Quantum stochastic resonance in an a.c.-driven single-electron quantum dot


In stochastic resonance, the combination of a weak signal with noise leads to its amplification and optimization1. This phenomenon has been observed in several systems in contexts ranging from palaeoclimatology, biology, medicine, sociology and economics to physics1,2,3,4,5,6,7,8,9. In all these cases, the systems were either operating in the presence of thermal noise or were exposed to external classical noise sources. For quantum-mechanical systems, it has been theoretically predicted that intrinsic fluctuations lead to stochastic resonance as well, a phenomenon referred to as quantum stochastic resonance1,10,11, but this has not been reported experimentally so far. Here we demonstrate tunnelling-controlled quantum stochastic resonance in the a.c.-driven charging and discharging of single electrons on a quantum dot. By analysing the counting statistics12,13,14,15,16, we demonstrate that synchronization between the sequential tunnelling processes and a periodic driving signal passes through an optimum, irrespective of whether the external frequency or the internal tunnel coupling is tuned.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Experimental set-up, device operation and statistical analysis.
Fig. 2: Frequency-dependent stochastic resonance.
Fig. 3: Temporal modulation of the tunnelling process.
Fig. 4: Tunnel coupling-dependent stochastic resonance.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon request.


  1. 1.

    Gammaitoni, L., Hänggi, P., Jung, P. & Marchesoni, F. Stochastic resonance. Rev. Mod. Phys. 70, 223–288 (1998).

    ADS  Article  Google Scholar 

  2. 2.

    Lee, I. Y., Liu, X. L., Kosko, B. & Zhou, C. W. Nanosignal processing: stochastic resonance in carbon nanotubes that detect subthreshold signals. Nano Lett. 3, 1683–1686 (2003).

    ADS  Article  Google Scholar 

  3. 3.

    Badzey, R. L. & Mohanty, P. Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance. Nature 437, 995–998 (2005).

    ADS  Article  Google Scholar 

  4. 4.

    Nishiguchi, K. & Fujiwara, A. Detecting signals buried in noise via nanowire transistors using stochastic resonance. Appl. Phys. Lett. 101, 193108 (2012).

    ADS  Article  Google Scholar 

  5. 5.

    Venstra, W. J., Westra, H. J. R. & van der Zant, H. S. J. Stochastic switching of cantilever motion. Nat. Commun. 4, 2624 (2013).

    ADS  Article  Google Scholar 

  6. 6.

    Abbaspour, H., Trebaol, S., Morier-Genoud, F., Portella-Oberli, M. T. & Deveaud, B. Stochastic resonance in collective exciton–polariton excitations inside a GaAs microcavity. Phys. Rev. Lett. 113, 057401 (2014).

    ADS  Article  Google Scholar 

  7. 7.

    Sun, G. et al. Detection of small single-cycle signals by stochastic resonance using a bistable superconducting quantum interference devices. Appl. Phys. Lett. 106, 172602 (2015).

    ADS  Article  Google Scholar 

  8. 8.

    Stroescu, I., Hume, D. B. & Oberthaler, M. K. Dissipative double-well potential for cold atoms: kramers rate and stochastic resonance. Phys. Rev. Lett. 117, 243005 (2016).

    ADS  Article  Google Scholar 

  9. 9.

    Monifi, F. et al. Optomechanically induced stochastic resonance and chaos transfer between optical fields. Nat. Photon. 10, 399–405 (2016).

    ADS  Article  Google Scholar 

  10. 10.

    Löfstedt, R. & Coppersmith, S. N. Quantum stochastic resonance. Phys. Rev. Lett. 72, 1947–1950 (1994).

    ADS  Article  Google Scholar 

  11. 11.

    Grifoni, M. & Hänggi, P. Coherent and incoherent quantum stochastic resonance. Phys. Rev. Lett. 76, 1611–1614 (1996).

    ADS  Article  Google Scholar 

  12. 12.

    Callenbach, L., Hänggi, P., Linz, S. J., Freund, J. A. & Schimansky-Geier, L. Oscillatory systems driven by noise: frequency and phase synchronization. Phys. Rev. E 65, 051110 (2002).

    ADS  Article  Google Scholar 

  13. 13.

    Talkner, P. Statistics of entrance times. Physica A 325, 124–135 (2003).

    ADS  MathSciNet  Article  Google Scholar 

  14. 14.

    Talkner, P., Machura, Ł., Schindler, M., Hänggi, P. & Łuczka, J. Statistics of transition times, phase diffusion and synchronization in periodically driven bistable systems. New J. Phys. 7, 14 (2005).

    Article  Google Scholar 

  15. 15.

