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

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 1.8×106 [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 10×106. 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 1.8×106 [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 10×106, which would support both historic and new determinations.

Publié le :
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

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
@article{CRPHYS_2009__10_9_849_0,
     author = {Samuel Benz and D. Rod White and JiFeng Qu and Horst Rogalla and Weston Tew},
     title = {Electronic measurement of the {Boltzmann} constant with a quantum-voltage-calibrated {Johnson} noise thermometer},
     journal = {Comptes Rendus. Physique},
     pages = {849--858},
     publisher = {Elsevier},
     volume = {10},
     number = {9},
     year = {2009},
     doi = {10.1016/j.crhy.2009.10.008},
     language = {en},
}
TY  - JOUR
AU  - Samuel Benz
AU  - D. Rod White
AU  - JiFeng Qu
AU  - Horst Rogalla
AU  - Weston Tew
TI  - Electronic measurement of the Boltzmann constant with a quantum-voltage-calibrated Johnson noise thermometer
JO  - Comptes Rendus. Physique
PY  - 2009
SP  - 849
EP  - 858
VL  - 10
IS  - 9
PB  - Elsevier
DO  - 10.1016/j.crhy.2009.10.008
LA  - en
ID  - CRPHYS_2009__10_9_849_0
ER  - 
%0 Journal Article
%A Samuel Benz
%A D. Rod White
%A JiFeng Qu
%A Horst Rogalla
%A Weston Tew
%T Electronic measurement of the Boltzmann constant with a quantum-voltage-calibrated Johnson noise thermometer
%J Comptes Rendus. Physique
%D 2009
%P 849-858
%V 10
%N 9
%I Elsevier
%R 10.1016/j.crhy.2009.10.008
%G en
%F CRPHYS_2009__10_9_849_0
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/

[1] J.B. Johnson Thermal agitation of electricity in conductors, Nature, Volume 119 (1927), pp. 50-51

[2] J.B. Johnson Thermal agitation of electricity in conductors, Phys. Rev., Volume 32 (1928), pp. 97-109

[3] H. Nyquist Thermal agitation of electric charge in conductors, Phys. Rev., Volume 32 (1928), pp. 110-113

[4] H.B. Callen; T.A. Welton Irreversibility and generalized noise, Phys. Rev., Volume 83 (1951), pp. 34-40

[5] A. Einstein On the motion—required by the molecular kinetic theory of heat—of small particles suspended in a stationary liquid, Annalen der Physik, Volume 17 (1905), pp. 549-560

[6] R.J. Soulen; R.L. Rusby; D. Van Vechten A self-calibrating rhodium–iron resistive SQUID thermometer for the range below 0.5 K, J. Low Temp. Phys., Volume 40 (1980), pp. 553-569

[7] J.C. Gallop; B.W. Petley Josephson noise thermometry with HTS devices, IEEE Trans. Instrum. Meas., Volume 44 (1995), pp. 234-237

[8] J.P. Pekola; K.P. Hirvi; J.P. Kauppinen; M.A. Paalanen Thermometry of arrays of tunnel junctions, Phys. Rev. Lett., Volume 73 (1994), p. 2903

[9] L. Spietz; K.W. Lehnert; I. Siddiqi; R.J. Schoelkopf Primary electronic thermometry using the shot noise of a tunnel junction, Science, Volume 300 (2003), pp. 1929-1932

[10] J.P. Pekola; T. Holmqvist; M. Meschke Primary tunnel junction thermometry, Phys. Rev. Lett., Volume 101 (2008) (206801-1–4)

[11] R.A. Webb; R.P. Giffard; J.C. Wheatley Noise thermometry at ultralow temperatures, J. Low Temp. Phys., Volume 13 (1973), pp. 383-429

[12] D.R. White; R. Galleano; A. Actis; H. Brixy; M. De Groot; J. Dubbeldam; A.L. Reesink; F. Edler; H. Sakurai; R.L. Shepard; J.C. Gallop The status of Johnson noise thermometry, Metrologia, Volume 33 (1996), pp. 325-335

[13] H.J. Fink A new absolute noise thermometer at low temperatures, Can. J. Phys., Volume 37 (1959), pp. 1397-1406

[14] H. Brixy; R. Hecker; J. Oehmen; K.F. Rittinghaus; W. Setiawan; E. Zimmermann Noise thermometry for industrial and metrological applications at KFA Jülich (J.F. Schooley, ed.), Temperature, Its Measurement and Control in Science and Industry, vol. 6, Am. Inst. Phys., New York, 1992, pp. 993-996

[15] R. Willink; D.R. White Detection of corruption in Gaussian processes with application to noise thermometry, Metrologia, Volume 35 (1998), pp. 787-798

[16] D.R. White; E. Zimmermann Preamplifier limitations on the accuracy of Johnson noise thermometers, Metrologia, Volume 37 (2000), pp. 11-23

[17] D.R. White; R.S. Mason; P. Saunders Progress towards a determination of the indium freezing point by Johnson noise thermometry (B. Fellmuth; J. Seidel; G. Scholz, eds.), Proceedings of TEMPMEKO 2001, VDE Verlag, Berlin, 2001, pp. 129-134

[18] H. Howener, Noise Thermometry in Nuclear Power Plants, KFA, Jülich GmbH, JUL-2107, 1986

[19] H. Saleh, E. Zimmerman, G. Brandenburg, H. Halling, Efficient FPGQ-based multistage two-path decimation filter for noise thermometer, in: Proceedings of ICM 2001, IEEE Catalog No. 01EX481, Rabat, Morocco, 2001, pp. 161–164

