Skip to main content
SpringerLink
Log in

Determination of the elementary charge and the quantum metrological triangle experiment

  • Review
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

The elementary charge e is of fundamental importance in physics. The determination of its value, which is closely linked to progress of the measurement techniques, started in the beginning of the twentieth century and is still on-going. Today, in the frame of the CODATA adjustment, the evaluation of the fundamental constant, e, is derived from a complex calculation and is no more related to a single experiment. But the development of single electron tunneling (SET) devices, started in the early 90s, has opened the path towards modern metrological systems as quantum current sources. Thus a new direct determination of e is possible by implementing an electron pump and the set-up of the quantum metrological triangle (QMT) in combination with the experiments linking mechanical and electrical units. Furthermore, we show how the QMT experiment can contribute to the establishment of a new system of units based on fundamental constants of physics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • R.A. Millikan, Phys. Rev. 2, 109 (1913)

  • D. Wineland, P. Ekstrom, H. Dehmelt, Phys. Rev. Lett. 31, 1279 (1973)

    Google Scholar 

  • R.S. van Dyck Jr., P.B. Schwinberg, H.G. Dehmelt, in Atomic Physics 9, edited by R.S. van Dyck Jr., E.N. Forston (World Scientific, Singapore, 1984), p. 53

  • F. Piquemal, A. Bounouh, L. Devoille, N. Feltin, O. Thevenot, G. Trapon, C.R. Physique 5, 857 (2004)

    Google Scholar 

  • CIPM (1988), Recommandations 1 and 2 (CI-1988), 77e session; Resolution 6 of the 18th CGPM, Metrologia 25, 115 (1988)

  • W. Poirier, F. Schopfer, Eur. Phys. J. Special Topics 172, 207 (2009)

    Google Scholar 

  • B. Jeanneret, S. Benz, Eur. Phys. J. Special Topics 172, 181 (2009)

    Google Scholar 

  • I.M. Mills, P.J. Mohr, T.J. Quinn, B.N. Taylor, E.R. Williams, Metrologia 42, 71 (2005)

  • C. Bordé, Phil. Trans. R. Soc. Lond. Ser. A 363, 2177 (2005)

    Google Scholar 

  • I.M. Mills, P.J. Mohr, T.J. Quinn, B.N. Taylor, E.R. Williams, Metrologia 43, 227 (2006)

  • P.J. Mohr, Metrologia 45, 129 (2008)

  • J.J. Thomson, Philos. Mag. 44, 293 (1897)

    Google Scholar 

  • W. Crookes, Lecture delivered to the British Association for the Advancement of Science at Sheffield, Friday August 22, 1879

  • J. Perrin, Comptes Rendus de l’Académie des Sciences CXXI, 1130 (1895)

  • H.L.F. von Helmholtz, J. Chem. Soc. 39, 290 (1881)

    Google Scholar 

  • M. Faraday, Philos. Trans. 123, 48 (1833)

    Google Scholar 

  • G.J. Stoney, in Proceedings of the British Association for the advancement of science, Belfast, 1874; G.J. Stoney, Scient. Proc. Royal Dublin Soc. 3, 51 (1881)

  • G.J. Stoney, Phil. Mag. 38, 418 (1894)

    Google Scholar 

  • G.J. Stoney, Phys. Mag. (series 5) 11, 381 (1881)

    Google Scholar 

  • G. Cohen Tannoudji, Eur. Phys. J. Special Topics 172, 5 (2009)

    Google Scholar 

  • R.A. Millikan, Philos. Mag. J. Sci. 19, 209 (1910)

  • R.A. Millikan, Phil. Mag. 34, 1 (1917); R.A. Millikan, Phys. Rev. 22, 1 (1923)

    Google Scholar 

  • F.W. Clarke, J. Am. Chem. Soc. 16, 179 (1894)

    Google Scholar 

  • E. Bäcklin, Ph.D. thesis, Uppsala University, 1928; E. Bäcklin, Nature, Lond. 135, 32 (1935)

  • R.T. Birge, Phys. Rev. Supl. 1, 1 (1929)

    Google Scholar 

  • F.G. Dunnington, Rev. Mod. Phys. 11, 65 (1939)

    Google Scholar 

  • Kellström, Nature, Lond. 136, 682 (1935)

  • H.R. Robinson, Rep. Prog Phys. 2, 247 (1935); H.R. Robinson, Rep. Prog. Phys. 4, 212 (1937)

  • R.T. Birge, Phys. Rev. 13, 233 (1941)

    Google Scholar 

  • W.E. Lamb, R.C. Rutherford, Phys. Rev. 86, 1014 (1952)

