Journal of Computational Electronics

, Volume 12, Issue 3, pp 397–404 | Cite as

Floquet scattering matrix approach to the phase noise of a single-electron source in the adiabatic regime

  • Michael Moskalets


We give the basic elements of the Floquet scattering matrix approach (Moskalets in Scattering Matrix Approach to Non-stationary Quantum Transport. Imperial College Press, London, 2011) to the dynamic quantum transport in mesoscopic and nanoscopic conductors. We use the scattering formalism to discuss the noise power spectrum of a single electron source working in the adiabatic regime and emitting particles into a chiral electron waveguide. The noise power is found to be quadratic at low frequencies and exponentially suppressed at high frequencies.


Floquet scattering matrix Single-electron source Finite-frequency noise 



I thank Mathias Albert and Markus Büttiker for helpful discussions and valuable comments on the manuscript. I thank the University of Geneva for warm hospitality, where part of this work was carried out.


  1. 1.
    Moskalets, M.V.: Scattering Matrix Approach to Non-Stationary Quantum Transport. Imperial College Press, London (2011) CrossRefGoogle Scholar
  2. 2.
    Blumenthal, M.D., Kaestner, B., Li, L., Giblin, S., Janssen, T.J.B.M., Pepper, M., Anderson, D., Jones, G., Ritchie, D.A.: Gigahertz quantized charge pumping. Nat. Phys. 3, 343–347 (2007) CrossRefGoogle Scholar
  3. 3.
    Fève, G., Mahé, A., Berroir, J.-M., Kontos, T., Plaçais, B., Glattli, D.C., Cavanna, A., Etienne, B., Jin, Y.: An on-demand coherent single-electron source. Science 316, 1169–1172 (2007) CrossRefGoogle Scholar
  4. 4.
    Kaestner, B., Kashcheyevs, V., Amakawa, S., Blumenthal, M., Li, L., Janssen, T.J.B.M., Hein, G., Pierz, K., Weimann, T., Siegner, U., Schumacher, H.W.: Single-parameter nonadiabatic quantized charge pumping. Phys. Rev. B 77, 153301 (2008) CrossRefGoogle Scholar
  5. 5.
    Fujiwara, A., Nishiguchi, K., Ono, Y.: Nanoampere charge pump by single-electron ratchet using silicon nanowire metal-oxide-semiconductor field-effect transistor. Appl. Phys. Lett. 92, 042102 (2008) CrossRefGoogle Scholar
  6. 6.
    Dubois, J., Jullien, T., Roulleau, P., Portier, F., Roche, P., Cavanna, A., Jin, Y., Wegscheider, W., Glattli, D.C.: (2013, in preparation) Google Scholar
  7. 7.
    Giblin, S.P., Kataoka, M., Fletcher, J.D., See, P., Janssen, T.J.B.M., Griffiths, J.P., Jones, G.A.C., Farrer, I., Ritchie, D.A.: Towards a quantum representation of the ampere using single electron pumps. Nat. Commun. 3, 930 (2012) CrossRefGoogle Scholar
  8. 8.
    Hohls, F., Welker, A.C., Leicht, C., Fricke, L., Kaestner, B., Mirovsky, P., Müller, A., Pierz, K., Siegner, U., Schumacher, H.W.: Semiconductor quantized voltage source. Phys. Rev. Lett. 109, 56802 (2012) CrossRefGoogle Scholar
  9. 9.
    Pekola, J.P., Saira, O.P., Maisi, V.F., Kemppinen, A., Möttönen, M., Pashkin, Y.A., Averin, D.V.: Single-electron current sources: towards a refined definition of ampere (unpublished). arXiv:1208.4030v1
  10. 10.
    Jehl, X., Voisin, B., Charron, T., Clapera, P., Ray, S., Roche, B., Sanquer, M., Djordjevic, S., Devoille, L., Wacquez, R., Vinet, M.: A hybrid metal/semiconductor electron pump for practical realization of a quantum ampere (unpublished). arXiv:1302.6470v1
