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 Josephsonjunction waveform synthesizer. The measured value of k = 1.380651(18)×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.

Development of high frequency and wide bandwidth Johnson noise thermometry

“…Temperature is measured by passively monitoring fluctuations of the conducting components within the nanoscale device without current excitations. Difficulties in measuring low level voltage noise 5 have limited the applications of JNT to metrology 9,10 and extreme environments such as nuclear reactors 11 and ultralow temperatures. 5 Recently, considerable progress has been made in the measurement of noise on mesoscopic devices by applying radiometry techniques, 4,7,12 opening up the possibility of using JNT to study a wide range of mesoscopic phenomena.…”

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

“…1) was chosen to be 200 Ω, which increased the signal-to-noise ratio relative to earlier 100 Ω JNT experiments [34]. This increase in resistance did not significantly change the measurement bandwidth of our system because the effective RC cutoff frequency associated with the measurement circuit is larger than the sampling frequency.…”

“…1) was used to switch the voltage source signal every 100 s. A second, identical ground relay circuit board (represented by green relays in Fig. 1) was used to switch the ground connection; earlier measurements did not use this second circuit-board and instead tied all the ground wires together in a static manner [34]. In Ref.…”

“…The National Institute of Standards and Technology (NIST) has been developing precision QVNS-JNT systems since 1999 in cooperation with the Measurement Standards Laboratory of New Zealand [18][19][20][21][22][23][24][25][26][27][28][29][30], and since 2009 in collaboration with the National Institute of Metrology (NIM) of China [31][32][33]. Different iterations of QVNS-JNT systems at NIST and NIM have produced independent measurements of k in 2011-2017 [34][35][36], with the most recent NIM measurement determining k to a relative uncertainty of 2.7 × 10 −6 , meeting CCT's 3.0 × 10 −6 threshold [1]. The most recent NIST determination of k was reported with a relative uncertainty of 5.0 × 10 −6 [37].…”

“…[37]. Emphasis will be placed on modifications incorporated since our earlier 2015 determination of k [34]. Major differences include an increase in the thermal noise resistance from 100 Ω to 200 Ω, attempts to match the frequency response of the measurement channels using trim resistors and capacitors, separate shielding of the twisted pairs of wires to reduce interchannel cross-talk, and selection of noise ratio spectra models with an automated cross-validation method developed by Coakley et al [40].…”