Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Computational Electronics Aims and scope Submit manuscript

Abstract

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.

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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. This supposition seems to be applicable also to the case of a DC biased quantum point contact with non-perfect transmission [29, 43].

References

  1. Moskalets, M.V.: Scattering Matrix Approach to Non-Stationary Quantum Transport. Imperial College Press, London (2011)

    Book  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  6. Dubois, J., Jullien, T., Roulleau, P., Portier, F., Roche, P., Cavanna, A., Jin, Y., Wegscheider, W., Glattli, D.C.: (2013, in preparation)

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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. Likharev, K., Zorin, A.B.: Theory of the Bloch-wave oscillations in small Josephson junctions. J. Low Temp. Phys. 59, 347–382 (1985)

    Article  Google Scholar 

  12. Flowers, J.: The route to atomic and quantum standards. Science 306, 1324–1330 (2004)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  14. Scherer, H., Camarota, B.: Quantum metrology triangle experiments: a status review. Meas. Sci. Technol. 23, 124010 (2012)

    Article  Google Scholar 

  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)

    MATH  Google Scholar 

  16. Bennett, C.H., DiVincenzo, D.P.: Quantum information and computation. Nature 404, 247–255 (2000)

    Article  Google Scholar 

  17. Ol’khovskaya, S., Splettstoesser, J., Moskalets, M., Büttiker, M.: Shot noise of a mesoscopic two-particle collider. Phys. Rev. Lett. 101, 166802 (2008)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  20. Albert, M., Flindt, C., Büttiker, M.: Accuracy of the quantum capacitor as a single-electron source. Phys. Rev. B 82, 041407(R) (2010)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  22. Moskalets, M., Büttiker, M.: Floquet scattering theory of quantum pumps. Phys. Rev. B 66, 205320 (2002)

    Article  Google Scholar 

  23. Landauer, R.: Spatial variation of currents and fields due to localized scatterers in metallic conduction. IBM J. Res. Dev. 32, 306–316 (1988)

    Article  MathSciNet  Google Scholar 

  24. Switkes, M., Marcus, C.M., Campman, K., Gossard, A.C.: An adiabatic quantum electron pump. Science 283, 1905–1908 (1999)

    Article  Google Scholar 

  25. Platero, G., Aguado, R.: Photon-assisted transport in semiconductor nanostructures. Phys. Rep. 395, 1–157 (2004)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  27. Moskalets, M., Büttiker, M.: Adiabatic quantum pump in the presence of external ac voltages. Phys. Rev. B 69, 205316 (2004)

    Article  Google Scholar 

  28. Büttiker, M.: Scattering theory of current and intensity noise correlations in conductors and wave guides. Phys. Rev. B 46, 12485–12507 (1992)

    Article  Google Scholar 

  29. Blanter, Y.M., Büttiker, M.: Shot noise in mesoscopic conductors. Phys. Rep. 336, 1–166 (2000)

    Article  Google Scholar 

  30. Büttiker, M., Thomas, H., Prêtre, A.: Mesoscopic capacitors. Phys. Lett. A 180, 364–369 (1993)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  33. Büttiker, M.: Absence of backscattering in the quantum Hall effect in multiprobe conductors. Phys. Rev. B 38, 9375 (1988)

    Article  Google Scholar 

  34. Prêtre, A., Thomas, H., Büttiker, M.: Dynamic admittance of mesoscopic conductors: discrete-potential model. Phys. Rev. B 54, 8130 (1996)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  36. Moskalets, M., Samuelsson, P., Büttiker, M.: Quantized dynamics of a coherent capacitor. Phys. Rev. Lett. 100, 086601 (2008)

    Article  Google Scholar 

  37. Moskalets, M., Büttiker, M.: Dynamic scattering channels of a double barrier structure. Phys. Rev. B 78(12), 035301 (2008)

    Article  Google Scholar 

  38. Moskalets, M., Büttiker, M.: Time-resolved noise of adiabatic quantum pumps. Phys. Rev. B 75, 035315 (2007)

    Article  Google Scholar 

  39. Gardiner, C.W., Zoller, P.: Quantum Noise. Springer, New York (2000)

    MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  41. Breit, G., Wigner, E.: Capture of slow neutrons. Phys. Rev. 49, 519 (1936)

    Article  MATH  Google Scholar 

  42. Splettstoesser, J., Ol’khovskaya, S., Moskalets, M., Büttiker, M.: Electron counting with a two-particle emitter. Phys. Rev. B 78, 205110 (2008)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  44. Battista, F., Moskalets, M., Albert, M., Samuelsson, P.: Quantum heat fluctuations of single particle sources. Phys. Rev. Lett. 110, 126602 (2013)

    Article  Google Scholar 

  45. Moskalets, M., Büttiker, M.: Heat production and current noise for single- and double-cavity quantum capacitors. Phys. Rev. B 80, 081302(R) (2009)

    Article  Google Scholar 

  46. Haack, G., Moskalets, M., Splettstoesser, J., Büttiker, M.: Coherence of single-electron sources from Mach-Zehnder interferometry. Phys. Rev. B 84, 081303 (2011)

    Article  Google Scholar 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

  1. Department of Metal and Semiconductor Physics, NTU “Kharkiv Polytechnic Institute”, 61002, Kharkiv, Ukraine

    Michael Moskalets

Authors
  1. Michael Moskalets
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael Moskalets.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moskalets, M. Floquet scattering matrix approach to the phase noise of a single-electron source in the adiabatic regime. J Comput Electron 12, 397–404 (2013). https://doi.org/10.1007/s10825-013-0481-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10825-013-0481-8

Keywords

Search

Navigation