Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
, 54 (5), 730-737

A Boltzmann Constant Determination Based on Johnson Noise Thermometry

Affiliations

A Boltzmann Constant Determination Based on Johnson Noise Thermometry

N E Flowers-Jacobs et al. Metrologia.

Abstract

A value for the Boltzmann constant was measured electronically using an improved version of the Johnson Noise Thermometry (JNT) system at the National Institute of Standards and Technology (NIST), USA. This system is different from prior ones, including those from the 2011 determination at NIST and both 2015 and 2017 determinations at the National Institute of Metrology (NIM), China. As in all three previous determinations, the main contribution to the combined uncertainty is the statistical uncertainty in the noise measurement, which is mitigated by accumulating and integrating many weeks of cross-correlated measured data. The second major uncertainty contribution also still results from variations in the frequency response of the ratio of the measured spectral noise of the two noise sources, the sense resistor at the triple-point of water and the superconducting quantum voltage noise source. In this paper, we briefly describe the major differences between our JNT system and previous systems, in particular the input circuit and approach we used to match the frequency responses of the two noise sources. After analyzing and integrating 49 days of accumulated data, we determined a value: k = 1.380 642 9(69)×10-23 J/K with a relative standard uncertainty of 5.0×10-6 and relative offset -4.05×10-6 from the CODATA 2014 recommended value.

Figures

Figure 1
Figure 1
JNT schematic diagram. The sense resistor of 200 Ω is composed of two series resistors RT = 100 Ω, while the QVNS is composed of two arrays with a total of NJJ = 20 Josephson junctions and two pairs of resistors RQ ~ 100 Ω. The QVNS lines have additional matching resistors Rm ~ 1 Ω and matching capacitors Cm. A custom switch board is used to determine which noise source is connected to the two signal processing channels (Ch A and Ch B). The amplifiers (Amp) are stabilized using a combination of toroidal ferrite-core inductors (light grey boxes) and resistors Ramp. The center of each source is grounded (green lines) at the amplifier input, and that ground is used to shield each differential twisted pair. After the custom high-gain low-noise amplifier [–20, 32, 34], there is a steep 11th-order 850 kHz low-pass filter (LPF) and an AC-coupled 16-bit 2.083 Msample/s digitizer (ADC). There is an additional grounded shield surrounding the entire system (grey boxes), and the entire system is also in an electromagnetically shielded room. The switchboard and ADCs are optically controlled by a computer (PC) outside of the shielded room.
Figure 2
Figure 2
Summary of all of the ratio data SR/SQa0,calc; each line is the average of data collected with a different QVNS transfer function, i.e., different parallel capacitances Cm (overall change is <20 pF).
Figure 3
Figure 3
(a) Average data SR/SQa0,calc (blue) with fit to a d=4 even order polynomial from 5 kHz to 350 kHz (based on the cross-validation results, red line). The spectral densities reported by the cross-correlation measurement are complex. In this paper, SR and SQ are defined as the real parts of each measurement; the imaginary parts of the complex ratio (gray) are small at low frequencies but become significant at higher frequencies. We will discuss the complex analysis in more detail in [34]. (b) a0 − a0,calc as a function of time extracted from fits to the data divided into subsets with equal integration time as well as from the fit to the average from plot (a) (solid black line with uncertainty as dotted black line). This plot is a diagnostic tool and shows that there is minimal impact on a0 from intentional changes to the system (in particular matching capacitors) and that there are no unknown sources of drift as a function of time.
Figure 4
Figure 4
Summary of cross-validation results. (a) Estimated minimum uncertainty σ̂tot versus maximum fit frequency fmax. The arrows in each plot indicate the point selected for the k determination, that is, to the minimum value of σ̂tot. (b) Polynomial order d which yields the minimum uncertainty given in (a) as a function of fmax. (c) Estimated a0a0,calc as a function of fmax and approximate 68% coverage interval.

Similar articles

See all similar articles

Cited by 1 article

  • The Boltzmann project.
    Fischer J, Fellmuth B, Gaiser C, Zandt T, Pitre L, Sparasci F, Plimmer MD, de Podesta M, Underwood R, Sutton G, Machin G, Gavioso RM, Ripa DM, Steur PPM, Qu J, Feng XJ, Zhang J, Moldover MR, Benz SP, White DR, Gianfrani L, Castrillo A, Moretti L, Darquié B, Moufarej E, Daussy C, Briaudeau S, Kozlova O, Risegari L, Segovia JJ, Martín MC, Del Campo D. Fischer J, et al. Metrologia. 2018;55:10.1088/1681-7575/aaa790. doi: 10.1088/1681-7575/aaa790. Metrologia. 2018. PMID: 31080297 Free PMC article.

LinkOut - more resources

Feedback