An Electronic Measurement of the Boltzmann Constant

Abstract

The Boltzmann constant was measured by comparing the Johnson noise of a resistor at the triple point of water with a quantum-based voltage reference signal generated with a superconducting Josephson-junction waveform synthesizer. The measured value of k = 1.380651(18) \times 10^-23 J/K is consistent with the current CODATA value and the combined uncertainties. This is our first measurement of k with this electronic technique, and the first noise thermometry measurement to achieve a relative combined uncertainty of 13 parts in 10^6. We describe the most recent improvements to our Johnson Noise Thermometer that enabled the statistical uncertainty contribution to be reduced to seven parts in 10^6, as well as the further reduction of spurious systematic errors and EMI effects. The uncertainty budget for this measurement is discussed in detail.