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A quantum electromechanical interface for long-lived phonons

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Abstract

In single crystals, the suppression of intrinsic loss channels at low temperatures leads to exceptionally long mechanical lifetimes. Quantum electrical control of such long-lived mechanical oscillators would enable the development of phononic memory elements, sensors and transducers. The integration of piezoelectric materials is one approach to introducing electrical control, but the challenges of combining heterogeneous materials lead to severely limited phonon lifetimes. Here we present a non-piezoelectric silicon electromechanical system capable of operating in the gigahertz frequency band. Relying on a driving scheme based on electrostatic fields and the kinetic inductance effect in disordered superconductors, we demonstrate a parametrically enhanced electromechanical coupling of g/2π = 1.1 MHz, sufficient to enter the strong-coupling regime with a cooperativity of \({{{\mathcal{C}}}}={1,200}\). In our best devices, we measure mechanical quality factors approaching Q ≈ 107, measured at low-phonon numbers and millikelvin temperatures. Despite using strong electrostatic fields, we find the cavity mechanics system in the quantum ground state, verified by thermometry measurements. Simultaneously achieving ground-state operation, long mechanical lifetimes and strong coupling sets the stage for employing silicon electromechanical devices in hybrid quantum systems and as a tool for studying the origins of acoustic loss in the quantum regime.

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Fig. 1: Electrostatic transduction.
Fig. 2: Microwave spectrum.
Fig. 3: Mechanical lifetime measurements.
Fig. 4: Probing the limits of parametric enhancement.
Fig. 5: Demonstration of the strong-coupling regime.
Fig. 6: Interaction of the mechanical resonator with the TLS bath.

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Data availability

The datasets utilized to generate the plots in the paper are available on Zenodo (https://doi.org/10.5281/zenodo.7793615). All other data generated and/or analysed during the current study are available from the corresponding author upon reasonable request.

References

  1. McGuigan, D. F. et al. Measurements of the mechanical Q of single-crystal silicon at low temperatures. J. Low Temp. Phys. 30, 621–629 (1978).

    Article  ADS  Google Scholar 

  2. Renninger, W. H., Kharel, P., Behunin, R. O. & Rakich, P. T. Bulk crystalline optomechanics. Nat. Phys. 14, 601–607 (2018).

    Article  Google Scholar 

  3. Beccari, A. et al. Strained crystalline nanomechanical resonators with quality factors above 10 billion. Nat. Phys. 18, 436–441 (2022).

    Article  Google Scholar 

  4. MacCabe, G. S. et al. Nano-acoustic resonator with ultralong phonon lifetime. Science 370, 840–843 (2020).

    Article  ADS  Google Scholar 

  5. Clerk, A. A., Lehnert, K. W., Bertet, P., Petta, J. R. & Nakamura, Y. Hybrid quantum systems with circuit quantum electrodynamics. Nat. Phys. 16, 257–267 (2020).

    Article  Google Scholar 

  6. Safavi-Naeini, A. H., Thourhout, D. V., Baets, R. & Laer, R. V. Controlling phonons and photons at the wavelength scale: integrated photonics meets integrated phononics. Optica 6, 213–232 (2019).

    Article  ADS  Google Scholar 

  7. Han, X., Fu, W., Zou, C.-L., Jiang, L. & Tang, H. X. Microwave-optical quantum frequency conversion. Optica 8, 1050–1064 (2021).

    Article  ADS  Google Scholar 

  8. Wallucks, A., Marinković, I., Hensen, B., Stockill, R. & Gröblacher, S. A quantum memory at telecom wavelengths. Nat. Phys. 16, 772–777 (2020).

    Article  Google Scholar 

  9. Satzinger, K. J. et al. Quantum control of surface acoustic-wave phonons. Nature 563, 661–665 (2018).

    Article  ADS  Google Scholar 

  10. Lüpke, U. V. et al. Parity measurement in the strong dispersive regime of circuit quantum acoustodynamics. Nat. Phys. 18, 794–799 (2022).

    Article  Google Scholar 

  11. Wollack, E. A. et al. Quantum state preparation and tomography of entangled mechanical resonators. Nature 604, 463–467 (2022).

