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The comprehensive analysis of low-frequency excess flux noise both in terms of magnetic flux noise SΦ,1/f and energy sensitivity ϵ1∕f of 84 superconducting quantum devices studied at temperatures below 1 K reveals a universal behavior. When analyzing data in terms of ϵ1∕f, we find that noise spectra of independent devices cross each other all at certain crossing frequencies fc. Besides this main result of our paper, we further show that superconducting quantum interference device (SQUID) arrays systematically feature higher noise exponents than single SQUIDs and give evidence for a material and device type dependence of low-frequency excess flux noise. The latter results facilitate to engineer the shape of magnetic flux noise spectra and thus to experimentally modify key properties such as coherence or measurement times of superconducting quantum devices.

We demonstrate the operation of a single-flux-quantum (SFQ) pump that is electromagnetically dual to the single-electron pump. The circuit is composed of a three-junction superconducting quantum interference device with three control lines. By applying two phase-shifted rf signals magnetically, the SFQ-pump transfers one SFQ per one cycle of the rf signals even at zero- and negatively-biased condition. The circuit was fabricated using a Nb/AlOx/Nb Josephson junction technology. When we fed rf signals of 4.5 GHz, we observed a Shapiro step crossing the zero-current axis. Periodic dependence of voltage at the zero-biasing state upon dc offset flux was also confirmed.

Calculations of the shape and the timing of single-magnetic-flux quanta (SFQs) generated by high-current-density “self-shunted” Josephson junctions are presented. The junction current is assumed to be due in part to multiple Andreev reflections within the high-transparency barrier. The SFQ pulses from these junctions show several differences when compared to those from lower-current-density resistively shunted Josephson junctions, the most important being that the pulses are significantly delayed in the self-shunted junctions, by as much as many times the pulse width.

The thermally induced bit error rate of a rapid single flux quantum logic circuit is theoretically examined using the Fokker–Planck equation. The error rate versus design parameters of a high Tc dc/single flux quantum converter is derived. In comparison with other design methodologies, a vanishingly small error rate at optimal parameters can be achieved.

An on-chip, low-jitter clock technology is essential for future multi-GHz digital electronics. In this article, we describe an on-chip clock technology for superconducting rapid single flux quantum (RSFQ) circuits built around an unshunted long Josephson junction (LJJ) oscillator that acts as a master clock source. The clock technology also includes clock frequency divider and selector circuits as well as a clock distribution network. These LJJ oscillators, implemented in linear and annular geometries using 3 μm Nb technology, have quality factors of 106. This clock technology potentially has widespread use in 10–100 GHz superconducting digital circuits and systems, including analog-to-digital converters, time-to-digital converters, correlators, and processors for ultrahigh performance computers.

A superconductor frequency divider based on rapid single flux quantum (RSFQ) logic has been demonstrated to operate from dc to 750 GHz with an error rate less than the measurement limit (25 MHz). This high operating frequency is made possible by the use of small (0.25 μm2), high critical current density Josephson junctions along with an optimized design having parameter margins of ±30%. Simulations based on the Werthamer model are in reasonable agreement with the data and give a SFQ pulse width of 1 ps and a maximum power dissipation of 1.5 μW.

The application of high temperature superconductor (HTS) Josephson junctions in digital rapid single flux quantum circuits requires a careful study of the influence of thermal noise on the bit error rate (BER). We have determined experimentally, for the first time, the BER of a HTS rapid single flux quantum circuit. A comparator, formed by two Josephson junctions, was integrated in a Josephson transmission line ring oscillator, allowing us to perform high speed testing of the comparator at GHz frequencies. For fabrication, focused-electron-beam-irradiated junctions have been used because of their small parameter spread and excellent alignment possibilities. A BER of less than 10−11 was obtained at 39 K.

