The discovery of the Josephson effect and the quantum-Hall effect made it possible to bind up via the physical constants KJ =2e/h and RK = h/e2 the pairs "voltage-frequency" and "current-voltage" respectively. Modern experimental techniques allowed these fundamental relations to be accurately measured and the quantum standards of the voltage and resistance to be established. The third side of this triangle, i.e. the relation between current and frequency, can be established by means of the single charge (single electrons or single Cooper pair) tunneling effect.
The quantum metrological triangle [1] reflects the fundamental relationships between the basic electrical quantities, namely the voltage, current and frequency, given by quantum mechanical laws. The numbers k, m and n are integer.
At present, this effect is realized in single electron pumps driven by a stable rf source [2,3]. An experiment aiming at realization of all three effects with the accuracy level better than one part in 108 in one setup could reveal possible fundamental corrections to the laws of quantum electrodynamics. The most severe technical problem from the side "current-frequency" is a small magnitude of current I maintained by a pump. Typically, I is about of few picoampere and this level is still insufficient for the ultimate performance of the modern current comparators. Since the superconducting charge carriers, the Cooper pairs, are capable to tunnel across a tunnel junction elastically, one can expect that a pump operating on pairs instead of electrons is faster and, hence, can generate a larger current I.
For fairness sake note, that as an alternative to the metallic tunnel-junction systems, GaAs devices with a surface acoustic wave drive [4] and silicon charge-coupled MOSFET devices [5], carrying a quantized current I = nef, are also extensively examined from the metrology viewpoint.
1. K. K. Likharev and A. B. Zorin, J. Low Temp. Phys. 59, 347 (1985).
2. M. W. Keller, J. M. Martinis, N. M. Zimmerman and A. H. Steinbach, Appl. Phys. Lett. 69, 1804 (1996).
3. S. V. Lotkhov, S. A. Bogoslovsky, A. B. Zorin and J. Niemeyer, Appl. Phys. Lett. 78, 1804 (2001).
4. V. I. Talyanskii et al., Phys. Rev. B 56, 15180 (1997).
5. A. Fujiwara and Y. Takahashi, Nature 410, 560 (2001).
