Determination of the von Klitzing constant and the fine-structure constant through a comparison of the quantized Hall resistance and the ohm derived from the NIST calculable capacitor

Abstract

This paper describes a recent determination of the von Klitzing constant and the fine-structure constant by comparisons of values of the ohm as defined in the International System of Units (SI), derived from the National Institute of Standards and Technology (NIST) calculable cross-capacitor, and values of the international practical unit of resistance derived from the integral quantum Hall effect. In this determination, the comparisons were made in a series of measurements lasting three years. A small difference is observed between this determination and an earlier comparison carried out in this laboratory and reported in 1988. The most recent value of the fine-structure constant based on the experimental value and theoretical expression for the magnetic moment anomaly of the electron, which has the smallest uncertainty of any value currently available, is consistent with both of these results. The new value exceeds the 1990 conventional value of the von Klitzing constant by slightly more than twice the relative standard uncertainty of the present measurement, which is 2.4 10 -8 .

R K /100 and RK/200 quantum Hall array resistance standards

“…Metrological characteristics and Hall resistance measurements by means of direct and indirect comparisons with R K are given: we analyse the contact resistance, current and temperature effects on the quantization of the equivalent Hall resistance. Our work shows that the Hall resistance of QHARS agrees with their expected nominal value within 5 parts in 10 9 . This high level of quantization is directly related to the efficiency of the triple connection which is explained through the equivalent electrical circuit analysis of the arrays.…”

“…However, a relative uncertainty of one part in 10 7 is assigned to its 25812,807 Ω value. Although SI direct measurements 6,7 of R K via calculable capacitors have been obtained with uncertainties as low as 2.4 parts 8,9 in 10 8 , the CIPM established the value of R K with a larger uncertainty because, assuming that R K is presumably equal to h/e 2 , it took into account indirect determinations of h/e 2 and calculations of the fine structure constant. That still remains a big metrological stake to prove that the relation R K =h/e 2 is true with a better accuracy.…”

The watt balance: determination of the Planck constant and redefinition of the kilogram

“…Since the measurements of mutual inductance are made at AC, the result needs to be extrapolated to DC. The uncertainty of the extrapolated value is estimated at less than 1 part in 10 6 . Other aspects of the experiment are also being developed; for example, the balance necessary for the force measurement and an optical system to determine the vertical position of the moving coil.…”

“…In 2011, the experiment will be moved to a new laboratory, where it will be placed in a vacuum system installed on a concrete block to reduce vibration. It is expected that the uncertainty will then be reduced to about 5 parts in 10 6 . The long-term goal is to reach a level of several parts in 10 8 around 2015.…”

A new photon recoil experiment: towards a determination of the fine structure constant

“…6.7 Photon Recoil h/mCs [6,7] 6.0001(11) 7.7 Quantum Hall effect RK [8,9] 6.0037(33) 24 Neutron Interferometry [10] 6.0015(47) 34 AC Josephson effect Γ ′ p−90 (lo) [11] 5.9880(51) 37 Muonium Hyperfine structure [12] methods can dramatically be reduced in the near future.…”