  11. 11.
    Likharev, K., Zorin, A.B.: Theory of the Bloch-wave oscillations in small Josephson junctions. J. Low Temp. Phys. 59, 347–382 (1985) CrossRefGoogle Scholar
  12. 12.
    Flowers, J.: The route to atomic and quantum standards. Science 306, 1324–1330 (2004) CrossRefGoogle Scholar
  13. 13.
    Feltin, N., Piquemal, F.: Determination of the elementary charge and the quantum metrological triangle experiment. Eur. Phys. J. Spec. Top. 172, 267–296 (2009) CrossRefGoogle Scholar
  14. 14.
    Scherer, H., Camarota, B.: Quantum metrology triangle experiments: a status review. Meas. Sci. Technol. 23, 124010 (2012) CrossRefGoogle Scholar
  15. 15.
    Grenier, C., Hervé, R., Fève, G., Degiovanni, P.: Electron quantum optics in quantum Hall edge channels. Int. J. Mod. Phys. B 25, 1053–1073 (2011) MATHGoogle Scholar
  16. 16.
    Bennett, C.H., DiVincenzo, D.P.: Quantum information and computation. Nature 404, 247–255 (2000) CrossRefGoogle Scholar
  17. 17.
    Ol’khovskaya, S., Splettstoesser, J., Moskalets, M., Büttiker, M.: Shot noise of a mesoscopic two-particle collider. Phys. Rev. Lett. 101, 166802 (2008) CrossRefGoogle Scholar
  18. 18.
    Bocquillon, E., Freulon, V., Berroir, J.-M., Degiovanni, P., Plaçais, B., Cavanna, A., Jin, Y., Fève, G.: Coherence and indistinguishability of single electrons emitted by independent sources. Science 339, 1054–1057 (2013) CrossRefGoogle Scholar
  19. 19.
    Mahé, A., Parmentier, F.D., Bocquillon, E., Berroir, J.-M., Glattli, D., Kontos, T., Plaçais, B., Fève, G., Cavanna, A., Jin, Y.: Current correlations of an on-demand single-electron emitter. Phys. Rev. B 82, 201309(R) (2010) CrossRefGoogle Scholar
  20. 20.
    Albert, M., Flindt, C., Büttiker, M.: Accuracy of the quantum capacitor as a single-electron source. Phys. Rev. B 82, 041407(R) (2010) CrossRefGoogle Scholar
  21. 21.
    Parmentier, F.D., Bocquillon, E., Berroir, J.-M., Glattli, D., Plaçais, B., Fève, G., Albert, M., Flindt, C., Büttiker, M.: Current noise spectrum of a single-particle emitter: theory and experiment. Phys. Rev. B 85, 165438 (2012) CrossRefGoogle Scholar
  22. 22.
    Moskalets, M., Büttiker, M.: Floquet scattering theory of quantum pumps. Phys. Rev. B 66, 205320 (2002) CrossRefGoogle Scholar
  23. 23.
    Landauer, R.: Spatial variation of currents and fields due to localized scatterers in metallic conduction. IBM J. Res. Dev. 32, 306–316 (1988) MathSciNetCrossRefGoogle Scholar
  24. 24.
    Switkes, M., Marcus, C.M., Campman, K., Gossard, A.C.: An adiabatic quantum electron pump. Science 283, 1905–1908 (1999) CrossRefGoogle Scholar
  25. 25.
    Platero, G., Aguado, R.: Photon-assisted transport in semiconductor nanostructures. Phys. Rep. 395, 1–157 (2004) CrossRefGoogle Scholar
  26. 26.
    Arrachea, L.: Exact Green’s function renormalization approach to spectral properties of open quantum systems driven by harmonically time-dependent fields. Phys. Rev. B 75, 035319 (2007) CrossRefGoogle Scholar
  27. 27.
    Moskalets, M., Büttiker, M.: Adiabatic quantum pump in the presence of external ac voltages. Phys. Rev. B 69, 205316 (2004) CrossRefGoogle Scholar
  28. 28.
