Nanotechnology for next generation Josephson voltage standards

We have developed two voltage standard systems: 1) the programmable Josephson voltage standard and 2) the Josephson arbitrary waveform synthesizer. The programmable system is fully automated and provides stable programmable dc voltages from -1.2 V to +1.2 V. The synthesizer is the first quantum-based ac voltage standard source. It uses perfectly quantized Josephson pulses to generate arbitrary waveforms with low harmonic distortion and stable, calculable time-dependent voltages. Both systems are presently limited to output voltages less than 10 V as a result of frequency requirements and the limits of junction fabrication technology. We describe the development of fabrication technology for these systems and describe the circuit- and fabrication-related constraints that presently limit system performance. Finally, we propose the use of lumped arrays of junctions to achieve higher practical voltages through development of a nanoscale junction technology, in which 13 000 junctions are closely spaced at 50 nm-100 nm intervals     

Error and Transient Analysis of Stepwise-Approximated Sine Waves Generated by Programmable Josephson Voltage Standards

We are developing a quantum-based 60 Hz power standard that exploits the precision sinusoidal reference voltages synthesized by a programmable Josephson voltage standard (PJVS). PJVS systems use series arrays of Josephson junctions as a multibit digital-to-analog converter to produce accurate quantum-based dc voltages. Using stepwise-approximation synthesis, the system can also generate arbitrary ac waveforms [i.e., an ac programmable Josephson voltage standard (ACPJVS)] and, in this application, produces sine waves with calculable root mean square (rms) voltage and spectral content. The primary drawback to this ACPJVS synthesis technique is the uncertainty that results from switching between the discrete voltages due to finite rise times and transient signals. In this paper, we present measurements and simulations that elucidate some of the error sources that are intrinsic to the ACPJVS when used for rms measurements. In particular, we consider sine waves synthesized at frequencies up to the audio range, where the effect of these errors is more easily measured because the fixed transition time becomes a greater fraction of the time in each quantized voltage state. Our goal for the power standard is to reduce all error sources and uncertainty contributions from the PJVS-synthesized waveforms at 60 Hz to a few parts in 10⁷ so that the overall uncertainty in an ac power standard will be a few parts in 10⁶.     

Coupling of Josephson Radiation to Voltage Standard Arrays

We coupled the radiation emitted by arrays of Josephson junctions oscillators to detector arrays of small Josephson junctions. The number of junctions in the detector array ranges up to 1536, which is typical for a 1V standard array operation. Evidence is presented that both uniform coupling of the emitted radiation over all the small junctions arrays and coherent emission of the Josephson oscillators can be achieved. PACS numbers: 74.50. + r, 74.40. + k.     

10 V SINIS Josephson junction series arrays for programmablevoltage standards

A programmable dc voltage standard for output voltages of up to 10 V has been realized. The series arrays, consisting of about 69120 overdamped superconductor/insulator/normal metal/insulator/superconductor (SINIS) Josephson junctions, have been fabricated using the reliable Nb-Al/Al₂O₃ technology. The arrays can be operated in conventional Josephson voltage standards at microwave frequencies from 70 GHz to 75 GHz. Steps of constant voltage are observed at very low microwave power levels, since the major part of the microwave power is generated by the junctions themselves. The operation of the arrays and the formation of Shapiro steps are discussed     

Development of a 60 Hz Power Standard Using SNS Programmable Josephson Voltage Standards

We are implementing a new standard for 60 Hz power measurements based on precision sinusoidal reference voltages from two independent programmable Josephson voltage standards (PJVS): one for voltage and one for current. The National Institute of Standards and Technology PJVS systems use series arrays of Josephson junctions to produce accurate quantum-based DC voltages. Using stepwise-approximation synthesis, the PJVS systems produce sinewaves with precisely calculable RMS voltage and spectral content. We present measurements and calculations that elucidate the sources of error in the RMS voltage that are intrinsic to the digital-synthesis technique and that are due to the finite rise times and transients that occur when switching between the discrete voltages. Our goal is to reduce all error sources and uncertainty contributions from the PJVS synthesized waveforms to a few parts in 10 ⁷ so that the overall uncertainty in the AC-power standard is a few parts in 10⁶     

Operating Margins for a Pulse-Driven Josephson Arbitrary Waveform Synthesizer Using a Ternary Bit-Stream Generator

We describe measurements with a pulse-driven Josephson arbitrary waveform synthesizer (JAWS) that uses a ternary arbitrary bit-stream generator as the bias source. This system is designed to be used as an ac Josephson voltage standard. From these measurements, we conclude that the system is operational for root-mean-square voltages of up to 220 mV. We measured the operating margins for different voltages synthesized with different numbers of junctions, waveforms, and bias conditions. We also present results on the influence of the critical current on the operating margins.      

