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 Système 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.

A new dual system for the fundamental units including and going beyond the newly revised SI

“…This unconventional formulation defines directly the metre as a submultiple of the second. It may be taken as an improved definition of the metre, reconciling the present one in (21,22) with the choice c = 1 suggested by relativity. Conversely, the metre also appears as a unit of time, as is natural owing to the symmetry between space and time provided by relativity.…”

“…In practice the precision of quantum electromagnetic effects is essential to get a precise determination of h through K J = 2e/h and R K = h/e 2 , and taking full advantage of fixing h [19]. This motivates a more precise definition of electrical units than the usual one through the traditional definition of the ampere [10, 14,21].…”

Dual Fraunhofer interference and charge fluctuations in long quantum phase slip wires

“…Here, Q i is the charge operator and q i is the induced charge (applied via the gate) on each grain, respectively, normalized to 2e. Assuming only nearest-neighbor coupling, and equal coupling capacitances C i,i = 2C, C i,±1 = C after a transformation to the conjugate phase variable, this results in H = 2 , where θ i = ϕ i+1 − ϕ i is the phase difference between islands. The charge contribution to the Lagrangian is, then, given by…”

“…Significant efforts have been made in the past decades to observe so-called "dual" Shapiro steps, an important milestone towards realizing a quantum current standard, dual to that of the Josephson volt [1,2]. Experimental demonstration of robust dual Shapiro steps remains challenging [3,4], and a voltage blockade due to coherent quantum phase slips (CQPS) [5], the dual of Cooper pair tunneling, is often difficult to distinguish from conventional Coulomb blockade due to wire inhomogeneities [6].…”

A Resistance Bridge Based on a Cryogenic Current Comparator Achieving Sub-10⁻⁹ Measurement Uncertainties

“…I N the SI [1], the ohm can be realized from R K = h/e 2 [2], where h is the Planck constant, e is the elementary charge, using the quantum Hall effect. In national metrology institutes (NMIs), the quantized Hall resistance, R K /i, where i is an integer, is used as an universal primary reference to disseminate the ohm by means of resistance comparisons [3]. Performing these resistance comparisons is challenging since the measurement current of the quantum Hall resistance (QHR) devices must remain small, i.e.…”