We measured the static error rate of a high-Tc superconductor dc superconducting quantum interference device (SQUID), which, in the form as a storage loop for single flux quanta, is a basic element of rapid single flux quantum circuits. Using high-Tc multilayer bicrystal technology, we fabricated a stacked dc SQUID pair, one SQUID serving as the storage loop, the other one as the readout device. The escape rate of a stored flux quantum was measured as a function of the bias current at a temperature of 28 K. The measured error rates were in good agreement with a model calculation based on thermally activated barrier crossing.

A clock recovery circuit has been successfully tested at frequencies up to 20 GHz. This cell is designed for a rapid-single-flux-quantum (RSFQ) telecommunication data switch. It serves to set the receiver clock in phase with the incoming digital signal. The circuit consists of a dc-to-SFQ converter, ring oscillator [(RO) is a closed-loop RSFQ Josephson transmission line], confluence buffer, and an 8-bit binary counter. The input signal transforms to SFQ pulses, and each pulse resets the phase of the ring oscillator, giving a locking time of 1 bit. Thus, the pull-in (capture) range and hold-in (tracking) range are the same, and strictly depend on the encoding of the input signal. This range is estimated to be about 1 GHz at frequency 20 GHz, if the sequence of consecutive ONEs or ZEROs does not exceed 20 bits. The quality factor QRO of ring oscillator is about 2000, which gives a jitter of 50 fs for a 35-junction RO. A sampling technique was used to demonstrate phase recovery (phase locking) with only one incoming pulse per 512 clock periods.

A 3 bit single flux quantum (SFQ) shift register based on high-Tc bicrystal Josephson junctions has been designed, fabricated, and experimentally tested. The circuit consists of 26 bicrystal Josephson junctions and includes the shift register itself, two dc-SFQ converters, one readout superconducting quantum interference device, serving as a SFQ-dc converter, and three Josephson transmission lines. The correct operation of all circuit components has been demonstrated by low frequency testing at a temperature of 50 K.

A balanced current comparator based on high‐Tc bicrystal Josephson junctions has been designed, fabricated, and experimentally tested. The operation of the balanced comparator has been demonstrated in the temperature range from 4.2 to 70 K. The correct sequence of switching of the Josephson junctions has been determined by dc measurements for different values of operating frequency and signal current Ix. The threshold uncertainty ΔIx of the balanced comparator, measured at 40 K, was 60 μA at 40 GHz and 300 μA at 240 GHz.

We have implemented a simple circuit of the rapid single‐flux‐quantum (RSFQ) logic family using a single‐layer YBa2Cu3O7−x thin‐film structure with 14 in‐plane Josephson junctions formed by direct electron beam writing. The circuit includes two dc/SFQ converters, two Josephson transmission lines, a complete RS SFQ flip‐flop, and an SFQ/dc converter (readout SQUID). Low‐frequency testing has shown that the dc‐current‐biased circuit operates correctly and reliably at T∼30 K, a few degrees below the effective critical temperature of the junctions. Prospects for a further increase of the operation temperature and implementation of more complex RSFQ circuits are discussed in brief.

Experiments on a model of rapid single flux quantum (RSFQ) flip‐flop cell, based on high‐Tc (HTS) Josephson junctions show that it can operate as a voltage divider at frequency up to 400 GHz. The junctions were formed in YBaCuO film, deposited on novel Y–ZrO2 bicrystals with two asymmetric 32° grain boundaries, about 10 μm apart, and allow a new design of RSFQ logic based on a single HTS layer. Small inductances (≂10 pH) were made as narrow, submicron size slits. The junction widths were between 4 and 10 μm and for ten junctions located close to the tested circuits, the linear critical current densities at T=4.4 K were 10.7 μA/μm±50% for one grain boundary and 8.3 μA/μm±50% for the other one. IcRn was about 1 mV±50%. A current density of half the expected value meant that the test circuit did not act as an ideal flip–flop down to the lowest frequency. As a voltage divider it gave a half value division up to 0.82 mV at T=4.4 K and to 0.4 mV at 30 K.

We suggest a new design of rapid single flux quantum (RSFQ) logic circuits which is based on a single superconducting layer and does not require a superconducting ground plane. Small inductances of about 10 pH, obligatory for RSFQ circuits, are formed as narrow slits of widths comparable to the London penetration depth (≂0.15 μm). The design allows us to decrease the geometric size of the RSFQ cell. Test circuits with YBaCuO grain boundary junctions on asymmetric 32° Y– ZrO2 bicrystals were used to measure the slit inductance per unit length and the mutual inductance of neighboring slits. A typical inductance of a 0.4 μm slit was found to be 0.7–0.8 pH/μm.

We report on the direct observation of a single‐flux‐quantum (SFQ) pulse. The response of a metal–semiconductor–metal photodiode to a femtosecond laser pulse was used to switch Josephson junctions and to generate an SFQ voltage pulse on a superconducting microstrip line. The detailed shape of the pulse was measured optoelectronically, using a cryogenic electro‐optic sampling system. The measured SFQ pulse had a width of 3.2 ps, an amplitude of 0.67 mV, and a total pulse content of 2.1±0.2 mV×ps, corresponding to the quantum of magnetic flux h/2e. With larger excitation, multiple SFQ pulses were observed. Numerical simulations are shown to be qualitatively similar to our experimental results.

We have simulated fluxon propagation within a Josephson transmission line that is one of the elements of a rapid single flux quantum (RSFQ) circuit. This line is a parallel connection of damped Josephson junctions coupled by superconducting inductances. Geometries with and without mutual inductances between neighboring cells are considered. If the time interval between two fluxons is less than 0.3 φ0Vc−1 (Vc characteristic voltage) a repulsion between them was observed. The repulsion sets a specific time delay between the fluxons that impose a rigid limitation for high frequency performance of RSFQ logic. The delay depends on the shunting parameter, bias current, and values of interconnecting inductances.

A simple test circuit of the rapid single‐flux‐quantum (RSFQ) logic family has been implemented in a planarized all‐refractory technology using only two superconducting layers and small Nb/AlOx/Nb Josephson junctions (nominally 1.5×1.5 μm2) with critical current density jc≊6 kA/cm2. A special layout design of the integrated circuit (including a SFQ pulse generator, Josephson transmission line, and T flip–flop) was used to reduce 3D inductances resulting from absence of the ground plane. For samples with various junction parameters, the maximum frequency of the SFQ pulse train, which could be divided by 2 by the flip–flop, ranged from 200 to 370 GHz.

The 0–π transition in Superconductor-Insulator-superconductor-Ferromagnet-Superconductor (SIsFS) Josephson junctions (JJs) was investigated experimentally. As predicted by theory, an s-layer inserted into a ferromagnetic SIFS junction can enhance the critical current density up to the value of an SIS tunnel junction. We fabricated Nb′ | AlOx | Nb | Ni60Cu40 | Nb JJs with wedge-like s (Nb) and F (Ni60Cu40) layers and studied the Josephson effect as a function of the s- and F-layer thickness, ds and dF, respectively. For ds = 11 nm, π-JJs with SIFS-type jc(dF) and critical current densities up to jcπ=60 A/cm2 were obtained at 4.2 K. Thicker ds led to a drastic increase of the critical current decay length, accompanied by the unexpected disappearance of the 0–π transition dip in the jc(dF) dependence. Our results are relevant for superconducting memories, rapid single flux quantum logic circuits, and solid state qubits.

We consider a ballistic detector formed in an interferometer manner which operational principle relies on Josephson vortex scattering at a measurement potential. We propose an approach to symmetrize the detector scheme and explore arising advantages in the signal-to-noise ratio and in the back-action on a measured object by means of recently presented numerical and analytical methods for modeling of a soliton scattering dynamics in the presence of thermal fluctuations. The obtained characteristics for experimentally relevant parameters reveal practical applicability of the considered schemes including possibility of coupling with standard digital rapid single flux quantum circuits.

