Electronic measurement of the Boltzmann constant with a quantum-voltage-calibrated Johnson noise thermometer

Samuel Benz; D. Rod White; JiFeng Qu; Horst Rogalla; Weston Tew

doi:10.1016/j.crhy.2009.10.008

Electronic measurement of the Boltzmann constant with a quantum-voltage-calibrated Johnson noise thermometer
[Mesures de la constante de Boltzmann à l'aide d'un thermomètre résistif à bruit Johnson étalonné par une source de tension quantique]

Samuel Benz ¹ ; D. Rod White ² ; JiFeng Qu ¹ ; Horst Rogalla ³ ; Weston Tew ⁴

¹ National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA
² Measurement Standards Laboratory, P.O. Box 31310, Lower Hutt 5040, New Zealand
³ Department of Applied Physics, Univ. Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
⁴ National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

Comptes Rendus. Physique, Volume 10 (2009) no. 9, pp. 849-858.

Résumé
Abstract

La valeur de la constante de Boltzmann recommandée par CODATA résulte presque uniquement de mesures obtenues par thermométrie à gaz avec une incertitude relative de $1.8 \times 10^{- 6}$ [P.J. Mohr, B.N. Taylor, D.B. Newell, CODATA recommended values of the fundamental physical constants: 2006, Rev. Mod. Phys. 80 (2008) 633–730]. Cet article présente une mesure électrique de la constante de Boltzmann effectuée en comparant le bruit Johnson d'une résistance placée à la température du point triple de l'eau avec un signal pseudo aléatoire généré par un synthétiseur quantique de tension alternative. La détermination du rapport des deux puissances spectrales obtenues relie la constante de Boltzmann à la constante de Planck. Une analyse détaillée des incertitudes obtenues pour des mesures récentes de bruit montre que la constante de Boltzmann peut être obtenue avec une incertitude relative inférieure à $10 \times 10^{- 6}$ . Un tel niveau d'incertitude rend pertinente la mise en œuvre de cette méthode nouvelle pour mesurer la constante de Boltzmann.

Currently, the CODATA value of the Boltzmann constant is dominated by a single gas-based thermometry measurement with a relative standard uncertainty of $1.8 \times 10^{- 6}$ [P.J. Mohr, B.N. Taylor, D.B. Newell, CODATA recommended values of the fundamental physical constants: 2006, Rev. Mod. Phys. 80 (2008) 633–730]. This article describes an electronic approach to measuring the Boltzmann constant that compares Johnson noise from a resistor at the water triple point with a pseudo-random noise generated using quantized ac-voltage synthesis. Measurement of the ratio of the two power spectral densities links Boltzmann's constant to Planck's constant. Recent experiments and detailed uncertainty analysis indicate that Boltzmann's constant can presently be determined using Johnson noise with a relative standard uncertainty below $10 \times 10^{- 6}$ , which would support both historic and new determinations.

Publié le : 2009-11-01

DOI : 10.1016/j.crhy.2009.10.008

Keywords: Boltzmann constant, Johnson noise, Josephson arrays, Noise thermometry, Temperature
Mot clés : Constante de Boltzmann, Bruit Johnson, Réseau de jonctions Josephson, Mesure de bruit thermique, Température

Affiliations des auteurs :

Samuel Benz ¹ ; D. Rod White ² ; JiFeng Qu ¹ ; Horst Rogalla ³ ; Weston Tew ⁴

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Samuel Benz; D. Rod White; JiFeng Qu; Horst Rogalla; Weston Tew. Electronic measurement of the Boltzmann constant with a quantum-voltage-calibrated Johnson noise thermometer. Comptes Rendus. Physique, Volume 10 (2009) no. 9, pp. 849-858. doi : 10.1016/j.crhy.2009.10.008. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2009.10.008/

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^☆ This work is a contribution of an agency of the U.S. government and is thus not subject to U.S. copyright.

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