Josephson voltage standard

A Josephson voltage standard is a complex system that uses a superconductive integrated circuit chip operating at a temperature of 4 K to generate stable voltages that depend only on an applied frequency and fundamental constants. It is an intrinsic standard in the sense that it does not depend on any physical artifact. It is the most accurate method to generate or measure voltage and, by international agreement in 1990, is the basis for voltage standards around the world. A Josephson voltage standard is a complex system that uses a superconductive integrated circuit chip operating at a temperature of 4 K to generate stable voltages that depend only on an applied frequency and fundamental constants. It is an intrinsic standard in the sense that it does not depend on any physical artifact. It is the most accurate method to generate or measure voltage and, by international agreement in 1990, is the basis for voltage standards around the world. In 1962, Brian Josephson, a graduate student at Cambridge University, derived equations for the current and voltage across a junction consisting of a thin insulating barrier separating two superconductors – now generally known as a Josephson junction. His equations predicted that if a junction is driven at frequency f {displaystyle f} , then its current–voltage (I–V) curve will develop regions of constant voltage at the values n h f / 2 e {displaystyle nhf/2e} , where n {displaystyle n} is an integer and h / e {displaystyle h/e} is the ratio of the Planck constant h {displaystyle h} to the elementary charge e {displaystyle e} . This prediction was verified experimentally by Shapiro in 1963 and has become known as the AC Josephson effect. This effect found immediate application in metrology because it relates the volt to the second through a proportionality involving only fundamental constants. Initially, this led to an improved value of the ratio h / e {displaystyle h/e} . Today it is the basis for all primary voltage standards. Josephson's equation for the supercurrent through a superconductive tunnel junction is given by where I {displaystyle I} is the junction current, I c {displaystyle I_{ ext{c}}} is the critical current, V {displaystyle V} is the junction voltage. I c {displaystyle I_{ ext{c}}} is a function of the junction geometry, the temperature, and any residual magnetic field inside the magnetic shields that are used with voltage standard devices. When a dc voltage is applied across the junction, Eq. (1) shows that the current will oscillate at a frequency f J = 2 e V / h {displaystyle f_{ ext{J}}=2eV/h} , where 2 e / h {displaystyle 2e/h} is approximately equal to 484 GHz/mV. The very high frequency and low level of this oscillation make it difficult to observe directly. However, if an AC current at frequency f {displaystyle f} is applied to the junction, the junction oscillation f J {displaystyle f_{ ext{J}}} tends to phase lock to the applied frequency. Under this phase lock, the average voltage across the junction equals h f / 2 e {displaystyle hf/2e} . This effect, known as the AC Josephson effect, is observed as a constant voltage step at V = h f / 2 e {displaystyle V=hf/2e} in the voltage–current (I–V) curve of the junction. It is also possible for the junction to phase lock to harmonics of f {displaystyle f} . This results in a series of steps at voltages V = n h f / 2 e {displaystyle V=nhf/2e} , where n {displaystyle n} is an integer, as shown in Fig. 1a. The Josephson effect was initially used to improve the measurement of the constant 2 e / h {displaystyle 2e/h} based on voltage values derived from the SI volt realization as maintained by Weston cells. The uncertainty of these measurements was limited by the uncertainty of the SI volt realization and the stability of the Weston cells. The stability of the Josephson volt depends only on the stability of f {displaystyle f} (which can easily be a part in 1012), and is at least four orders of magnitude better than the stability of Weston cells. Thus, in the early 1970s, many national standards laboratories adopted a value for the Josephson constant K J = 2 e / h {displaystyle K_{ ext{J}}=2e/h} and began using the AC Josephson effect as the practical standard of voltage. Owing to small differences in existing national standards, different values of K J {displaystyle K_{ ext{J}}} were adopted by various countries. This inconsistency was corrected in 1990 when, by international agreement, the constant K J-90 {displaystyle K_{ ext{J-90}}} was assigned the value 483597.9 GHz/V and adopted by all standards laboratories. The assigned value is based on a weighted average of volt realization measurements made prior to 1990 at many national measurement institutions. The uncertainty in K J-90 {displaystyle K_{ ext{J-90}}} is 0.4 ppm. Standards such as the Josephson volt that depend on fundamental constants rather than physical artifacts are known as intrinsic standards. Although the Josephson voltage standard (JVS) does not realize the SI definition of the volt, it provides a very stable reference voltage that can be reproduced anywhere without the need to transfer artifacts such as Weston cells. The accuracy of the Josephson voltage–frequency relation V = n f / K J {displaystyle V=nf/K_{ ext{J}}} , and its independence from experimental conditions, such as bias current, temperature, and