    Article  ADS  Google Scholar 

  12. Wollack, E. A. et al. Loss channels affecting lithium niobate phononic crystal resonators at cryogenic temperature. Appl. Phys. Lett. 118, 123501 (2021).

    Article  ADS  Google Scholar 

  13. Mirhosseini, M., Sipahigil, A., Kalaee, M. & Painter, O. Superconducting qubit to optical photon transduction. Nature 588, 599–603 (2020).

    Article  ADS  Google Scholar 

  14. Chu, Y. & Gröblacher, S. A perspective on hybrid quantum opto- and electromechanical systems. Appl. Phys. Lett. 117, 150503 (2020).

    Article  ADS  Google Scholar 

  15. Teufel, J. D. et al. Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359–363 (2011).

    Article  ADS  Google Scholar 

  16. Peterson, G. A. et al. Ultrastrong parametric coupling between a superconducting cavity and a mechanical resonator. Phys. Rev. Lett. 123, 247701 (2019).

    Article  ADS  Google Scholar 

  17. Kalaee, M. et al. Quantum electromechanics of a hypersonic crystal. Nat. Nanotechnol. 14, 334–339 (2019).

    Article  ADS  Google Scholar 

  18. Rouxinol, F. et al. Measurements of nanoresonator-qubit interactions in a hybrid quantum electromechanical system. Nanotechnology 27, 364003 (2016).

    Article  Google Scholar 

  19. Van Laer, R., Patel, R. N., McKenna, T. P., Witmer, J. D. & Safavi-Naeini, A. H. Electrical driving of X-band mechanical waves in a silicon photonic circuit. APL Photon. 3, 086102 (2018).

    Article  ADS  Google Scholar 

  20. Teufel, J. D. et al. Circuit cavity electromechanics in the strong-coupling regime. Nature 471, 204–208 (2011).

    Article  ADS  Google Scholar 

  21. Mason, W. P. & McSkimin, H. J. Attenuation and scattering of high frequency sound waves in metals and glasses. J. Acoust. Soc. Am. 19, 464–473 (1947).

  22. Zeng, F., Agnew, S. R., Raeisinia, B. & Myneni, G. R. Ultrasonic attenuation due to grain boundary scattering in pure niobium. J. Nondestr. Eval. 29, 93–103 (2010).

  23. Shearrow, A. et al. Atomic layer deposition of titanium nitride for quantum circuits. Appl. Phys. Lett. 113, 212601 (2018).

    Article  ADS  Google Scholar 

  24. Hazard, T. M. et al. Nanowire superinductance fluxonium qubit. Phys. Rev. Lett. 122, 010504 (2019).

    Article  ADS  Google Scholar 

  25. Pechenezhskiy, I. V., Mencia, R. A., Nguyen, L. B., Lin, Y.-H. & Manucharyan, V. E. The superconducting quasicharge qubit. Nature 585, 368–371 (2020).

    Article  ADS  Google Scholar 

  26. Zmuidzinas, J. Superconducting microresonators: physics and applications. Annu. Rev. Condens. Matter Phys. 3, 169–214 (2012).

    Article  Google Scholar 

  27. Xu, M., Han, X., Fu, W., Zou, C.-L. & Tang, H. X. Frequency-tunable high-Q superconducting resonators via wireless control of nonlinear kinetic inductance. Appl. Phys. Lett. 114, 192601 (2019).

    Article  ADS  Google Scholar 

  28. Vitale, S. A., Kedzierski, J., Healey, P., Wyatt, P. W. & Keast, C. L. Work-function-tuned TiN metal gate FDSOI transistors for subthreshold operation. IEEE Trans. Electron Devices 58, 419–426 (2010).

    Article  ADS  Google Scholar 

  29. Fleetwood, D. M. et al. Effects of oxide traps, interface traps, and ‘border traps’ on metal-oxide-semiconductor devices. J. Appl. Phys. 73, 5058–5074 (1993).

    Article  ADS  Google Scholar 

  30. Gutiérrez-D., E., Deen, J. & Claeys, C. Low Temperature Electronics (Academic Press, 2001); https://doi.org/10.1016/B978-012310675-9/50000-1

  31. Zhang, Y., Moser, J., Güttinger, J., Bachtold, A. & Dykman, M. I. Interplay of driving and frequency noise in the spectra of vibrational systems. Phys. Rev. Lett. 113, 255502 (2014).

