Quantum metrological triangle experiment at LNE: measurements on a three-junction R-pump using a 20 000:1 winding ratio cryogenic current comparator

The direct closure of the quantum metrological triangle consists in achieving Ohm's law with the three effects used and investigated in quantum electrical metrology: the Josephson effect (JE), the quantum Hall effect (QHE) and the single-electron tunnelling effect (SET). The aim is to check the consistency of the phenomenological constants K-J, R-K and Q(X) associated with these effects and theoretically expressed with the fundamental constants e and h (elementary charge and Planck constant, respectively). Such an experiment is a contribution to a future redefinition of the International System of units (SI). In this paper, the experimental setup developed at LNE is described and the main obtained results are given. From a set of four measurements, agreement at a level of 1.3 parts in 10(5) was found between the quantum charge involved in the SET, i.e. Q(X), and the CODATA value of the elementary charge. The best measurement has shown a relative type-A uncertainty of 1.9 parts in 10(6), while the amplitude of the current generated by a metallic electron pump was as low as 3.6 pA.