    Google Scholar 

  • J.W.M. Dumond, E.R. Cohen, Rev. Mod. Phys. 25, 691 (1953)

    Google Scholar 

  • J.W.M. Dumond, E.R. Cohen, Rev. Mod. Phys. 37, 537 (1965)

    Google Scholar 

  • E.R. Cohen, B.N. Taylor, J. Phys. Chem. Ref. Data 2, 663 (1973)

    Google Scholar 

  • B.D. Josephson, Phys. Lett. 1, 251 (1962)

  • J. Clarke, Phys. Rev. Lett. 21, 1566 (1968)

    Google Scholar 

  • Le Système International d’Unités – The International System of Units, 8th edition, BIPM (2006)

  • R.E. Elmquist, M.E. Cage, Y. Tang, A.-M. Jeffery, J.R. Kinard Jr., R.F. Dziuba, N.M. Oldham, E.R. Williams, J. Res. Natl. Inst. Stand. Technol. 106, 65 (2001)

    Google Scholar 

  • P.J. Mohr, B.N. Taylor, D. Newell, Rev. Modern Phys. 80, 633 (2008)

    Google Scholar 

  • A.M. Thompson, D.G. Lampard, Nature 177, 888 (1956)

    Google Scholar 

  • H. Bachmair, Eur. Phys. J. Special Topics 172, 257 (2009)

    Google Scholar 

  • K. Von Klitzing, G. Dorda, M. Pepper, Phys. Rev. Lett. 45, 494 (1980)

    Google Scholar 

  • E.R. Cohen, B.N. Taylor, Rev. Mod. Phys. 59, 1121 (1987)

    Google Scholar 

  • P.J. Mohr, B.N. Taylor, Rev. Mod. Phys. 72, 351 (2000)

    Google Scholar 

  • P.J. Mohr, B.N. Taylor, Rev. Mod. Phys. 77, 1 (2005)

    Google Scholar 

  • S. Karshenboïm, Eur. Phys. J. Special Topics 172, 385 (2009)

    Google Scholar 

  • D.V. Averin, K.K. Likharev, in Mesoscopic Phenomena in Solids, edited by Alsthuler B.L., Lee P.A. and Webb R.A., Mesoscopic Phenomena in Solids (Amsterdam, Noth-Holland: Elsevier, 1991), p. 173

  • H. Grabert, M.H. Devoret, Single charge tunneling Coulomb blockade phenomena in nanostructures, NATO ASI Series, Series B: Physics 294 (New York, Plenum Press, 1991)

  • K.K. Likharev, Proc. IEEE 87, 606 (1999)

    Google Scholar 

  • K. Flensberg, A.A. Odintsov, F. Liefrink, P. Teunissen, Int. J. Mod. Phys. B. 13, 2651 (1999)

    Google Scholar 

  • A. Kemppinen, M. Meschke, M. Möttönen, D.V. Averin, J.P. Pekola, Eur. Phys. J. Special Topics 172, 311 (2009)

    Google Scholar 

  • T.A. Fulton, G.J. Dolan, Phys. Rev. Lett. 59, 109 (1987)

    Google Scholar 

  • D.V. Averin, K.K. Likharev, J. Low Temp. Phys. 62, 345 (1986)

    Google Scholar 

  • H.R. Zeller, I. Giaver, Phys. Rev. 181, 789 (1969)

    Google Scholar 

  • H. Pothier, et al., Europhys. Lett. 17, 249 (1992)

  • B. Steck, Ph.D. thesis, University of Caen, 2007

  • B. Steck, A. Gonzalez-Cano, N. Feltin, L. Devoille, F. Piquemal, S. Lotkhov, A.B. Zorin, Metrologia 45, 482 (2008)

  • M.W. Keller, J.M. Martinis, A.H. Steinbach, N.M. Zimmerman, IEEE Trans. Inst. Meas. 46, 307 (1997)

    Google Scholar 

  • H. Pothier, Ph.D. thesis, Paris 6, 1991

  • H.D. Jensen, J.M. Martinis, Phys. Rev. B 46, 13 407 (1992)

    Google Scholar 

  • M. Covington, M. Keller, R.L. Kautz, J. Martinis, Phys. Rev. Lett. 84, 5192 (2000)

    Google Scholar 

  • M.W. Keller, Eur. Phys. J. Special Topics 172, 297 (2009)

    Google Scholar 

  • J.M. Martinis, M.H. Devoret, J. Clarke, Phys. Rev. B 35, 4682 (1987)

