The ampere and the electrical units in the quantum era

Abstract: By fixing two fundamental constants from quantum mechanics, the Planck constant $h$ and the elementary charge $e$, the revised Syst`eme International (SI) of units endorses explicitly quantum mechanics. This evolution also highlights the importance of this theory which underpins the most accurate realization of the units. From 20 May 2019, the new definitions of the kilogram and of the ampere, based on fixed values of $h$ and $e$ respectively, will particularly impact the electrical metrology. The Josephson effect (JE) and the quantum Hall effect (QHE), used to maintain voltage and resistance standards with unprecedented reproducibility since 1990, will henceforth provide realizations of the volt and the ohm without the uncertainties inherited from the older electromechanical definitions. More broadly, the revised SI will sustain the exploitation of quantum effects to realize electrical units, to the benefit of end-users. Here, we review the state-of-the-art of these standards and discuss further applications and perspectives.