The NIST Johnson Noise Thermometry System for the Determination of the Boltzmann Constant

Abstract

In preparation for the redefinition of the International System of Units (SI), five different electronic measurements of the Boltzmann constant have been performed using different Johnson noise thermometry (JNT) systems over the past seven years. In this paper, we describe in detail the JNT system and uncertainty components associated with the most recent National Institute of Standards and Technology (NIST) determination of the Boltzmann constant: k = 1.380642 9(69) × 10 −23 J/K, with a relative standard uncertainty of 5.0 × 10 −6 and relative offset of −4.05 × 10 −6 from the Committee on Data for Science and Technology (CODATA) 2014 recommended value. We discuss the input circuits and the approach we used to match the frequency response of two noise sources. We present new measurements of the correlated noise of the 4 K on-chip resistors in the quantum-accurate, pseudorandom, voltagenoise source, which we used to estimate the correlated, frequency-dependent, nonthermal noise in our system. Finally, we contrast our system with those used in other measurements and speculate on future improvements.

A Boltzmann constant determination based on Johnson noise thermometry

“…Compared to earlier NIST measurements, the shielding was also dramatically improved to reduce electromagnetic interference (EMI). We will briefly discuss these differences here; full details will be given in a future publication [34]. …”

“…As described in section 2, we model the ratio S R / S Q as a d -th order even polynomial function of frequency (further details are given in [34, 35]). We consider candidate polynomial models with orders ranging from d =2 to d =14.…”

“…We define σ̂ stat to be the statistical uncertainty associated with the selected model, assuming the model is valid. Then the additional uncertainty associated with model ambiguity, that is, imperfect knowledge of the polynomial order d of the ratio spectrum model, is defined as ${\hat{\sigma }}_{\text{model}}=\sqrt{{\hat{\sigma }}_{\text{tot}}^2-{\hat{\sigma }}_{\text{stat}}^2}$ assuming σ̂ tot ≥ σ̂ stat (see [34] and [35] for details).…”

“…These categories are: 1) the uncertainty in the measurement of the ratio of power spectral densities; 2) the uncertainties of the QVNS waveform; 3) the uncertainties in the realization of the kelvin through use of the TPW cell; and 4) the uncertainties in the resistance measurements and traceability to the QHR representation of the ohm. A more detailed description of these uncertainty components will be available in a future publication [34]. …”

“…Here, we report our new measurement result for the determination of the Boltzmann constant. A more detailed description of this system, the experiment, and the data analysis will be published in the near future [34]. …”