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Picosecond coherent electron motion in a silicon single-electron source

Abstract

An advanced understanding of ultrafast coherent electron dynamics is necessary for the application of submicrometre devices under a non-equilibrium drive to quantum technology, including on-demand single-electron sources1, electron quantum optics2,3,4, qubit control5,6,7, quantum sensing8,9 and quantum metrology10. Although electron dynamics along an extended channel has been studied extensively2,3,4,11, it is hard to capture the electron motion inside submicrometre devices. The frequency of the internal, coherent dynamics is typically higher than 100 GHz, beyond the state-of-the-art experimental bandwidth of less than 10 GHz (refs. 6,12,13). Although the dynamics can be detected by means of a surface-acoustic-wave quantum dot14, this method does not allow for a time-resolved detection. Here we theoretically and experimentally demonstrate how we can observe the internal dynamics in a silicon single-electron source that comprises a dynamic quantum dot in an effective time-resolved fashion with picosecond resolution using a resonant level as a detector. The experimental observations and the simulations with realistic parameters show that a non-adiabatically excited electron wave packet15 spatially oscillates quantum coherently at ~250 GHz inside the source at 4.2 K. The developed technique may, in future, enable the detection of fast dynamics in cavities, the control of non-adiabatic excitations15 or a single-electron source that emits engineered wave packets16. With such achievements, high-fidelity initialization of flying qubits5, high-resolution and high-speed electromagnetic-field sensing8 and high-accuracy current sources17 may become possible.

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Fig. 1: Internal coherent dynamics in the single-electron source.
Fig. 2: Schematic three-dimensional (left) and top (right) images of the device structure.
Fig. 3: Experimental observation of current oscillations related to the coherent dynamics.
Fig. 4: Frequency dependence of the current oscillations.
Fig. 5: Calculated frequency dependence of the current oscillations.

Data availability

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

Code availability

The computer codes that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

References

  1. 1.

    Bäuerle, C. et al. Coherent control of single electrons: a review of current progress. Rep. Prog. Phys. 81, 056503 (2018).

    Article  Google Scholar 

  2. 2.

    Bocquillon, E. et al. Electron quantum optics: partitioning electrons one by one. Phys. Rev. Lett. 108, 196803 (2012).

    CAS  Article  Google Scholar 

  3. 3.

    Jullien, T. et al. Quantum tomography of an electron. Nature 514, 603–607 (2014).

    CAS  Article  Google Scholar 

  4. 4.

    Ubbelohde, N. et al. Partitioning of on-demand electron pairs. Nat. Nanotechnol. 10, 46–49 (2015).

    CAS  Article  Google Scholar 

  5. 5.

    Yamamoto, M. et al. Electrical control of a solid-state flying qubit. Nat. Nanotechnol. 7, 247–251 (2012).

    CAS  Article  Google Scholar 

  6. 6.

    Hayashi, T., Fujisawa, T., Cheong, H. D., Jeong, Y. H. & Hirayama, Y. Coherent manipulation of electronic states in a double quantum dot. Phys. Rev. Lett. 91, 226804 (2003).

    CAS  Article  Google Scholar 

  7. 7.

    Koppens, F. H. L. et al. Driven coherent oscillations of a single electron spin in a quantum dot. Nature 442, 766–771 (2006).

    CAS  Article  Google Scholar 

  8. 8.

    Johnson, N. et al. Ultrafast voltage sampling using single-electron wavepackets. Appl. Phys. Lett. 110, 102105 (2017).

    Article  Google Scholar 

  9. 9.

    Degen, C. L., Reinhard, F. & Cappellaro, P. Quantum sensing. Rev. Mod. Phys. 89, 035002 (2017).

    Article  Google Scholar 

  10. 10.

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

    Article  Google Scholar 

  11. 11.

    Johnson, N. et al. LO-phonon emission rate of hot electrons from an on-demand single-electron source in a GaAs/AlGaAs heterostructure. Phys. Rev. Lett. 121, 137703 (2018).

    CAS  Article  Google Scholar 

  12. 12.

    Petersson, K. D., Petta, J. R., Lu, H. & Gossard, A. C. Quantum coherence in a one-electron semiconductor charge qubit. Phys. Rev. Lett. 105, 246804 (2010).

    CAS  Article  Google Scholar 

  13. 13.

    Kim, D. et al. Microwave-driven coherent operation of a semiconductor quantum dot charge qubit. Nat. Nanotechnol. 10, 243–247 (2015).

    CAS  Article  Google Scholar 

  14. 14.

    Kataoka, M. et al. Coherent time evolution of a single-electron wave function. Phys. Rev. Lett. 102, 156801 (2009).

    CAS  Article  Google Scholar 

  15. 15.

    Kataoka, M. et al. Tunable nonadiabatic excitation in a single-electron quantum dot. Phys. Rev. Lett. 106, 126801 (2011).

    CAS  Article  Google Scholar 

  16. 16.

    Ryu, S., Kataoka, M. & Sim, H.-S. Ultrafast emission and detection of a single-electron Gaussian wave packet: a theoretical study. Phys. Rev. Lett. 117, 146802 (2016).

