Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

A squeezed mechanical oscillator with millisecond quantum decoherence

Nature Physics volume 19, pages 1697–1702 (2023)Cite this article

Subjects

Abstract

An enduring challenge in constructing mechanical-oscillator-based hybrid quantum systems is to ensure engineered coupling to an auxiliary degree of freedom and maintain good mechanical isolation from the environment, that is, low quantum decoherence, consisting of thermal decoherence and dephasing. Here we overcome this challenge by introducing a superconducting-circuit-based optomechanical platform that exhibits low quantum decoherence and has a large optomechanical coupling, which allows us to prepare the quantum ground and squeezed states of motion with high fidelity. We directly measure a thermal decoherence rate of 20.5 Hz (corresponding to T1 = 7.7 ms) as well as a pure dephasing rate of 0.09 Hz, yielding a 100-fold improvement in the quantum state lifetime compared with prior optomechanical systems. This enables us to reach a motional ground-state occupation of 0.07 quanta (93% fidelity) and realize mechanical squeezing of –2.7 dB below the zero-point fluctuation. Furthermore, we observe the free evolution of the mechanical squeezed state, preserving its non-classical nature over millisecond timescales. Such ultralow quantum decoherence not only increases the fidelity of quantum control and measurement of macroscopic mechanical systems but may also benefit interfacing with qubits, and places the system in a parameter regime suitable for tests of quantum gravity.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Ultracoherent circuit optomechanics.
Fig. 2: High-fidelity optomechanical ground-state cooling.
Fig. 3: Recording the motional heating rate out of the quantum ground state.
Fig. 4: Tracking the free evolution of a mechanical squeezed state.

Similar content being viewed by others

Data availability

The data used to produce the plots within this paper are available via Zenodo at https://doi.org/10.5281/zenodo.7833893. All other data used in this study are available from the corresponding authors on reasonable request. Source data are provided with this paper.

Code availability

The code used to produce the plots within this paper is available via Zenodo at https://doi.org/10.5281/zenodo.7833893.

References

  1. Aasi, J. et al. Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light. Nat. Photon. 7, 613–619 (2013).

    ADS  Google Scholar 

  2. Mason, D., Chen, J., Rossi, M., Tsaturyan, Y. & Schliesser, A. Continuous force and displacement measurement below the standard quantum limit. Nat. Phys. 15, 745–749 (2019).

    Google Scholar 

  3. Whittle, C. et al. Approaching the motional ground state of a 10-kg object. Science 372, 1333–1336 (2021).

    ADS  Google Scholar 

  4. Pechal, M., Arrangoiz-Arriola, P. & Safavi-Naeini, A. H. Superconducting circuit quantum computing with nanomechanical resonators as storage. Quantum Sci. Technol. 4, 015006 (2018).

    ADS  Google Scholar 

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

    Google Scholar 

  6. Fiaschi, N. et al. Optomechanical quantum teleportation. Nat. Photon. 15, 817–821 (2021).

    ADS  MathSciNet  Google Scholar 

  7. Marinković, I. et al. Optomechanical bell test. Phys. Rev. Lett. 121, 220404 (2018).

    ADS  Google Scholar 

  8. Carney, D. et al. Mechanical quantum sensing in the search for dark matter. Quantum Sci. Technol. 6, 024002 (2021).

    ADS  Google Scholar 

  9. Manley, J., Chowdhury, M. D., Grin, D., Singh, S. & Wilson, D. J. Searching for vector dark matter with an optomechanical accelerometer. Phys. Rev. Lett. 126, 061301 (2021).

    ADS  Google Scholar 

  10. Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391 (2014).

    ADS  Google Scholar 

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

    Google Scholar 

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

    ADS  Google Scholar 

  13. Wollman, E. E. et al. Quantum squeezing of motion in a mechanical resonator. Science 349, 952–955 (2015).

    ADS  MathSciNet  MATH  Google Scholar 

  14. Pirkkalainen, J.-M., Damskägg, E., Brandt, M., Massel, F. & Sillanpää, M. A. Squeezing of quantum noise of motion in a micromechanical resonator. Phys. Rev. Lett. 115, 243601 (2015).

    ADS  Google Scholar 

  15. Lecocq, F., Clark, J. B., Simmonds, R. W., Aumentado, J. & Teufel, J. D. Quantum nondemolition measurement of a nonclassical state of a massive object. Phys. Rev. X 5, 041037 (2015).

    Google Scholar 

  16. Reed, A. et al. Faithful conversion of propagating quantum information to mechanical motion. Nat. Phys. 13, 1163–1167 (2017).