[20] M. Frigo, S.G. Johnson, FFTW, Massachusetts Institute of Technology, 2003, http://www.fftw.org

[21] D.R. White; R.S. Mason An EMI test for Johnson noise thermometry (D. Zvizdic; L.G. Bermanec; T. Stasic; T. Veliki, eds.), Proceedings of TEMPMEKO 2004, Faculty of Mechanical Eng. and Naval Arch., Zagreb, 2004, pp. 485-490

[22] J.T. Zhang; S.Q. Xue A noise thermometry investigation of the melting point of gallium at the NIM, Metrologia, Volume 43 (2006), pp. 273-277

[23] W.L. Tew; J.R. Labenski; S.W. Nam; S.P. Benz; P.D. Dresselhaus; C.J. Burroughs Johnson noise thermometry near the zinc freezing point using resistance-based scaling, Int. J. Thermophys., Volume 28 (2007), pp. 629-645

[24] J.R. Labenski; W.L. Tew; S.W. Nam; S.P. Benz; P.D. Dresselhaus; C.J. Burroughs A determination of the ratio of the zinc freezing point to the tin freezing point by noise thermometry, Int. J. Thermophys., Volume 29 (2008), pp. 1-17

[25] R.H. Dicke The measurement of thermal radiation at microwave frequencies, Rev. Sci. Instrum., Volume 17 (1964), pp. 268-275

[26] S.P. Benz; C.A. Hamilton A pulse-driven programmable Josephson voltage standard, Appl. Phys. Lett., Volume 68 (1996), pp. 3171-3173

[27] S.P. Benz; C.A. Hamilton; C.J. Burroughs; T.E. Harvey; L.A. Christian; J.X. Przybysz Pulse-driven Josephson digital/analog converter, IEEE Trans. Appl. Supercond., Volume 8 (1998), pp. 42-47

[28] S.P. Benz; J.M. Martinis; S.W. Nam; W.L. Tew; D.R. White A new approach to Johnson noise thermometry using a Josephson quantized voltage source for calibration (B. Fellmuth; J. Seidel; G. Scholz, eds.), Proceedings of TEMPMEKO 2001, the 8th International Symposium on Temperature and Thermal Measurements in Industry and Science, VDE Verlag, Berlin, April 2002 , pp. 37-44

[29] S.W. Nam; S.P. Benz; P.D. Dresselhaus; W.L. Tew; D.R. White; J.M. Martinis Johnson noise thermometry measurements using a quantum voltage noise source for calibration, IEEE Trans. Instrum. Meas., Volume 52 (2003), pp. 550-553

[30] S.P. Benz; P.D. Dresselhaus; J.M. Martinis An ac Josephson source for Johnson noise thermometry, IEEE Trans. Instrum. Meas., Volume 52 (2003), pp. 545-549

[31] S.W. Nam; S.P. Benz; P.D. Dresselhaus; C.J. Burroughs; W.L. Tew; D.R. White; J.M. Martinis Progress on Johnson noise thermometry using a quantum voltage noise source for calibration, IEEE Trans. Instrum. Meas., Volume 54 (2005), pp. 653-657

[32] S.W. Nam; S.P. Benz; J.M. Martinis; P.D. Dresselhaus; W.L. Tew; D.R. White A ratiometric method for Johnson noise thermometry using a quantized voltage noise source (D.C. Ripple, ed.), Temperature: Its Measurement and Control In Science and Industry, vol. 7, American Institute of Physics, Melville, New York, 2003, pp. 37-42

[33] D.R. White; S.P. Benz Constraints on a synthetic-noise source for Johnson noise thermometry, Metrologia, Volume 45 (2008), pp. 93-101

[34] D.R. White; S.P. Benz; J.R. Labenski; S.W. Nam; J.F. Qu; H. Rogalla; W.L. Tew Measurement time and statistics for a noise thermometer with a synthetic-noise reference, Metrologia, Volume 45 (2008), pp. 395-405

[35] S.P. Benz; H. Rogalla; D.R. White; J.F. Qu; P.D. Dresselhaus; W.L. Tew; S.W. Nam Improvements in the NIST Johnson noise thermometry system, IEEE Trans. Inst. Meas., Volume 58 (2009), pp. 884-890

[36] K. von Klitzing; G. Dorda; M. Pepper New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett., Volume 45 (1980), pp. 494-497

[37] B.D. Josephson Possible new effects in superconductive tunneling, Phys. Lett., Volume 1 (1962), pp. 251-253

[38] L. Storm Measurement of small noise signals with a correlator and noise thermometry at low temperatures, Z. Angew. Phys., Volume 6 (1969), pp. 331-333

[39] E. Takano, Contact current distortion due to tunnel effect, in: Proceedings of the Forty-Fifth IEEE Holm Conference on Electrical Contacts, 4–6 Oct. 1999, Pittsburgh, PA, USA, pp. 136–140

[40] Jifeng Qu; S.P. Benz; H. Rogalla; D.R. White Reduced nonlinearities and improved temperature measurements for the NIST Johnson noise thermometer, Metrologia, Volume 46 (2009), pp. 512-524

[41] P.J. Mohr; B.N. Taylor; D.B. Newell CODATA recommended values of the fundamental physical constants: 2006, Rev. Mod. Phys., Volume 80 (2008), pp. 633-730

Cité par Sources :

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

Commentaires - Politique