    Article  ADS  Google Scholar 

  32. Grünhaupt, L. et al. Loss mechanisms and quasiparticle dynamics in superconducting microwave resonators made of thin-film granular aluminum. Phys. Rev. Lett. 121, 117001 (2018).

    Article  ADS  Google Scholar 

  33. Serniak, K. et al. Hot nonequilibrium quasiparticles in transmon qubits. Phys. Rev. Lett. 121, 157701 (2018).

    Article  ADS  Google Scholar 

  34. Phillips, W. A. Two-level states in glasses. Rep. Prog. Phys. 50, 1657 (1987).

    Article  ADS  Google Scholar 

  35. Müller, C., Cole, J. H. & Lisenfeld, J. Towards understanding two-level-systems in amorphous solids: insights from quantum circuits. Rep. Prog. Phys. 82, 124501 (2019).

    Article  ADS  Google Scholar 

  36. Ramos, T., Sudhir, V., Stannigel, K., Zoller, P. & Kippenberg, T. J. Nonlinear quantum optomechanics via individual intrinsic two-level defects. Phys. Rev. Lett. 110, 193602 (2013).

    Article  ADS  Google Scholar 

  37. Manenti, R. et al. Surface acoustic wave resonators in the quantum regime. Phys. Rev. B 93, 041411 (2016).

    Article  ADS  Google Scholar 

  38. Andersson, G. et al. Acoustic spectral hole-burning in a two-level system ensemble. npj Quantum Inf. 7, 15 (2021).

    Article  ADS  Google Scholar 

  39. Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Inf. 5, 105 (2019).

    Article  ADS  Google Scholar 

  40. Machielse, B. et al. Quantum interference of electromechanically stabilized emitters in nanophotonic devices. Phys. Rev. X 9, 031022 (2019).

    Google Scholar 

  41. Peruzzo, M., Trioni, A., Hassani, F., Zemlicka, M. & Fink, J. M. Surpassing the resistance quantum with a geometric superinductor. Phys. Rev. Appl. 14, 044055 (2020).

    Article  ADS  Google Scholar 

  42. Zhao, H., Bozkurt, A. & Mirhosseini, M. Electro-optic transduction in silicon via GHz-frequency nanomechanics. Preprint at https://arxiv.org/abs/2210.13549 (2022).

  43. Chamberland, C. et al. Building a fault-tolerant quantum computer using concatenated cat codes. PRX Quantum 3, 010329 (2022).

    Article  ADS  Google Scholar 

  44. Hann, C. T. et al. Hardware-efficient quantum random access memory with hybrid quantum acoustic systems. Phys. Rev. Lett. 123, 250501 (2019).

    Article  ADS  Google Scholar 

  45. Pechal, M., Arrangoiz-Arriola, P. & Safavi-Naeini, A. H. Superconducting circuit quantum computing with nanomechanical resonators as storage. Quantum Sci. Technol. 4, 015006 (2019).

    Article  ADS  Google Scholar 

  46. Leduc, H. G. et al. Titanium nitride films for ultrasensitive microresonator detectors. Appl. Phys. Lett. 97, 102509 (2010).

    Article  ADS  Google Scholar 

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Acknowledgements

We thank O. Painter and M. Kalaee for the fruitful discussions that led to the conception of this work. This work was supported by start-up funds from the EAS division at Caltech, National Science Foundation (grant no. 2137776), and a KNI-Wheatley scholarship. This material is based on work supported by the US Department of Energy Office of Science National Quantum Information Science Research Centers. C.J. acknowledges support from an IQIM/AWS Postdoctoral Fellowship.

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A.B. and M.M. came up with the concept and designed the experiment. A.B. and H.Z. worked on the fabrication of the devices, conducted the measurements and analysed the data. C.J. established the measurement set-up. H.G.L. and P.K.D. performed the deposition of superconducting thin films. A.B., C.J. and M.M. wrote the paper with input from all authors. M.M. supervised the project.

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Correspondence to Mohammad Mirhosseini.

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Bozkurt, A., Zhao, H., Joshi, C. et al. A quantum electromechanical interface for long-lived phonons. Nat. Phys. 19, 1326–1332 (2023). https://doi.org/10.1038/s41567-023-02080-w

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