    Article  Google Scholar 

  17. 17.

    Giblin, S. P. et al. Evidence for universality of tunable-barrier electron pumps. Metrologia 56, 044004 (2019).

    Article  Google Scholar 

  18. 18.

    Kaestner, B. & Kashcheyevs, V. Non-adiabatic quantized charge pumping with tunable-barrier quantum dots: a review of current progress. Rep. Prog. Phys. 78, 103901 (2015).

    Article  Google Scholar 

  19. 19.

    Kashcheyevs, V. & Kaestner, B. Universal decay cascade model for dynamic quantum dot initialization. Phys. Rev. Lett. 104, 186805 (2010).

    Article  Google Scholar 

  20. 20.

    Friesen, M., Chutia, S., Tahan, C. & Coppersmith, S. N. Valley splitting theory of SiGe/Si/SiGe quantum wells. Phys. Rev. B 75, 115318 (2007).

    Article  Google Scholar 

  21. 21.

    van der Vaart, N. C. et al. Resonant tunneling through two discrete energy states. Phys. Rev. Lett. 74, 4702–4705 (1995).

    Article  Google Scholar 

  22. 22.

    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 

  23. 23.

    Yamahata, G., Giblin, S. P., Kataoka, M., Karasawa, T. & Fujiwara, A. Gigahertz single-electron pumping in silicon with an accuracy better than 9.2 parts in 107. Appl. Phys. Lett. 109, 013101 (2016).

    Article  Google Scholar 

  24. 24.

    Yamahata, G., Nishiguchi, K. & Fujiwara, A. Gigahertz single-trap electron pumps in silicon. Nat. Commun. 5, 5038 (2014).

    CAS  Article  Google Scholar 

  25. 25.

    Yamahata, G., Giblin, S. P., Kataoka, M., Karasawa, T. & Fujiwara, A. High-accuracy current generation in the nanoampere regime from a silicon single-trap electron pump. Sci. Rep. 7, 45137 (2017).

    CAS  Article  Google Scholar 

  26. 26.

    Rossi, A. et al. Gigahertz single-electron pumping mediated by parasitic states. Nano Lett. 18, 4141–4147 (2018).

    CAS  Article  Google Scholar 

  27. 27.

    Fujisawa, T. et al. Spontaneous emission spectrum in double quantum dot devices. Science 282, 932–935 (1998).

    CAS  Article  Google Scholar 

  28. 28.

    Yamahata, G., Karasawa, T. & Fujiwara, A. Gigahertz single-hole transfer in Si tunable-barrier pumps. Appl. Phys. Lett. 106, 023112 (2015).

    Article  Google Scholar 

  29. 29.

    Weber, C. et al. Probing confined phonon modes by transport through a nanowire double quantum dot. Phys. Rev. Lett. 104, 036801 (2010).

    CAS  Article  Google Scholar 

  30. 30.

    Liang, W. et al. Fabry–Perot interference in a nanotube electron waveguide. Nature 411, 665–669 (2001).

    CAS  Article  Google Scholar 

  31. 31.

    Dupont-Ferrier, E. et al. Coherent coupling of two dopants in a silicon nanowire probed by Landau–Zener–Stückelberg interferometry. Phys. Rev. Lett. 110, 136802 (2013).

    CAS  Article  Google Scholar 

  32. 32.

    Koch, M. et al. Spin read-out in atomic qubits in an all-epitaxial three-dimensional transistor. Nat. Nanotechnol. 14, 137–140 (2019).

    CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank K. Chida, H. Tanaka, T. Karasawa, S. P. Giblin, J. D. Fletcher and T. J. B. M. Janssen for useful discussions. This work was partly supported by JSPS KAKENHI Grant no. JP18H05258, by the UK Department for Business, Innovation, and Skills and by the EMPIR 15SIB08 e-SI-Amp Project. The latter project has received funding from the EMPIR programme co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme. This work was also supported by the National Research Foundation (Korea NRF) funded by the Korea Government via the SRC Center for Quantum Coherence in Condensed Matter (Grant no.2016R1A5A1008184).

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G.Y. measured the device, analysed the data, and performed the calculation of the pump map. S.R. performed the numerical calculation of the Schrödinger equation. G.Y. and M.K. conceived the idea of the experiment. S.R. and H.-S.S. developed the theory of the coherent dynamics and the scheme for the effective time-resolved detection with picosecond resolution. N.J. took supporting data of the current oscillations. A.F. fabricated the device. All the authors discussed the results. G.Y., S.R. and H.-S.S. wrote the manuscript with feedback from all authors. M.K., A.F. and H.-S.S. supervised the project.

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Correspondence to Gento Yamahata or H.-S. Sim or Masaya Kataoka.

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Supplementary Information

Supplementary Sections I–XV, Figs. 1–13, Table 1 and refs. 1–26.

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Yamahata, G., Ryu, S., Johnson, N. et al. Picosecond coherent electron motion in a silicon single-electron source. Nat. Nanotechnol. 14, 1019–1023 (2019). https://doi.org/10.1038/s41565-019-0563-2

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