This review provides a theoretical basis for understanding the current-phase relation (CPhiR) for the stationary (dc) Josephson effect in various types of superconducting junctions The authors summarize recent theoretical developments with an emphasis on the fundamental physical mechanisms of the deviations of the CPhiR from the standard sinusoidal form A new experimental tool for measuring the CPhiR is described and its practical applications are discussed The method allows one to measure the electrical currents in Josephson junctions with a small coupling energy as compared to the thermal energy A number of examples illustrate the importance of the CPhiR measurements for both fundamental physics and applications

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The current-phase relation in Josephson junctions

Compact solid-state sources of terahertz (THz) radiation are being sought for sensing, imaging, and spectroscopy applications across the physical and biological sciences. We demonstrate that coherent continuous-wave THz radiation of sizable power can be extracted from intrinsic Josephson junctions in the layered high-temperature superconductor Bi2Sr2CaCu2O8. In analogy to a laser cavity, the excitation of an electromagnetic cavity resonance inside the sample generates a macroscopic coherent state in which a large number of junctions are synchronized to oscillate in phase. The emission power is found to increase as the square of the number of junctions reaching values of 0.5 microwatt at frequencies up to 0.85 THz, and persists up to ∼50 kelvin. These results should stimulate the development of superconducting compact sources of THz radiation.

http://absimage.aps.org/image/MAR08/MWS_MAR08-2007-004672.pdf

Emission of Coherent THz-Radiation from Superconductors.

The control electrons at the level of the elementary charge e was demonstrated experimentally already in the 1980s. Ever since, the production of an electrical current ef, or its integer multiple, at a drive frequency f has been in a focus of research for metrological purposes.This review discusses the generic physical phenomena and technical constraints that influence single-electron charge transport and presents a broad variety of proposed realizations. Some of them have already proven experimentally to nearly fulfill the demanding needs, in terms of transfer errors and transfer rate, of quantum metrology of electrical quantities, whereas some others are currently ‘‘just’’ wild ideas, still often potentially competitive if technical constraints can be lifted. The important issues of readout of singleelectron events and potential error correction schemes based on them are also discussed. Finally, an account is given of the status of single-electron current sources in the bigger framework of electric quantum standards and of the future international SI system of units, and applications and uses of single-electron devices outside the metrological context are briefly discussed.

/pdf/single-electron-current-sources-toward-a-refined-definition-5atnvohwg2.pdf

Single-electron current sources: Toward a refined definition of the ampere

Solitons in Josephson junctions

The measurement of the Planck constant, h, is entering a new phase. The CODATA 2010 recommended value is 6.626 069 57 × 10(-34) J s, but it has been a long road, and the trip is not over yet. Since its discovery as a fundamental physical constant to explain various effects in quantum theory, h has become especially important in defining standards for electrical measurements and soon, for mass determination. Measuring h in the International System of Units (SI) started as experimental attempts merely to prove its existence. Many decades passed while newer experiments measured physical effects that were the influence of h combined with other physical constants: elementary charge, e, and the Avogadro constant, N(A). As experimental techniques improved, the precision of the value of h expanded. When the Josephson and quantum Hall theories led to new electronic devices, and a hundred year old experiment, the absolute ampere, was altered into a watt balance, h not only became vital in definitions for the volt and ohm units, but suddenly it could be measured directly and even more accurately. Finally, as measurement uncertainties now approach a few parts in 10(8) from the watt balance experiments and Avogadro determinations, its importance has been linked to a proposed redefinition of a kilogram unit of mass. The path to higher accuracy in measuring the value of h was not always an example of continuous progress. Since new measurements periodically led to changes in its accepted value and the corresponding SI units, it is helpful to see why there were bumps in the road and where the different branch lines of research joined in the effort. Recalling the bumps along this road will hopefully avoid their repetition in the upcoming SI redefinition debates. This paper begins with a brief history of the methods to measure a combination of fundamental constants, thus indirectly obtaining the Planck constant. The historical path is followed in the section describing how the improved techniques and discoveries in quantum mechanics steadily reduced the uncertainty of h. The central part of this review describes the technical details of the watt balance technique, which is a combination of the mechanical and electronic measurements that now determine h as a direct result, i.e. not requiring measured values of additional fundamental constants. The first technical section describes the basics and some of the common details of many watt balance designs. Next is a review of the ongoing advances at the (currently) seven national metrology institutions where these experiments are pursued. A final summary of the recent h determinations of the last two decades shows how history keeps repeating itself; there is again a question of whether there is a shift in the newest results, albeit at uncertainties that are many orders of magnitude less than the original experiments. The conclusion is that there is room for further development to resolve these differences and find new ideas for a watt balance system with a more universal application. Since the next generation of watt balance experiments are expected to become kilogram realization standards, the historical record suggests that there is yet a need for proof that Planck constant results are finally reproducible at an acceptable uncertainty.

