$) characteristics was explained by the appearance of the phase slip centers in the shunted wire, and the whole wire was modeled as a single Josephson junction. The kinetic inductance of the long nanowires used in experiments is generally large. Here we argue that the shunted superconducting nanowire acts as a Josephson junction in series with an inductor. The inductance depends on t…
We have fabricated the Bloch transistor shunted on-chip by a small-sized Cr resistor with Rs about 1 kOhm. The Bloch transistor normally consists of two small Josephson junctions connected in series, which in our case have been replaced by two superconducting interferometer loops, each with two junctions in parallel. A capacitively coupled gate is supplied to control the induced charge of the small intermediate electrode (island) of the transistor. The measured I-V curves show no hysteresis and correspond to the operation of a effective Josephson junction at the high-damping and strong-noise l…
We study vortex structure in three different models of long Josephson junctions: exponentially shaped Josephson junction and Josephson junctions with resistor and shunt inhomogeneities in barrier layer. Numerical calculations of the possible magnetic flux distributions and corresponding bifurcation curves have done. For these three models the critical curves ``critical current-magnetic field'' are constructed. We develop an idea of the equivalence of exponentially shaped Josephson junction and rectangular junction with distributed inhomogeneity and demonstrate that at some parameters of shunt …
The form of the fluctuation-dissipation theorem for a resistively shunted Josephson juction array is derived with the help of the method which explicitely takes into acoount screening effects. This result is used to express the flux noise power spectrum in terms of frequency dependent sheet impedance of the array. The relation between noise amplitude and parameters of the detection coil is analysed for the simplest case of a single-loop coil.
The RCSJ (Resistor-Capacitor Shunted Junction) model provides us an analytical formula for the conversion efficiency for a resonant Josephson effect mixer. An external rf signal is applied to a long Josephson junction operating in the fluxon oscillating regime. The sine-Gordon equation is used to investigate the dynamics of the phase-locking between the fluxon oscillations and the external signal. We obtain that it is possible to have conversion efficiency greater than unity.
Josephson radiation is a useful signature for detecting Majorana zero modes in topological superconductors. We study the Josephson radiation of the underdamped topological Josephson junction within the quantum resistively and capacitively shunted junction model. We show that the quantum dynamics of the Majorana two-level system induce oscillatory patterns in the Josephson emission spectra. With the Floquet method, we obtain analytical results for these oscillatory patterns and find that they are well described by Bessel functions. We perform numerical simulations to verify the analytical resul…
Operation of a Superconducting Quantum Interference Device (SQUID) made of stacked Josephson junctions is analyzed numerically for a variety of junction parameters. Due to a magnetic coupling of junctions in the stack, such a SQUID has certain advantages as compared to an uncoupled multi-junction SQUID. Namely, metastability of current-flux modulation can be reduced and a voltage-flux modulation can be improved if junctions in the stack are phase-locked. Optimum operation of the SQUID is expected for moderately long, strongly coupled stacked Josephson junctions. A possibility of making a stack…
The properties of Josephson junction including a ferromagnetic insulating layer are studied theoretically. The calculated current shows the anomalous dependence on the magnitude of the exchange interaction at the interface. The Josephson junction changes from 0-junction to $π$-junction with the increase of the magnitude of the exchange interaction.
Magnetotransport measurements were done on $\Nb/\Al_2Ø_3/\Cu/\Ni/\Nb$ superconductor-insulator-ferromagnet-superconductor Josephson tunnel junctions. Depending on ferromagnetic $\Ni$ interlayer thickness and geometry the standard (1d) magnetic field dependence of critical current deviates from the text-book model for Josephson junctions. The results are qualitatively explained by a short Josephson junction model based on anisotropy and 2d remanent magnetization.
We clarify the applicability of the quasistatic approximation used in Ref. [\onlinecite{VE}], where coupled spin and Josephson plasma waves have been predicted to exist in SIFS Josephson junctions. We show, contrary to the claim of the authors of Ref. [\onlinecite{Maekawa}], that this approximation is very accurate in realistic systems studied experimentally.