    Büttiker, M.: Scattering theory of current and intensity noise correlations in conductors and wave guides. Phys. Rev. B 46, 12485–12507 (1992) CrossRefGoogle Scholar
  29. 29.
    Blanter, Y.M., Büttiker, M.: Shot noise in mesoscopic conductors. Phys. Rep. 336, 1–166 (2000) CrossRefGoogle Scholar
  30. 30.
    Büttiker, M., Thomas, H., Prêtre, A.: Mesoscopic capacitors. Phys. Lett. A 180, 364–369 (1993) CrossRefGoogle Scholar
  31. 31.
    Klitzing, K., Dorda, G., Pepper, M.: New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980) CrossRefGoogle Scholar
  32. 32.
    Halperin, B.I.: Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential. Phys. Rev. B 25, 2185 (1982) MathSciNetCrossRefGoogle Scholar
  33. 33.
    Büttiker, M.: Absence of backscattering in the quantum Hall effect in multiprobe conductors. Phys. Rev. B 38, 9375 (1988) CrossRefGoogle Scholar
  34. 34.
    Prêtre, A., Thomas, H., Büttiker, M.: Dynamic admittance of mesoscopic conductors: discrete-potential model. Phys. Rev. B 54, 8130 (1996) CrossRefGoogle Scholar
  35. 35.
    Gabelli, J., Fève, G., Berroir, J.-M., Plaçais, B., Cavanna, A., Etienne, B., Jin, Y., Glattli, D.: Violation of Kirchhoff’s laws for a coherent RC circuit. Science 313, 499–502 (2006) CrossRefGoogle Scholar
  36. 36.
    Moskalets, M., Samuelsson, P., Büttiker, M.: Quantized dynamics of a coherent capacitor. Phys. Rev. Lett. 100, 086601 (2008) CrossRefGoogle Scholar
  37. 37.
    Moskalets, M., Büttiker, M.: Dynamic scattering channels of a double barrier structure. Phys. Rev. B 78(12), 035301 (2008) CrossRefGoogle Scholar
  38. 38.
    Moskalets, M., Büttiker, M.: Time-resolved noise of adiabatic quantum pumps. Phys. Rev. B 75, 035315 (2007) CrossRefGoogle Scholar
  39. 39.
    Gardiner, C.W., Zoller, P.: Quantum Noise. Springer, New York (2000) MATHGoogle Scholar
  40. 40.
    Clerk, A.A., Girvin, S.M., Marquardt, F., Schoelkopf, R.J.: Introduction to quantum noise, measurement, and amplification. Rev. Mod. Phys. 82, 1155–1208 (2010) MathSciNetMATHCrossRefGoogle Scholar
  41. 41.
    Breit, G., Wigner, E.: Capture of slow neutrons. Phys. Rev. 49, 519 (1936) MATHCrossRefGoogle Scholar
  42. 42.
    Splettstoesser, J., Ol’khovskaya, S., Moskalets, M., Büttiker, M.: Electron counting with a two-particle emitter. Phys. Rev. B 78, 205110 (2008) CrossRefGoogle Scholar
  43. 43.
    Aguado, R., Kouwenhoven, L.P.: Double quantum dots as detectors of high-frequency quantum noise in mesoscopic conductors. Phys. Rev. Lett. 84, 1986–1989 (2000) CrossRefGoogle Scholar
  44. 44.
    Battista, F., Moskalets, M., Albert, M., Samuelsson, P.: Quantum heat fluctuations of single particle sources. Phys. Rev. Lett. 110, 126602 (2013) CrossRefGoogle Scholar
  45. 45.
    Moskalets, M., Büttiker, M.: Heat production and current noise for single- and double-cavity quantum capacitors. Phys. Rev. B 80, 081302(R) (2009) CrossRefGoogle Scholar
  46. 46.
    Haack, G., Moskalets, M., Splettstoesser, J., Büttiker, M.: Coherence of single-electron sources from Mach-Zehnder interferometry. Phys. Rev. B 84, 081303 (2011) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Metal and Semiconductor PhysicsNTU “Kharkiv Polytechnic Institute”KharkivUkraine

Personalised recommendations