# The Quantum Metrological Triangle

An important consequence of the proposed redefinition of the SI units is the possibility to represent the electric units directly by electrical quantum standards. Using the two quantum standards already established in metrology – the Volt based on the Josephson Effect and the Ohm based on the Quantum Hall Effect – crucially relies on the assumption that the relations KJ = 2e/h for the Josephson Constant and RK = h/e2 for the von-Klitzing Constant hold exactly. Here, e is the elementary charge, and h is the Planck constant. Although the validity of these relations is generally postulated and partly underpinned theoretically, an experimental verification of these basic assumptions is an objective of metrological basic research for over two decades already.

Empirical information on possible corrections to these relations can be attained through consistency tests that combine the Josephson and the quantum Hall effect together with the single-electron transport effect (SET). The combination of these three electrical quantum effects in one experiment is called "Quantum Metrological Triangle". Such combination can, for instance, be realized via Ohm's law (voltage = electrical resistance times current). Mathematically this leads to the product of the "phenomenological" constants KJ, RK, and QS, the latter being the charge of the single charge quanta transported in an SET circuit. This product term only contains integer numbers and frequencies – quantities that can be quantified experimentally with very high precision.

Schematic representation of the Quantum Metrological Triangle in two variants: i) the "current" version, realized by exploiting Ohm's law (electrical current I, voltage U and resistance R, see small triangle). ii) The "charge" version, implemented via electrical charge Q, voltage U and capacitance C (large triangle). The latter variant corresponds to the "Electron Counting Capacitance Standard". The impedance of the capacitance C is traced to unit of resistance via the ac Quantum Hall Effect [H. Scherer, B. Camarota, Meas. Sci. Technol. 23, 124010 (2012)].

If such experiment is accomplished with a relative uncertainty of less than about one part in a million, this will have impact on the understanding of the electrical quantum effects and, thus, further secure the foundations of the future SI unit system based on fundamental constants.

So far, the working group has pursued the realization of Quantum Metrological Triangle via the Electron Counting Capacitance Standard Experiment. Here, a high-precision capacitor is charged with a certain number of electrons by using a single-electron pump, and the resulting voltage between the capacitor terminals is measured. This experiment was performed with a relative uncertainty of less than two parts in a million [B. Camarota, H. Scherer, et al., Metrologia 49, 8 (2012)].

A promising alternative for the realization of Quantum Metrological Triangle could be possible by using novel SET pumps which are able to generate currents > 100 pA. If, using an accurate amplifier, the current is amplified by a factor of 1000 and driven through a quantum Hall resistor, it causes a voltage that can be measured by means of the Josephson effect. This "current" version for the realization of Quantum Metrological Triangle subject of the research presently pursued.