The dynamical vortex response of a two-dimensional array of the resistively shunted Josephson junctions in a perpendicular magnetic field is inferred from simulations. It is found that, as the magnetic field is increased at a fixed temperature, the response crosses over from normal to anomalous, and that this crossover can be characterized by a single dimensionless parameter. It is described how this crossover should be reflected in measurements of the complex impedance for Josephson junction arrays and superconducting films.
We highlight the reproducibility and level of control over the electrical properties of YBa$_2$Cu$_3$O$_7$ Josephson junctions fabricated with irradiation from a focused helium ion beam. Specifically, we show the results of electrical transport properties for several junctions fabricated using a large range of irradiation doses. At the lower end of this range, junctions exhibit superconductor-normal metal-superconductor (SNS) Josephson junction properties. However, as dose increases there is a transition to electrical characteristics consistent with superconductor-insulator-superconductor (SIS…
We calculate the current phase relation of a planar Josephson junction with a ferromagnetic weak link located on top of a thin normal metal film. Following experimental observations we assume transparent superconductor-ferromagnet interfaces. This provides the best interlayer coupling and a low suppression of the superconducting correlations penetrating from the superconducting electrodes into the ferromagnetic layer. We show that this Josephson junction is a promising candidate for an experimental ϕ junction realization.
The spontaneous flux generation and magnetic field modulation of the critical current in a 0-pi Josephson junction are calculated for different ratios of the junction length to the Josephson penetration depth, and different ratios of the 0-junction length to the pi-junction length. These calculations apply to a Pb-YBCO c-axis oriented junction with one YBCO twin boundary, as well as other experimental systems. Measurements of such a junction can provide information on the nature of the c-axis Josephson coupling and the symmetry of the order parameter in YBCO. We find spontaneous flux even for …
The effect of microwave irradiation on the phase dynamics of intrinsic Josephson junctions in high temperature superconductors is investigated. We compare the current-voltage characteristics for a stack of coupled Josephson junctions under external irradiation calculated in the framework of CCJJ and CCJJ+DC models.
We observed splitting of the low-bias vortex-flow branch in a dense-Josephson-vortex state into multiple sub-branches in current-voltage characteristics of intrinsic Josephson junctions (IJJs) of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ single crystals in the long-junction limit. Each sub-branch corresponds to a plasma mode in serially coupled Josephson junctions. Splitting into low-bias linear sub-branches with a spread in the slopes and the inter-sub-branch mode-switching character are in good quantitative agreement with the prediction of the weak but finite inter-junction capacitive-coupling mod…
We study magnetization reversal in a $φ_0$ Josephson junction with direct coupling between magnetic moment and Josephson current. Our simulations of magnetic moment dynamics show that by applying an electric current pulse, we can realize the full magnetization reversal. We propose different protocols of full magnetization reversal based on the variation of the Josephson junction and pulse parameters, particularly, electric current pulse amplitude, damping of magnetization and spin-orbit interaction. We discuss experiments which can probe the magnetization reversal in $φ_0$-junctions.
We report on an experimental and theoretical study of the high-frequency mixing properties of ion-irradiated YBa2Cu3O7 Josephson junctions embedded in THz antennas. We investigated the influence of the local oscillator power and frequency on the device performances. The experimental data are compared with theoretical predictions of the general three-port model for mixers, in which the junction is described by the resistively shunted junction model. A good agreement is obtained for the conversion efficiency in different frequency ranges, spanning above and below the characteristic frequencies f…
In this paper, we report on different phenomena related to the magnetic properties of artificially prepared highly ordered (periodic) two-dimensional Josephson junction arrays (2D-JJA) of both shunted and unshunted Nb-AlOx-Nb tunnel junctions. By employing mutual-inductance measurements and using a high-sensitive bridge, we have thoroughly investigated (both experimentally and theoretically) the temperature and magnetic field dependence of complex AC susceptibility of 2D-JJA. We also demonstrate the use of the scanning SQUID microscope for imaging the local flux distribution within our unshunt…
We discuss how to control dc Josephson current by influencing the structure and nonequilibrium population of Andreev levels via external electrostatic gates, external current injection and electromagnetic radiation. In particular we will consider the "giant" Josephson current in "long" SIS tunnel junctions and the regular and anomalous nonequilibrium Josephson currents in three terminal SNS junctions. We will briefly discuss applications to the Josephson field effect transistor (JOFET) and to the newly invented Josephson interference transistor (JOINT).
Quantum fluctuations in a current biased Josephson junction, described in terms of the RCSJ-model, are considered. The fluctuations of the voltage and phase across the junction are assumed to be initiated by equilibrium current fluctuations in the shunting resistor. This corresponds to low enough temperatures, when fluctuations of the normal current in the junction itself can be neglected. We used the quantum Langevin equation in terms of random variables related to the limit cycle of the nonlinear Josephson oscillator. This allows to go beyond the perturbation theory and calculate the widths …
The most important practical characteristic of a Josephson junction is its critical current. The shape of the junction determines the specific form of the magnetic-field dependence of the its Josephson current. Here we address the magnetic diffraction patterns of specially shaped planar Josephson tunnel junctions. We focus on a wide ensemble of generalized ellipses, called superellipses, which retain the second order symmetry. We analyze the implications of this type of isometry and derive the explicit expressions for the threshold curves of superelliptic Josephson junctions. A detailed study …
We consider theoretically and numerically magnetic field dependencies of the maximum supercurrent across Josephson tunnel junctions with spatially alternating critical current density. We find that two flux-penetration fields and one-splinter-vortex equilibrium state exist in long junctions.
The development of superconducting memory and logic based on magnetic Josephson junctions relies on an understanding of junction properties and, in particular, the dependence of critical current on external magnetic flux (i.e. Fraunhofer patterns). With the rapid development of Josephson junctions with various forms of inhomogeneous barrier magnetism, Fraunhofer patterns are increasingly complex. In this paper we model Fraunhofer patterns for magnetic Josephson junctions in which the barrier magnetic susceptibility is position- and external magnetic field dependent. The model predicts anomalou…
The physics of Josephson tunnel junctions drastically depends on their geometrical configurations. The shape of the junction determines the specific form of the magnetic-field dependence of the its Josephson current. Here we address the magnetic diffraction patterns of specially shaped planar Josephson tunnel junctions in the presence of an in-plane magnetic field of arbitrary orientations. We focus on a wide ensemble of junctions whose shape is invariant under point reflection. We analyze the implications of this type of isometry and derive the threshold curves of junctions whose shape is the…
We investigate stationary charge imbalance effect in the system of coupled overdamped Josephson junctions. We show that coupling between junction and nonzero stationary charge imbalance in the resistive state bring to a decrease of the Josephson frequency in the Josephson junctions of the stack. The formed difference in Josephson frequency leads to the nonuniform switch to the Shapiro step regime in the presence of external electromagnetic radiation and appearance of kinks of voltage on the IV-characteristics of the stack. We also show that stationary charge imbalance brings to the slope of th…
We report systematic measurements of the critical current versus magnetic field patterns of annular Josephson junctions in a wide magnetic field range. A modulation of the envelope of the pattern, which depends on the junction width, is observed. The data are compared with theory and good agreement is found.
We confirmed the existence of the collective transverse plasma modes excited by the motion of the Josephson vortex lattice in stacked intrinsic Josephson junctions of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ by observing the multiple subbranches in the Josephson-vortex-flow current-voltage characteristics. We also observed the symptom of the microwave emission from the resonance between the Josephson vortex lattice and the collective transverse plasma modes, which provides the possibility of developing Josephson-vortex-flow electromagnetic oscillators.
A novel way to realize a pi Josephson junction is proposed, based on a weak link in an unconventional d-wave superconductor with appropriately chosen boundary geometry. The critical current of such a junction is calculated from a fully selfconsistent solution of microscopic Eilenberger theory of superconductivity. The results clearly show, that a transition to a pi Josephson junction occurs for both low temperatures and small sizes of the geometry.
