Marvin E. Cage

NBS determination of the fine-structure constant, and of the quantized Hall resistance and Josephson frequency-to-voltage quotient in SI units

Results of US National Bureau of Standards (NBS) experiments to realize the ohm and the watt, to determine the proton gyromagnetic ratio by the low-field method, to determine the time dependence of the NBS representation of the ohm using the quantum Hall effect, and to maintain the NBS representation of the volt using the Josephson effect, are appropriately combined to obtain an accurate value of the fine-structure constant and of the quantized Hall resistance in SI units, and values in SI units of the Josephson frequency-to-voltage quotient, Planck constant and elementary charge. >

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

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 RK-90 by slightly more than twice the relative standard uncertainty of the present measurement, which is 2.4 × 10-8.

Precision Tests of a Quantum Hall Effect Device DC Equivalent Circuit Using Double-Series and Triple-Series Connections

Precision tests verify the dc equivalent circuit used by Ricketts and Kemeny to describe a quantum Hall effect device in terms of electrical circuit elements. The tests employ the use of cryogenic current comparators and the double-series and triple-series connection techniques of Delahaye. Verification of the dc equivalent circuit in double-series and triple-series connections is a necessary step in developing the ac quantum Hall effect as an intrinsic standard of resistance.

Dependence of Quantized Hall Effect Breakdown Voltage on Magnetic Field and Current

When large currents are passed through a high-quality quantized Hall resistance device the voltage drop along the device is observed to assume discrete, quantized states if the voltage is plotted versus the magnetic field. These quantized dissipative voltage states are interpreted as occurring when electrons are excited to higher Landau levels and then return to the original Landau level. The quantization is found to be, in general, both a function of magnetic field and current. Consequently, it can be more difficult to verify and determine dissipative voltage quantization than previously suspected.

Investigating the use of multimeters to measure quantized hall resistance standards

A new generation of digital multimeters was used to compare the ratios of the resistances of wire-wound reference resistors and quantized Hall resistances (QHRs). Specifically, a digital multimeter was used to compare the DC voltage ratio of a QHR sample with that of a reference resistor connected in series with the sample. The accuracies are better than 0.1 p.p.m. for ratios as large as 4:1 if the multimeters are calibrated with a Josephson array. >

Quantised dissipative states at breakdown of the quantum Hall effect

The authors report the breakdown of the nearly dissipationless quantum Hall effect into a set of distinct, quantised dissipative states in a wide, high-quality GaAs/AlGaAs sample. They found 35 dissipative stages on one plateau and nine on another plateau which have longitudinal voltage drops accurately quantised in units of h(cross) omega c/e to within our +or-0.6% measurement uncertainty. This voltage quantisation implies that the energy dissipation per carrier is quantised in units of the Landau level spacing h(cross) omega c.

Determination of the time-dependence of Omega /sub NBS/ using the quantized Hall resistance

The quantum Hall effect is being used to monitor the US legal representation of the ohm, or as-maintained ohm, Omega /sub NBS/. Measurements have been made on a regular basis since August 1983. Individual transfers between the quantized Hall resistance R/sub H/ and the five 1- Omega resistors which comprise Omega /sub NBS/ can be made with a total of one standard deviation (1 sigma ) uncertainty of +or-0.014 p.p.m. This uncertainty is the root-sum-square of 32 individual components. The time-dependent expression for R/sub H/ in terms of Omega /sub NBS/ is: R/sub H/=25812.8(1+(1.842+or-0.012)*10/sup -6/=(0.0529+or-0.0040)(t-0.7785)*10/sup -6//year) Omega /sub NBS/, where t is measured in years from January 1, 1987. The value of Omega /sub NBS/ is, therefore, decreasing at the rate of (0.0529+or-0.0040) p.p.m./year. >

Intrinsic Capacitances and Inductances of Quantum Hall Effect Devices

Analytic solutions are obtained for the internal capacitances, kinetic inductances, and magnetic inductances of quantum Hall effect devices to investigate whether or not the quantized Hall resistance is the only intrinsic impedance of importance in measurements of the ac quantum Hall effect. The internal capacitances and inductances are obtained by using the results of Cage and Lavine, who determined the current and potential distributions across the widths of quantum Hall effect devices. These intrinsic capacitances and inductances produce small out-of-phase impedance corrections to the in-phase quantized Hall resistance and to the in-phase longitudinal resistance.

A Test of the Quantum Hall Effect as a Resistance Standard

This paper demonstrates that the quantum Hall effect can be used to monitor a laboratory unit of resistance. A 6453.2-¿ room temperature reference resistor was calibrated relative to two quantum Hall effect devices with a 0.017-ppm (1 ¿) uncertainty for each 1 h measurement period. This accuracy was achieved by correcting for a measurement system offset error and for the temperature dependences of each quantum Hall device. Hamon series-parallel resistor networks were then used to calibrate the 6453.2-¿ resistor in terms of the five one ohm resistors which comprise the NBS ohm. The total l¿ accuracy for the transfer between the quantum Hall devices and the 1-¿ resistors was 0.047 ppm.

The Realization of the Ampere at NBS

We present a method for the realization of the ampere based on Faradays induction law and using a modification of the classic Pellat balance. A preliminary apparatus has been constructed and initial measurements have been obtained. This balance is also compared with a balance similar to one proposed earlier.