junction materials, have been subjected to many tests. No significant deviation from this relation has ever been found. In the most precise of these experiments, two Josephson devices are driven by the same frequency source, biased on the same step, and connected in a series opposition loop across a small inductor. Since this loop is entirely superconductive, any voltage difference leads to a changing magnetic field in the inductor. This field is detected with a SQUID magnetometer and its constancy has set an upper limit on the voltage difference of less than 3 parts in 1019. Figure 2 is a semilog plot that illustrates how typical differences in dc voltage measurements among National Measurement Institutes (NMIs) have decreased over the last 70 years. The two major improvements coincide with the introduction of single-junction Josephson standards in the early 1970s and the introduction of series-array Josephson standards beginning in 1984. Although the ac Josephson effect provides a much more stable voltage reference than Weston cells, the first single-junction Josephson standardswere difficult to use because they generated very small voltages (1–10 mV). Several attempts were made to raise the voltage by connecting two or more junctions in series. The most ambitious of theseused 20 junctions in series to realize a voltage of 100 mV with an uncertainty of a few parts in 109. Ensuring that every junction was on a constant voltage step required individually adjusting the bias current to each of the 20 junctions. The difficulty of this procedure makes arrays of significantly more than 20 junctions impractical. In 1977, Levinson et al.made a suggestion that would ultimately lead to a solution to the multiple-bias problem. Levinson pointed out the importance of the parameter β c = 4 π e I c R 2 C / h {displaystyle eta _{ ext{c}}=4pi eI_{ ext{c}}R^{2}C/h} in determining the characteristics of rf-induced Josephson steps. β c {displaystyle eta _{ ext{c}}} is a measure of the damping of Josephson oscillations by the junction shunting resistance R {displaystyle R} . In particular, he showed that junctions with a large capacitance C {displaystyle C} and a large R {displaystyle R} ( β c > 100 {displaystyle eta _{ ext{c}}>100} ) could generate an I–V curve with hysteretic constant-voltage steps like those shown in Fig. 1b. These steps have become known as zero-crossing steps because they cross the zero-current axis of the I–V curve. The lack of stable regions between the first few steps means that for small dc bias currents, the junction voltage must be quantized. With a common bias current at or near zero, the voltage across a large array of these junctions must also be quantized. The possibility of obtaining constant-voltage steps at zero current over a wide range of junction and operating parameters suggested the possibility of building a voltage standard using large arrays of junctions. After several preliminary experiments,a joint effort in 1984 between the National Bureau of Standards in the U. S. and the Physikalisch-Technische Bundes-Anstalt in Germany resolved the problems of junction stability and microwave distribution and created the first large Josephson array based on Levinson's idea. Further design improvements and system development produced the first practical 1 V Josephson standards in 1985.Advances in superconductive integrated circuit technology, largely driven by the quest for a Josephson junction computer,soon made possible much larger arrays. In 1987, the design was extended to a chip with 14484 junctions that generated about 150000 quantized voltages spanning the range from −10 V to +10 V.Numerous further refinements were made as 10 V Josephson standards were implemented in many national standards laboratories.By 1989, all of the hardware and software for a complete voltage metrology system was commercially available. Today, there are Josephson array voltage standards in more than 70 national, industrial, and military standards laboratories around the world. A program of international comparisons carried out by the Bureau International des Poids et Mesures (BIPM) has measured differences between a traveling Josephson standard and those of NMIs that are typically less than 1 part in 109. Figure 3 illustrates the basic structure of one junction in a large series array. The junction is an overlap between two superconductive thin films that are separated by a thin oxide barrier. The junction sits above a ground plane and is separated from it by a few micrometers of insulation. A dc current I dc {displaystyle I_{ ext{dc}}} and a microwave current I ac {displaystyle I_{ ext{ac}}} are driven through the junction. The design parameters for the junction are its length L {displaystyle L} , width W {displaystyle W} , critical current density J {displaystyle J} (critical current per unit area), and the microwave drive frequency f {displaystyle f} . The practical realization of an array voltage standard requires a thorough understanding of how these parameters affect the stability of the quantized voltage levels shown in Fig. 1b. Stable operation requires that four conditions be satisfied: If any of these conditions is violated, the junction voltage is likely to switch randomly among several steps, making measurements impossible. A rigorous derivation of these conditions is the subject of several papers by Kautz.