    Google Scholar 

  17. Chu, Y. et al. Creation and control of multi-phonon Fock states in a bulk acoustic-wave resonator. Nature 563, 666–670 (2018).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  19. Andrews, R. W. et al. Bidirectional and efficient conversion between microwave and optical light. Nat. Phys. 10, 321–326 (2014).

    Google Scholar 

  20. Kotler, S. et al. Direct observation of deterministic macroscopic entanglement. Science 372, 622–625 (2021).

    ADS  Google Scholar 

  21. Rossi, M., Mason, D., Chen, J., Tsaturyan, Y. & Schliesser, A. Measurement-based quantum control of mechanical motion. Nature 563, 53–58 (2018).

    ADS  Google Scholar 

  22. Delaney, R. D., Reed, A. P., Andrews, R. W. & Lehnert, K. W. Measurement of motion beyond the quantum limit by transient amplification. Phys. Rev. Lett. 123, 183603 (2019).

    ADS  Google Scholar 

  23. Gardiner, C. & Zoller, P. Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer Science & Business Media, 2004).

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

    ADS  Google Scholar 

  25. Magrini, L. et al. Real-time optimal quantum control of mechanical motion at room temperature. Nature 595, 373–377 (2021).

    ADS  Google Scholar 

  26. Tebbenjohanns, F., Mattana, M. L., Rossi, M., Frimmer, M. & Novotny, L. Quantum control of a nanoparticle optically levitated in cryogenic free space. Nature 595, 378–382 (2021).

    ADS  Google Scholar 

  27. Delić, U. et al. Cooling of a levitated nanoparticle to the motional quantum ground state. Science 367, 892–895 (2020).

    ADS  Google Scholar 

  28. Piotrowski, J. et al. Simultaneous ground-state cooling of two mechanical modes of a levitated nanoparticle. Nat. Phys. 19, 1009–1013 (2023).

    Google Scholar 

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

    ADS  Google Scholar 

  30. Ockeloen-Korppi, C. et al. Stabilized entanglement of massive mechanical oscillators. Nature 556, 478–482 (2018).

    ADS  Google Scholar 

  31. Palomaki, T., Teufel, J., Simmonds, R. & Lehnert, K. W. Entangling mechanical motion with microwave fields. Science 342, 710–713 (2013).

    ADS  Google Scholar 

  32. Palomaki, T., Harlow, J., Teufel, J., Simmonds, R. & Lehnert, K. W. Coherent state transfer between itinerant microwave fields and a mechanical oscillator. Nature 495, 210–214 (2013).

    ADS  Google Scholar 

  33. Bernier, N. R. et al. Nonreciprocal reconfigurable microwave optomechanical circuit. Nat. Commun. 8, 604 (2017).

  34. Gely, M. F. & Steele, G. A. Phonon-number resolution of voltage-biased mechanical oscillators with weakly anharmonic superconducting circuits. Phys. Rev. A 104, 053509 (2021).

    ADS  Google Scholar 

  35. Gely, M. F. & Steele, G. A. Superconducting electro-mechanics to test Diósi–Penrose effects of general relativity in massive superpositions. AVS Quantum Sci. 3, 035601 (2021).

    ADS  Google Scholar 

  36. Liu, Y., Mummery, J., Zhou, J. & Sillanpää, M. A. Gravitational forces between nonclassical mechanical oscillators. Phys. Rev. Appl. 15, 034004 (2021).

    ADS  Google Scholar 

  37. Seis, Y. et al. Ground state cooling of an ultracoherent electromechanical system. Nat. Commun. 13, 1507 (2022).

    ADS  Google Scholar 

  38. Liu, Y. et al. Optomechanical anti-lasing with infinite group delay at a phase singularity. Phys. Rev. Lett. 127, 273603 (2021).

    Google Scholar 

  39. Tsaturyan, Y., Barg, A., Polzik, E. S. & Schliesser, A. Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution. Nat. Nanotechnol. 12, 776–783 (2017).

    Google Scholar 

  40. Leibfried, D., Blatt, R., Monroe, C. & Wineland, D. Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75, 281 (2003).

    ADS  Google Scholar 

  41. Gaebler, J. P. et al. High-fidelity universal gate set for 9Be+ ion qubits. Phys. Rev. Lett. 117, 060505 (2016).

    ADS  Google Scholar 

  42. Schmid, S., Jensen, K., Nielsen, K. & Boisen, A. Damping mechanisms in high-Q micro and nanomechanical string resonators. Phys. Rev. B 84, 165307 (2011).