https://iopscience.iop.org/article/10.1088/0034-4885/76/1/016101/pdf

History and progress on accurate measurements of the Planck constant

We present a study of the microwave characteristics of Josephson junctions based on a superconductor–insulator–normal–insulator–superconductor sandwich, fabricated in Nb/Al/AlOx technology. With the nonhysteretic Shapiro steps and the small parameter spread observed, the junctions are suitable for programmable Josephson voltage standards. Their characteristic voltage Vc≈100 μV enables operation at microwave frequencies up to 100 GHz.

Nb/al/alox/alox/al/nb josephson junctions for programmable voltage standards

The discovery of the Josephson effects 50 years ago initiated a revolution for electrical voltage metrology. This revolution started with single Josephson junctions delivering a few millivolt at most. Meanwhile, highly integrated series arrays containing more than 10 000 or even 300 000 junctions have been developed and fabricated for output voltages up to 10 V. Josephson voltage standards are nowadays used in many laboratories worldwide for dc applications. After their adoption for the representation of the unit of voltage in 1990, the focus of research shifted towards programmable Josephson series arrays. The increasing interest in highly precise ac voltages resulted in new developments for their metrological applications in the last 15 years. This paper summarizes the principal contributions from PTB to the present state of Josephson voltage standards with particular focus on developments and applications for ac standards in metrology and our proof-of-concept demonstrations. The presentation includes the two most promising versions of ac standards, being the programmable Josephson voltage standard based on binary divided series arrays and the Josephson arbitrary waveform synthesizer based on a pulse-driven series array.

https://iopscience.iop.org/article/10.1088/0957-0233/23/12/124002/pdf

Development and metrological applications of Josephson arrays at PTB

The fabrication and the chip layout of 69120 SINIS Josephson junction series arrays for a programmable 10 V Josephson dc voltage standard are presented Under 70 GHz microwave irradiation, the current-voltage characteristic exhibits a non-hysteretic voltage step with a step width of 200 µA The chip can be operated with the conventional SIS Josephson voltage standard systems

Design and fabrication of 10 V SINIS Josephson arrays for programmable voltage standards

A new method of driving series arrays of non-hysteretic Josephson junctions using optoelectronically generated pulses to synthesize a variable output voltage is described. Electrical pulses from a photodiode are coupled to the array, and the mean output voltage after filtering is proportional to the pulse repetition frequency with fundamental accuracy. Numerical simulations of the behaviour of the Josephson junctions have been carried out, and these results have been verified by experiment. This technique can be easily extended by using two photodiodes with opposite bias polarities in order to synthesize bipolar alternating or direct voltages.

The simulation and measurement of the response of Josephson junctions to optoelectronically generated short pulses

PTB started using the robust NbxSi1-x barrier junction technology for the fabrication of large arrays for the Programmable Josephson Voltage Standard (PJVS) and for the Josephson Arbitrary Waveform Synthesizer 3 years ago. We demonstrate how Nb-doping of the amorphous Si barrier causes the transition from an underdamped to a desired overdamped junction behavior. Special dc SQUIDs have been used to evaluate junction capacitance and noise properties. The critical current of small junctions as a function of applied magnetic field has been investigated. On the basis of an existing 70 GHz design previously used for 10 V PJVS chips, we fabricated for the first time 20 V circuits with nearly 140 000 double-stacked Josephson junctions. A direct on-chip comparison between the two 10 V halves of the binary-divided array confirmed the metrological suitability of the 20 V circuits for dc and ac applications.

F. Muller

Papers

Nb/al/alox/alox/al/nb josephson junctions for programmable voltage standards

Development and metrological applications of Josephson arrays at PTB

Design and fabrication of 10 V SINIS Josephson arrays for programmable voltage standards

The simulation and measurement of the response of Josephson junctions to optoelectronically generated short pulses

NbSi Barrier Junctions Tuned for Metrological Applications up to 70 GHz: 20 V Arrays for Programmable Josephson Voltage Standards