Underdamped Josephson Junctions Research Articles

Simulation of sub-kBT bit-energy operation of adiabatic quantum-flux-parametron logic with low bit-error-rate

Adiabatic quantum-flux-parametron (AQFP) logic can achieve high energy-efficiency. The bit energy and bit-error-rate (BER) of AQFP gates with under-damped Josephson junctions were simulated. The results indicate that the bit energy reaches 12 yJ, which is only 20% of the thermal energy at 4.2 K, using unshunted 50-μA junctions and excitation currents with a rise/fall time of 2000 ps. Although the bit energy is extremely small, the bias margin, where the BER is less than 10−23, is approximately ±22%. These results indicate there is no minimum energy limitation for the operation of AQFP gates unless the entropy of the system decreases.

A two-step transition description of underdamped phase diffusion

A two-step transition model describing phase diffusion and switching process in underdamped Josephson junctions is discussed. The model takes into account the phase particle's escape rate out of the potential well and transition rate from phase diffusion to the running state. Using as examples the experimental switching current distributions of two Nb/AlOx/Nb junctions of different sizes fabricated on the same chip, we extract the transition rate, which turns out to follow the predicted Arrhenius law in the thermal regime but is greatly enhanced when macroscopic quantum tunneling becomes the dominant escape mechanism. Our results show the validity of applying the model to obtain the transition rate out of the phase diffusion state into the running state from measured switching current distribution of underdamped Josephson junctions. The temperature and bias-current dependent data provide strong evidence for phase diffusion in both thermal and quantum regimes.

Drastic Suppression of Noise-Induced Errors in Underdamped Long Josephson Junctions

The fluctuational propagation of solitons (magnetic fluxons) in long Josephson junctions is studied both numerically and analytically. It is demonstrated that operation in conditions where solitons are subjected to Lorentz contraction for a significant part of the junctions length leads to drastic suppression of thermal jitter at the output junction end. Specifically, for large-to-critical damping and small values of bias current, the physically obvious dependence of the jitter versus length σ~√L is confirmed, while for small damping starting from the experimentally relevant α=0.1 and below, strong deviation from σ~√L is observed, up to nearly complete independence of the jitter versus length, which is supported by the obtained theory.

Investigation of Current Noise in Underdamped Josephson Devices by Switching Current Measurements

Experimental measurements on critical current noise in underdamped niobium based Josephson devices by a technique based on the switching current measurements is reported. By sweeping the junction with a current ramp we measure the critical current switching as a function of the time using the standard time of flight technique. In such a way it is possible to obtain the critical current fluctuations ΔIc=Ic(t)-<Ic(t)> and the relative standard deviations which corresponds to the root square of the current fluctuation power. Pointing at the white noise fluctuations (above few Hz) and taking into account the physical frequency of the device, it is possible to evaluate the power spectral density of the critical current. The analysis has involved high quality underdamped Josephson junctions having an area ranging from (4x4) μm 2 to (40x40) μm 2 in the temperature range from 4.2 K to few tenth of mK. These measurement provide very useful information about the intrinsic noise of Josephson devices involving SQUIDs and qubits.

Design and Evaluation of Multi-Flux-Quantum Drivers Using Under-Damped Josephson Junctions

The lack of driving ability is one weakness of single-flux-quantum (SFQ) devices. At present, pulse splitters, which generate double or triple flux quanta from an SFQ input, are used when multiple-flux quanta (MFQ) must be obtained from an SFQ input. However, the splitter-based MFQ driver requires a very large circuit area and high latency. In order to overcome these problems, we investigated an MFQ driver using under-damped Josephson junctions. The advantage of the proposed MFQ driver is its current driving ability. The proposed MFQ driver can be used as a bit-line driver in an SFQ memory or as an output driver in a current-recycling system, which requires a large gain. The proposed MFQ driver was implemented using the ISTEC 2.5 kA/cm2 Nb standard process (STP2), and its driving ability was investigated. We obtained a histogram of the output pulse number of the MFQ driver as a function of the bias current. In addition, we examined the propagation delay of the MFQ driver through circuit simulations. The results indicate that the MFQ driver can generate MFQ from an SFQ input more rapidly than splitter-based MFQ drivers.

Colored Noise Induced Net Voltage of the Underdamped Josephson Junction

The underdamped Josephson junction subjected to correlated colored noises was investigated. The results indicated that: (i) There are two critical phenomena in the system; (ii) Net voltage of the system is induced by multiplicative noise, and exhibits non-monotonic behaviors with noise autocorrelation rate and the Josephson junction capacitance.

Parametric resonance in small Josephson junctions in the presence of oscillating magnetic fields

Comparing the stationary states of a mechanical pendulum and of a small under-damped Josephson junction, parametric resonance in the latter system due to an oscillating magnetic field is studied by means of a Gedanken-experiment. A second conceptual experiment shows that for rapidly oscillating magnetic fields the superconducting phase difference ϕ across the junction in the absence of bias current can attain values of ±π in the vicinity of the lower lying stationary state at ϕ=0.

Design of Relaxation Oscillator Based Ultra-wideband SFQ Amplifier for Chip to Chip Interconnection

In Rapid Signal Flux Quantum (RSFQ) logic circuits, on-chip interconnects and multichip module implementations for nearby distances have already been established. However, the flexible interconnection of two distant chips is still not achieved reliably due to impedance mismatching and attenuation. In this work, we propose a circuit that allows the usage of Passive Transmission Lines (PTLs) to transfer single-flux-quantum (SFQ) pulses between two distant chips which are separated by a distance greater than 10 cm by using 50 Ω transmission lines. For this purpose, we design an SFQ amplifier circuit to deal with impedance mismatch and attenuation problems. The circuit consists of two main parts: a relaxation oscillator (RO) circuit and an impedance transformer. The RO circuit utilizes relaxation oscillations occur in the underdamped Josephson junctions. The impedance matching circuit is an 8-section Chebyshev quarter-wave transformer and it eliminates impedance mismatching problem between the amplifier circuit and PTL. We performed circuit simulations and obtained voltage amplitude of about 600 μV at the output of the circuit. The transformer has a broadband impedance matching with a fractional bandwidth (ratio of the bandwidth of a device to its central frequency) of 1.4 and a maximum Voltage Standing Wave Ratio (VSWR, the maximum voltage divided by minimum voltage on the transmission line) of 1.5.

Nonequilibrium effects in the thermal switching of underdamped Josephson junctions

We study the thermal escape problem in the low damping limit. We find that finiteness of the barrier is crucial for explaining the thermal activation results. In this regime, low barrier nonequilibrium corrections to the usual theories become necessary. We propose a simple theoretical extension accounting for these nonequilibrium processes which agrees numerical results. We apply our theory to the understanding of switching current curves in underdamped Josephson junctions.

All magnesium diboride Josephson junctions with MgO and native oxide barriers

We present results on all-MgB2 tunnel junctions, where the tunnel barrier is deposited MgO or native-oxide of base electrode. For the junctions with MgO, the hysteretic I-V curve resembles a conventional underdamped Josephson junction characteristic with critical current-resistance product nearly independent of the junction area. The dependence of the critical current with temperature up to 20 K agrees with the [Ambegaokar and Baratoff, Phys. Rev. Lett. 10, 486 (1963)] expression. For the junctions with native-oxide, conductance at low bias exhibits subgap features while at high bias reveals thick barriers. As a result no supercurrent was observed in the latter, despite the presence of superconducting-gaps to over 30 K.

Ratchet potential in superconducting quantum interference devices containing adouble-barrier junction

The periodic effective potential of a superconducting quantum interference devicecontaining an underdamped Josephson junction in the first branch and a double-barrierjunction in the second is studied. An effective non-sinusoidal expression for thecurrent–phase relation with an additional half harmonic term is used for the double-barrierjunction. The system allows voltage rectification under opportunely chosen parametervalues.

Switching dynamics and MQT in Bi2201 intrinsic Josephson junctions

We investigate the switching dynamics of Bi 2Sr 1.6La 0.4CuO 6+ δ (Bi2201) intrinsic Josephson junctions (IJJs) to clarify the effect of the strong coupling between junctions in the stack. We find that the number of junctions switching simultaneously to the finite voltage states can be tuned by changing the load resistance connected in series with IJJs. The width of the switching current distribution (SCD) becomes constant below 0.4 K indicating the crossover of switching mechanism from the thermal activation to the macroscopic quantum tunneling. The quality factors obtained based on the analysis of the SCD are in the range from 70 to 100, which implies that Bi2201 IJJs work as underdamped Josephson junctions similar to Bi 2Sr 2CaCu 2O 8+ δ IJJs.

COHERENCE RESONANCE OF A JOSEPHSON JUNCTION EQUATION IN A BISTABLE REGION

In this paper, the effect of noise in an underdamped Josephson junction equation without a periodic driving is numerically investigated. Two distinct phenomena of coherence resonance are observed by adjusting the damping coefficient and the sloping degree of the tilted periodic potential.