Using self-shunted MgB2/MgO/MgB2 Josephson junctions, we have designed, fabricated, and tested a rapid single flux quantum toggle flip flop (TFF) circuit. The junctions used MgB2 films grown by hybrid physical-chemical vapor deposition with MgO barrier layer and insulating layer deposited by RF magnetron sputtering. The result showed the frequency-division function of the TFF circuit, evidenced by the output voltage being half the input voltage, up to 63 GHz at 20 K and 180 GHz at 3.2 K, which demonstrates the potential of high operating speeds and high working temperatures in MgB2 superconducting integrated circuits.

We study the possibility to use frequency dependent damping in RSFQ circuits as means to reduce dissipation and consequent decoherence in RSFQ/qubit circuits. We show that stable RSFQ operation can be achieved by shunting the Josephson junctions with an $RC$ circuit instead of a plain resistor. We derive criteria for the stability of such an arrangement, and discuss the effect on decoherence and the optimisation issues. We also design a simple flux generator aimed at manipulating flux qubits.

We present the analysis of the mean switching time and its standard deviation of an overdamped Josephson junction, driven by a direct current and a single flux quantum (SFQ) pulse. The performed analysis allows us to find the optimal value of the bias current of the clock generator, responsible for the shape of SFQ pulse, which minimizes noise-induced switching errors.

We demonstrate that shunting of Superconductor-Insulator-Superconductor Josephson junctions by Superconductor-Insulator-Normal metal (S-I-N) structures having pronounced non-linear I-V characteristics can remarkably modify the Josephson dynamics. In the regime of Josephson generation the phase behaves as an overdamped coordinate, while in the superconducting state the damping and current noise are strikingly small, that is vitally important for application of such junctions for readout and control of Josephson qubits. Superconducting Nb/AlO${_x}$/Nb junction shunted by Nb/AlO${_x}$/AuPd junction of S-I-N type was fabricated and, in agreement with our model, exhibited non-hysteretic I-V characteristics at temperatures down to at least 1.4 K.

We have made what we believe is the first experimental observation of the switching transients resulting from single flux quantum transitions in superconducting devices. For that purpose, we used ``long'' Josephson junctions or interferometers which exhibit overlapping vortex modes. By applying a magnetic field to such devices, vortex‐mode transitions are induced. The resulting transients are detected by a small Josephson junction located nearby. The experimental results show unambiguously that the points where a signal is detected by the sense junction correspond to the vortex‐mode boundaries of the device. These results have important implications for memory applications.

Operation of a DRO single flux quantum Josephson junction memory cell is described. Writing and sensing is performed with coincident currents. The device acts as its own sense detector, switching to the gap voltage if a flux quantum was stored. Dense arrays not requiring standby power are potentially feasible.

A quantum interference Josephson junction logic device is disclosed which comprises three or more junctions connected in parallel which are capable of carrying Josephson current and includes means integral with at least one of the junctions for carrying a larger maximum Josephson current than the remaining junctions. This integral means includes means for carrying a maximum Josephson current which is twice as large as the maximum Josephson current in the remaining junctions. While the spacing between the lobes of the threshold curve (Im vs. Ic) is increased over that of a two junction interferometer by adding another junction resulting in an increased operating region in which logic circuits switch to the voltage state, good current gains with large lobe separation could not be achieved by the mere addition of junctions. Current gain with large lobe separation is obtained if the two outer junctions having a zero field threshold current, Io, are connected via an inductance, L, to the center junction with a maximum Josephson current, 2Io. The gain is maximized if the gate current, Ig, is fed into the device through inductances, Lp, having a value of inductance approximately equal to 3L in the center of inductances L which are disposed between pairs of junctions forming a symmetrical dual feed. Increased gain and operating range can be achieved using the symmetrical dual feed and interferometer arrangements where the maximum Josephson current in all the junctions thereof is the same.