    Google Scholar 

  • D. Vion, P.F. Orfila, P. Joyez, D. Esteve, M.H. Devoret, J. Appl. Phys. 77, 2519 (1995)

    Google Scholar 

  • A. Zorin, Rev. Sci. Instrum. 66, 4296 (1995)

    Google Scholar 

  • Y. De Wilde, F. Gay, F. Piquemal, G. Genevès, Trans. Inst. Meas. 50, 231 (2001)

    Google Scholar 

  • M.W. Keller, J.M. Martinis, N.M. Zimmerman, A.H. Steinbach, Appl. Phys. Lett. 69, 1804 (1996)

    Google Scholar 

  • S.V. Lotkhov, S.A. Bogoslovsky, A.B. Zorin, J. Niemeyer, Appl. Phys. Lett. 78, 946 (2001)

    Google Scholar 

  • A.B. Zorin, S.V. Lotkhov, H. Zangerle, J. Niemeyer, J. Appl. Phys. 88, 2665 (2000)

    Google Scholar 

  • H.E. Van der Brom, et al., IEEE Trans. Instrum. Meas. 52, 584 (2003)

    Google Scholar 

  • A. Fujiwara, N.M. Zimmerman, Y. Ono, Y. Takahashi, Appl. Phys. Lett. 84, 1323 (2004)

    Google Scholar 

  • N.M. Zimmerman, A. Fujiwara, H. Inokawa, Y. Takahashi, Appl. Phys. Lett. 89, 52102 (2006)

    Google Scholar 

  • N.M. Zimmerman, E. Hourdakis, Y. Ono, A. Fujiwara, Y. Takahashi, J. Appl. Phys. 96, 5254 (2004)

    Google Scholar 

  • N.M. Zimmerman, W.H. Huber, A. Fujiwara, Y. Takahashi, Appl. Phys. Lett. 79, 3188 (2001)

    Google Scholar 

  • A. Fujiwara, K. Nishiguchi, Y. Ono, Appl. Phys. Lett. 92, 42102 (2008)

    Google Scholar 

  • M.D. Blumenthal, B. Kaestner, L. Li, S. Giblin, T.J.B.M. Janssen, M. Pepper, D. Anderson, G. Jones, D.A. Ritchie, Nature 3, 343 (2007)

  • F. Hekking, Y.V. Nazarov, Phys. Rev. B 44, 9110 (1991)

    Google Scholar 

  • L.P. Kouwenhoven, A.T. Johnson, N.C. van der Vaart, C.J.P.M. Harmans, Phys. Rev. Lett. 67, 1626 (1991)

    Google Scholar 

  • J.M. Shilton, D.R. Mace, V.I. Talyanskii, Y. Galperin, M.Y. Simmons, M. Pepper, D.A. Ritchie, J. Phys. Condens. Matter. 8, L337 (1996)

  • V.I. Talyanskii, J.M. Shilton, M. Pepper, C.G. Smith, C.J.B. Ford, E.H. Linfield, D.A. Ritchie, G.A.C. Jones, Phys. Rev. B 56, 15180 (1997)

    Google Scholar 

  • N.E. Fletcher, T.J.B.M. Janssen, A. Hartland, BEMC Digest (2001)

  • N.E. Fletcher, J. Ebbecke, T.J.B. Janssen, F.J. Alhers, M. Pepper, H.E. Beere, D.A. Ritchie, Phys. Rev. B 68, 245310 (2003)

    Google Scholar 

  • J. Ebbecke, N.E. Fletcher, T.J.B.M. Janssen, F.J. Alhers, M. Pepper, H.E. Beere, D.A. Ritchie, Appl. Phys. Lett. 84, 4319 (2004)

    Google Scholar 

  • J. Ebbecke, C.J. Strobl, A. Wixforth, Phys. Rev. B 70, 233401 (2004)

    Google Scholar 

  • P.J. Leek, M.R. Buitelaar, V.I. Talyanskii, C.G. Smith, D. Anderson, G.A.C. Jones, J. Wei, D.H. Cobden, Phys. Rev. Lett. 95, 256802 (2005)

    Google Scholar 

  • P. Delsing, K.K. Likharev, L.S. Kuzmin, T. Claeson, Phys. Rev. Lett. 63, 1861 (1989)

    Google Scholar 

  • R.J. Schoelkopf, P. Wahlgren, A.A. Kozhevnikov, P. Delsing, D.E. Prober, Science 280, 1238 (1998)

  • J. Bylander, T. Duty, P. Delsing, Nature 434, 361 (2005)