    ADS  Google Scholar 

  43. Weinstein, A. et al. Observation and interpretation of motional sideband asymmetry in a quantum electromechanical device. Phys. Rev. X 4, 041003 (2014).

    Google Scholar 

  44. Macklin, C. et al. A near–quantum-limited Josephson traveling-wave parametric amplifier. Science 350, 307–310 (2015).

    ADS  Google Scholar 

  45. Kronwald, A., Marquardt, F. & Clerk, A. A. Arbitrarily large steady-state bosonic squeezing via dissipation. Phys. Rev. A 88, 063833 (2013).

    ADS  Google Scholar 

Download references

Acknowledgements

We thank MIT Lincoln Laboratory and W. D. Oliver for providing the Josephson travelling-wave parametric amplifier. We thank A. Arabmoheghi for helpful discussions on the theory of mechanical dissipation. This work was supported by the EU H2020 research and innovation programme under grant no. 101033361 (QuPhon), and from the European Research Council (ERC) grant no. 835329 (ExCOM-cCEO). This work was also supported by the Swiss National Science Foundation (SNSF) under grant no. NCCR-QSIT:51NF40_185902 and no. 204927. All the devices were fabricated in the Center of MicroNanoTechnology (CMi) at EPFL.

Author information

Author notes

  1. These authors contributed equally: Amir Youssefi, Shingo Kono, Mahdi Chegnizadeh.

Authors and Affiliations

  1. Laboratory of Photonics and Quantum Measurement (LPQM), Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland

    Amir Youssefi, Shingo Kono, Mahdi Chegnizadeh & Tobias J. Kippenberg

  2. Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland

    Amir Youssefi, Shingo Kono, Mahdi Chegnizadeh & Tobias J. Kippenberg

Authors
  1. Amir Youssefi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shingo Kono
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mahdi Chegnizadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tobias J. Kippenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

A.Y. conceived the experiment. S.K., M.C. and A.Y. developed the theory. A.Y. designed and simulated the devices. A.Y. developed the fabrication process with assistance from M.C. M.C. and A.Y. fabricated the samples. A.Y. and M.C. developed the experimental setup. The measurement was performed by A.Y. and M.C., with assistance from S.K. The data analysis was performed by A.Y. with assistance from S.K. S.K. introduced the phonon number calibration based on sideband asymmetry and conducted the numerical simulation for extracting the mechanical dephasing. The manuscript was written by A.Y., S.K., M.C. and T.J.K. T.J.K. supervised the project.

Corresponding author

Correspondence to Tobias J. Kippenberg.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

Additional information

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

Extended data

Extended Data Fig. 1 Overview on the fabrication technique for highly coherent circuit optomechanics.

The main steps of the process consists of etching a trench in the substrate followed by deposition of a sacrificial layer, planarization, top layer definition, release, and finally cool down. Due to the compressive stresses, the top plate may buckle up after the release. However, the drumhead shrinks and flattens at cryogenic temperatures, resulting in a controllable gap size.

Extended Data Fig. 2 Free evolution of a mechanical squeezed state.

a, Quadrature variances and average phonon number of a squeezed state as a function of the free-evolution time. The blue, red and purple circles are the data for the quadrature variances in the squeezed and anti-squeezed axes, and the average phonon number, respectively. The black dotted lines are linear fits, while the green lines are the numerical simulation results. Error bars are corresponding to standard deviations. b, The difference of the thermal decoherence rates for the quadrature variances in the squeezed and anti-squeezed axes as a function of the pure dephasing rate. The green line shows the numerical simulation results, while the blue line is the experimentally obtained value. The shaded regions show the errors, respectively.

Source data

Supplementary information

Supplementary Information

Supplementary Figs. 1–20, Tables 1 and 2 and References.

Source data

Source Data Fig. 1

Source data for ring-down and frequency fluctuation.

Source Data Fig. 2

Source data for sideband asymmetry.

Source Data Fig. 3

Source data for optomechanical amplification.

Source Data Fig. 4

Source data for squeezing.

Source Data Extended Data Fig. 2

Source data for dephasing rate extraction.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Youssefi, A., Kono, S., Chegnizadeh, M. et al. A squeezed mechanical oscillator with millisecond quantum decoherence. Nat. Phys. 19, 1697–1702 (2023). https://doi.org/10.1038/s41567-023-02135-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-023-02135-y

This article is cited by

Search

Advanced search

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