    Gustavsson, S. et al. Counting statistics of single-electron transport in a quantum dot. Phys. Rev. Lett. 96, 076605 (2006).

    ADS  Article  Google Scholar 

  16. 16.

    Wagner, T. et al. Strong suppression of shot noise in a feedback-controlled single-electron transistor. Nat. Nanotechnol. 12, 218–222 (2017).

    ADS  Article  Google Scholar 

  17. 17.

    Kouwenhoven, L. P., Austing, D. G. & Tarucha, S. Few-electron quantum dots. Rep. Prog. Phys. 64, 701–736 (2001).

    ADS  Article  Google Scholar 

  18. 18.

    Kouwenhoven, L. P., Johnson, A. T., van der Vaart, N. C., Harmans, C. J. P. M. & Foxon, C. T. Quantized current in a quantum-dot turnstile using oscillating tunnel barriers. Phys. Rev. Lett. 67, 1626–1629 (1991).

    ADS  Article  Google Scholar 

  19. 19.

    Platonov, S. et al. Lissajous rocking ratchet: realization in a semiconductor quantum dot. Phys. Rev. Lett. 115, 106801 (2015).

    ADS  Article  Google Scholar 

  20. 20.

    Blumenthal, M. D. et al. Gigahertz quantized charge pumping. Nat. Phys. 3, 343–347 (2007).

    Article  Google Scholar 

  21. 21.

    Pekola, J. P. et al. Single-electron current sources: toward a refined definition of the ampere. Rev. Mod. Phys. 85, 1421–1472 (2013).

    ADS  Article  Google Scholar 

  22. 22.

    Shulgin, B., Neiman, A. & Anishchenko, V. Mean switching frequency locking in stochastic bistable systems driven by a periodic force. Phys. Rev. Lett. 75, 4157–4160 (1995).

    ADS  Article  Google Scholar 

  23. 23.

    Burk, H., de Jong, M. J. M. & Schönberger, C. Shot-noise in the single-electron regime. Phys. Rev. Lett. 75, 1610–1613 (1995).

    ADS  Article  Google Scholar 

  24. 24.

    Pekola, J. P. Towards quantum thermodynamics in electronic circuits. Nat. Phys. 11, 118–123 (2015).

    Article  Google Scholar 

  25. 25.

    Féve, G. et al. An on-demand coherent single-electron source. Science 316, 1169–1172 (2007).

    ADS  Article  Google Scholar 

  26. 26.

    Albert, M., Flindt, C. & Büttiker, M. Distributions of waiting times of dynamic single-electron emitters. Phys. Rev. Lett. 107, 086805 (2011).

    ADS  Article  Google Scholar 

  27. 27.

    Mozyrsky, D., Martin, I. & Hastings, M. B. Quantum-limited sensitivity of single-electron-transistor-based displacement detectors. Phys. Rev. Lett. 92, 018303 (2004).

    ADS  Article  Google Scholar 

  28. 28.

    LaHaye, M. D., Buu, O., Camarota, B. & Schwab, K. C. Approaching the quantum limit of a nanomechanical resonator. Science 304, 74–77 (2004).

    ADS  Article  Google Scholar 

  29. 29.

    Bonet, E., Deshmukh, M. M. & Ralph, D. C. Solving rate equations for electron tunneling via discrete quantum states. Phys. Rev. B 65, 045317 (2002).

    ADS  Article  Google Scholar 

  30. 30.

    Hofmann, A. et al. Measuring the degeneracy of discrete energy levels using a GaAs/AlGaAs quantum dot. Phys. Rev. Lett. 117, 206803 (2017).

    ADS  Article  Google Scholar 

Download references


This work was supported financially by the Research Training Group 1991 (DFG), the School for Contacts in Nanosystems (NTH), the Center for Quantum Engineering and Space-Time Research (QUEST), the Laboratory for Nano and Quantum Engineering (LNQE) and the ‘Fundamentals of Physics and Metrology’ initiative (T.W, J.C.B., E.R. and R.J.H.).

Author information




T.W. carried out the experiments, analysed the data and wrote the manuscript. J.C.B. and T.W. fabricated the device. E.P.R. grew the wafer material. P.T. and P.H. provided theory support. T.W., P.T., P.H. and R.J.H discussed the results. R.J.H. supervised the research. All authors contributed to editing the manuscript.

Corresponding author

Correspondence to Timo Wagner.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Journal peer review information: Nature Physics thanks Christian Flindt and the other anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figures and Methods

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wagner, T., Talkner, P., Bayer, J.C. et al. Quantum stochastic resonance in an a.c.-driven single-electron quantum dot. Nat. Phys. 15, 330–334 (2019). https://doi.org/10.1038/s41567-018-0412-5

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing