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A coherent nanomechanical oscillator driven by single-electron tunnelling

Abstract

A single-electron transistor embedded in a nanomechanical resonator represents an extreme limit of electron–phonon coupling. While it allows fast and sensitive electromechanical measurements, it also introduces back-action forces from electron tunnelling that randomly perturb the mechanical state. Despite the stochastic nature of this back-action, it has been predicted to create self-sustaining coherent mechanical oscillations under strong coupling conditions. Here, we verify this prediction using real-time measurements of a vibrating carbon nanotube transistor. This electromechanical oscillator has some similarities with a laser. The single-electron transistor pumped by an electrical bias acts as a gain medium and the resonator acts as a phonon cavity. Although the operating principle is unconventional because it does not involve stimulated emission, we confirm that the output is coherent. We demonstrate other analogues of laser behaviour, including injection locking, classical squeezing through anharmonicity and frequency narrowing through feedback.

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Fig. 1: Strongly coupled single-electron electromechanics.
Fig. 2: Mechanical resonance and oscillation.
Fig. 3: Coherence of the free-running oscillator.
Fig. 4: Tuning the coherence with a gate voltage.
Fig. 5: Injection locking of the nanomechanical oscillator.
Fig. 6: Stabilizing the oscillator with feedback.

Data availability

The data represented in Figs. 26 are available as source data in Supplementary Data 15. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We acknowledge A. Bachtold, E. M. Gauger, Y. Pashkin, A. Romito and M. Woolley for discussions, and T. Orton for technical support. This work was supported by EPSRC (EP/N014995/1, EP/R029229/1), DSTL, Templeton World Charity Foundation, the Royal Academy of Engineering, the European Research Council (grant agreement 818751), and the EU H2020 European Microkelvin Platform (grant agreement 824109).

Author information

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Contributions

Y.W. fabricated the device following a recipe devised by T.P., and performed the experiment and analysis with contributions from N.A., F.J.S. and E.A.L. Y.W. and E.A.L. wrote the manuscript. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to E. A. Laird.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–9, Methods, Discussion and References.

Supplementary Data 1

Source Data for Fig. 2.

Supplementary Data 2

Source Data for Fig. 3.

Supplementary Data 3

Source Data for Fig. 4.

Supplementary Data 4

Source Data for Fig. 5.

Supplementary Data 5

Source Data for Fig. 6.

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Wen, Y., Ares, N., Schupp, F.J. et al. A coherent nanomechanical oscillator driven by single-electron tunnelling. Nat. Phys. 16, 75–82 (2020). https://doi.org/10.1038/s41567-019-0683-5

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