Application of Josephson series arrays to a DC quantum voltmeter

Josephson series arrays with a binary sequence of nonhysteretic superconductor-insulator-normal metal-insulator-superconductor (SINIS) junctions have been realized. The arrays of up to 8192 junctions (14 bits) are operated at microwave frequencies of about 70 GHz with low microwave power. An electronic system was built to drive an automated dc quantum voltmeter. Two electrically isolated quantum voltmeters (QVMs) in the same cryoprobe and driven by one frequency have been used for calibrating resistive dividers with the intention of demonstrating some advantages of these instruments     

Microwave-Induced Constant Voltage Steps at Series Arrays of Josephson Tunnel Junctions with Near-Zero Current Bias

Microwave-induced, constant-voltage steps in the current-voltage characteristics of Josephson tunnel junctions are used as a reference voltage in cryogenic voltage standards. This relatively low reference voltage of a few millivolts could be increased by using series arrays of tunnel junctions instead of a single junction. Series arrays consisting of 2, 6, 14, and 54 tunnel junctions were tested at a frequency of 70 GHz. The use of this relatively high frequency and of lead-alloy base electrodes allows zero crossing steps of up to 34 mV to be observed for an array with only 54 junctions when irradiated by an RF power of 32 mW. The measurements were performed at 4.2 K.     

New wave phenomena in series Josephson junctions

The use of electromagnetic waves to obtain coherence between widely spaced Josephson tunnel junctions is explored. A pair of coupled non-linear differential equations is developed for the case of junctions used as series elements in a microstrip transmission line. We use analysis to demonstrate the existence of oscillatory traveling waves, solitary waves, and standing waves on such a transmission line. We report simulations that demonstrate these waves, and an observation of standing waves in a real series array. It appears that substantial power at frequencies above 100 GHz may be obtained from these series arrays.     

AC–DC Transfer Standard Measurements and Generalized Compensation With the AC Josephson Voltage Standard

We present AC-DC transfer standard measurements using the National Institute of Standards and Technology's pulse-driven AC Josephson voltage standard source. We have investigated the frequency dependence for several output voltages up to 200 mV for frequencies from 2.5 to 100 kHz. We found that, as the frequency increases, the ac-dc differences for the two arrays on the same chip do not agree. We explored this deviation in ac-dc difference for the two arrays by investigating different configurations of the probe cabling and wiring, chip carriers, and on-chip circuit design. We found that the circuit design produced the greatest improvement, particularly at the highest frequency (100 kHz), where the deviation in ac-dc difference was reduced by more than 60%. In this paper, we also demonstrate tenfold higher output voltages and improved operating margins for arbitrary (nonsinusoidal) waveforms. These enhancements were accomplished by implementing a more general current bias to the arrays having the same harmonic content as that of the synthesized arbitrary waveform.     

Microwave-induced steps in Josephson junctions, DC-SQUIDs and parallel arrays

We have studied the characteristics of Shapiro steps in DC-SQUIDs and parallel Josephson junction arrays by means of numerical circuit simulation within the RCSJ model. Particular interest was dedicated to the occurence of fractional (subharmonic) steps, looking for possible relations to recent observations of this effect in high-T_C junctions. Besides this, some new, pecliar effects in the dependence of step height vs. RF amplitude have been found, that correspond to characteristics measured on high-T_C junctions and SQUIDs. The results can be useful for characterizing experimental Josephson junctions and circuits by studying dependencies of Shapiro steps.     

Voltage locking of dissimilar Josephson junctions in a resonant cavity

Effects of voltage locking in an array of dissimilar Josephson junctions via resonator coupling are investigated. Explicit conditions are given for N junctions connected in series to form a coherent array by using a common bias current. Problems due to losses in the connecting pads between junctions are studied.Research supported in part by the National Science Foundation.     

Intrinsic Josephson junctions in high temperature superconductors

The high temperature superconductors form natural superconducting multilayers where adjacent superconducting layers are weakly coupled by the Josephson effect. As a consequence, single crystals act intrinsically as vertical stacks of Josephson junctions. At present, intrinsic Josephson junctions are fabricated and investigated by several groups. There has been considerable progress both in production of high quality junctions and in theoretical understanding of the intrinsic Josephson effect. In this paper the basic physics of intrinsic Josephson junctions is outlined. Some examples of the present status of research are given.     