    Google Scholar 

  • H. Brenning, S. Kafanov, T. Duty, S. Kubatkin, P. Delsing, J. Appl. Phys. 100, 114321 (2006)

    Google Scholar 

  • F. Piquemal, L. Devoille, N. Feltin, B. Steck, edited by T.W. Hansch, S. Leschiutta, A.J. Wallard and M.L. Rastello, in Proceedings of the international school of physics “Enrico Fermi” course CLXVI “Metrology and fundamental constants” (IOS Press, 2007)

  • K.K. Likharev, A.B. Zorin, J. Low Temp. Phys. 59, 347-382 (1985)

    Google Scholar 

  • F. Piquemal, G. Genevès, Metrologia 37, 207 (2000)

  • M.W. Keller, Metrologia 45, 102 (2008)

  • J.S. Tsai, A.K. Jain, J.E. Lukens, Phys. Rev. Lett. 51, 316 (1983)

    Google Scholar 

  • A.K. Jain, J.E. Lukens, J.S. Tsai, Phys. Rev. Lett. 58, 1165 (1987)

    Google Scholar 

  • A. Hartland, K. Jones, J.M. Williams, B.L. Gallagher, T. Galloway, Phys. Rev. Lett. 66, 969 (1991)

    Google Scholar 

  • B. Jeckelmann, A.D. Inglis, B. Jeanneret, IEEE T. Instrum. Meas. 44, 269 (1995)

    Google Scholar 

  • B. Jeckelmann, B. Jeanneret, Rep. Prog. Phys. 64, 1603 (2000)

    Google Scholar 

  • P.J. Mohr, B.N. Taylor, D.B. Newell, Report, 18th meeting of the CCU (Comité Consultatif sur les Unités), 11–13 June (2007)

  • I.K. Harvey, Rev. Sci. Instrum. 43, 1626 (1972)

    Google Scholar 

  • J.C. Gallop, F. Piquemal, Chapter 9 in The SQUID Handbook Vol. II, edited by J. Clarke, A.I. Braginski (Wiley-VCH Verlag GmbH&Co.FgaA, Weinheim, 2006), p. 95

  • R. Elmquist, N.M. Zimmerman, W.H. Huber, IEEE Trans. Instrum. Meas. 52, 590 (2003)

    Google Scholar 

  • A. Manninen, O. Hahtela, P. Hokonen, P. Helistö, A. Kemppinen, M. Möttönen, M. Paalanen, J. Pekola, A. Satrapinski, H. Seppä H., in Proc. of the Conference on Precision Electromagnetic Measurements, edited by A.H. Cookson and T. Winter (Boulder, 2008), p. 630

  • J. Clarke, A.I. Braginski (Editors) The SQUID Handbook, Vols. I and II (Wiley-VCH Verlag GmbH&Co.FgaA, Weinheim, 2004–2006)

  • M.W. Keller, N.M. Zimmerman, A.L. Eichenberger, Metrologia 44, 505 (2007)

  • M.W. Keller, A.L. Eichenberger, J.M. Martinis, N.M. Zimmerman, Science 285, 1706 (1999)

  • H. Scherer, S.V. Lotkhov, G.D. Willenberg, in Proc. of the Conference on Precision Electromagnetic Measurements, edited by A.H. Cookson and T. Winter (Boulder, 2008), p. 278

  • F. Overney, B. Jeanneret, M. Furlan, IEEE Trans. Instrum. Meas. 49, 1326 (2000)

    Google Scholar 

  • B.P. Kibble, in Atomic Masses and Fundamental constants 5, edited by J.H. Sanders and A.H. Wapstra (Plenum, New York, 1976), p. 545

  • A. Eichenberger, G. Genevès, P. Gournay, Eur. Phys. J. Special Topics 172, 363 (2009)

    Google Scholar 

  • M.W. Keller, F. Piquemal, N. Feltin, B. Steck, L. Devoille, Metrologia 45, 330 (2008)

    Google Scholar 

  • J. Kovalevsky, Report of the Working Group of the Académie des Sciences, CIPM (2007)

Download references

Author information

Authors and Affiliations

  1. Laboratoire National de Métrologie et d’Essais (LNE), 29 Av. Roger Hennequin, 78197, Trappes, France

    N. Feltin & F. Piquemal

Authors
  1. N. Feltin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Piquemal
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feltin, N., Piquemal, F. Determination of the elementary charge and the quantum metrological triangle experiment. Eur. Phys. J. Spec. Top. 172, 267–296 (2009). https://doi.org/10.1140/epjst/e2009-01054-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2009-01054-2

Search

Navigation