Phase Dynamics of Ferromagnetic Josephson Junctions

We have investigated the classical phase dynamics of underdamped ferromagnetic Josephson junctions by measuring the switching probability in both the stationary and nonstationary regimes down to 350 mK. We found the escape temperature to be the bath temperature, with no evidence of additional spin noise. In the nonstationary regime, we have performed a pump-probe experiment on the Josephson phase by increasing the frequency of the junction current bias. We show that an incomplete energy relaxation leads to dynamical phase bifurcation. Bifurcation manifests itself as premature switching, resulting in a bimodal switching distribution. We directly measure the phase relaxation time tau_{phi} by following the evolution of the bimodal switching distribution when varying the bias frequency. Numerical simulations account for the experimental values of tau_{phi}.

Premature switching in graphene Josephson transistors

We investigate electronic transport in single layer graphene coupled to superconducting electrodes. In these Josephson transistors, we observe significant suppression in the critical current I c and large variations in the product I c R n in comparison to theoretical predictions in the ballistic limit. We show that the depression of I c can be explained by premature switching in underdamped Josephson junctions described within the resistively and capacitively shunted junction (RCSJ) model. By considering the effect of premature switching and dissipation, the calculated gate dependence of product I c R n agrees with experimental data. Our discovery underscores the crucial role of thermal fluctuations in electronic transport in graphene Josephson transistors.

The underdamped Josephson junction subjected to colored noises

The properties of the underdamped Josephson junction subjected to colored noises were investigated with large and small phase difference (φ). For the case of the large φ, we found numerically that: (i) the probability distribution function of φ exhibits monostability → bistability → monostability transitions as the autocorrelation rate (λ) of a colored noise increases; (ii) in the bistability region the multiplicative noise drives the phase difference to turn over periodically; (iii) the slope K of the linear response of the junction potential difference (〈V 〉) can be somewhat reduced by means of tuning an optimal λ; (iv) the amplitude of φ in response to external sinusoidal signals changes with λ. For the case of small φ, after deriving the analytical expressions of the potential difference amplitude (〈V 〉max) and the K in the presence of a dichotomous noise, we found nonmonotonic behavior of 〈V 〉max and the slope K as a function of λ.

MQT observation in Bi2212 intrinsic Josephson junctions

The quantum dynamics of Bi 2Sr 2CaCu 2O 8+ δ intrinsic Josephson junctions (IJJ’s) is studied based on the escape rate measurements. The saturations observed in the escape temperature and the width of the switching current below 0.45 K (= T ∗) indicate the transition of the switching mechanism from the thermal activation to the macroscopic quantum tunneling at T ∗. It is shown that most of the switching properties are consistently explained in terms of the underdamped Josephson junction with quality factor of about 70 in spite of possible damping due to d-wave superconductivity. The present result gives the upper limit of the dissipation of IJJ’s.

Experimental study of macroscopic quantum tunnelling in Bi2212 intrinsic Josephsonjunctions

The quantum dynamics of Bi2Sr2CaCu2O8+δ intrinsic Josephson junctions (IJJs) is studied based on escape rate measurements. The saturationsobserved in the escape temperature and in the width of the switching current below 0.5 K(= T*) indicate the transition of the switching mechanism from thermal activation to macroscopicquantum tunnelling. It is shown that the switching properties are consistentlyexplained in terms of the underdamped Josephson junction with a quality factor of70 ± 20 in spite of possible damping due to the nodal quasiparticles of d-wave superconductivity.The present result gives the upper limit of the damping of IJJs.

Dynamics of underdamped Josephson junctions with nonsinusoidal current-phase relation

Results on analytical and computational investigations of high frequency dynamics of Josephson junctions, characterized by nonzero capacitance and the second harmonic in the current-phase relation are presented. These attributes each influence on behaviour of integer Shapiro steps and lead to formation of non-integer Shapiro steps. Analytic theory of the integer and non-integer Shapiro steps has been developed for so-called high frequency limit. The analytical and numerical results are compared with experimental data for hybrid heterostructures YBCO/Au/Nb. Detector response for the case of high fluctuation level has been considered as well.

Dynamics of underdamped Josephson junctions with non-sinusoidal current-phase relation

Results on analytical and computational investigations of high-frequency dynamics of Josephson junctions, characterized by non-zero capacitance and the second harmonic in the current-phase relation are presented. These attributes each have influence on the behaviour of integer Shapiro steps and lead to the formation of non-integer Shapiro steps. Analytic theory of the integer and non-integer Shapiro steps has been developed for the so-called high-frequency limit. The analytical and numerical results are compared with experimental data for hybrid heterostructures YBCO/Au/Nb. Detector response for the case of high fluctuation level has been considered as well.