Macroscopic quantum tunneling in unshunted Josephson junctions

Macroscopic quantum tunneling (MQT) in a Josephson junction (JJ) is considered. The typical I–V curve of a JJ is used for the expressions of the tunneling and thermal activation rates of the phase of a JJ in order to help clarify the role of the dynamical resistance in MQT in Josephson junctions. The participating parameters in the expressions of the rates are experimentally independently measurable.Work at the Technion was supported by the Lidow Chair of Solid State Physics and the Oren Carmi Abraham and Laura and Irving Steinhorn Visiting Professorship.     

Superconducting and Insulating Behavior in One-Dimensional Josephson Junction Arrays

Experiments on one-dimensional small capacitance JosephsonJunction arrays are described. The arrays have a junctioncapacitance that is much larger than the stray capacitance ofthe electrodes, which we argue is important for observation ofCoulomb blockade. The Josephson energy can be tuned in situand an evolution from Josephson-like to Coulomb blockadebehavior is observed. This evolution can be described as asuperconducting to insulating, quantum phase transition. Inthe Coulomb blockade state, hysteretic current-voltagecharacteristics are described by a dynamic model which is dualto the resistively shunted junction model of classicalJosephson junctions.     

Nonlinear Josephson left-handed transmission lines

In the paper, a new nonlinear left-handed transmission line (NLHTL) that incorporates arrays of Josephson junctions (JJs) is proposed. The nonlinearity of the newly developed Josephson left-handed transmission line (JLHTL) is due to the highly nonlinear nature of the JJs that provide the shunt inductances required to realise an LHTL. The current-voltage relationship of an array of JJs is utilised to realise an inductively tunable LHTL. Dispersion analysis along with the scattering parameters of the JLHTL are presented to study the left-handed behaviour of the JLHTL. Finally, harmonic generation of the proposed JLHTL is studied     

Near-Zero Bias Arrays of Josephson Tunnel Junctions Providing Standard Voltages up to 1 V

Josephson voltage standards utilize microwave-induced constant voltage steps occurring due to the ac Josephson effect. Existing standards can be considerably simplified and their accuracy improved by using a large number of series-connected Josephson tunnel junctions which are operated in the zero current step mode. For this purpose superconducting millimeter wave integrated circuits have been designed, fabricated, and tested. The circuits consist of a broadband taper between the rectangular waveguide and the planar structure, the Josephson junction series, a well-matched load, and dc pads. Circuits with various numbers of junctions have been fabricated by photo-lithographic techniques and tested at 4.2 K in liquid helium. The version with 1474 junctions produced voltages up to 1.2 V when operated at 90 GHz.     

Josephson steps produced by critical current amplitude modulation

We discuss the possibility of inducing current steps in theI–V characteristic of Josephson junctions by a periodic modulation of their critical current amplitude. The particular characteristics of such amplitude modulation steps (as opposed to the usual phase modulation steps), as well as the experimental conditions appropriate to their observation, are outlined.     

Flux flow and resonant modes in multi-junction Josephson stacks

Magnetic field dependent current-voltage characteristics of stackled Nb/(Al−AlO_x/Nb)_n long Josephson junctions are investigated experimentally. The thickness of their common superconducting electrodes provides the magnetic coupling between the junctions. For stacks of n=7 Josephson junctions the current-voltage characteristics display collective flux-flow behaviour of Josephson vortices. In the interior layers Josephson vortices move simultaneously under the influence of the bias current. The flux-flow behaviour is modulated by a complicated structure of cavity-like resonances which show broad range of characteristic frequencies. The measurements can be qualitatively explained by the Kleiner model for the resonances in stacks. Mutual locking of junctions in the stack is indicated by pronounced cavity resonances with large voltage spacing.     

Kinetic Inductance and Coulomb Blockade in One Dimensional Josephson Junction Arrays

One dimensional Josephson junction arrays have been fabricated andcurrent-voltage characteristics (IVC) have been measured at cryogenic temperatures. The arrays were fabricated in a SQUID-geometry which allowed an in situ tuning of the Josephson energy by application of a magnetic field. The IVC of the arrays shows a clear Coulomb blockade state. In the Coulomb blockade regime the IVC are hysteretic. The array is modeled using a serial resistive-inductive-junction model which is able to qualitatively explain the IVC. In this model an inductance of the order of 0.1–10 mH per junction is needed to account for the hysteresis. Kinetic inductance, stemming from the inertia of the Cooper pairs, gives the correct order of magnitude. The problem of self-heating is also discussed as an alternative explanation of the hysteresis.