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.

Nonreciprocal control and cooling of phonon modes in an optomechanical system

Abstract

Mechanical resonators are important components of devices that range from gravitational wave detectors to cellular telephones. They serve as high-performance transducers, sensors and filters by offering low dissipation, tunable coupling to diverse physical systems, and compatibility with a wide range of frequencies, materials and fabrication processes. Systems of mechanical resonators typically obey reciprocity, which ensures that the phonon transmission coefficient between any two resonators is independent of the direction of transmission1,2. Reciprocity must be broken to realize devices (such as isolators and circulators) that provide one-way propagation of acoustic energy between resonators. Such devices are crucial for protecting active elements, mitigating noise and operating full-duplex transceivers. Until now, nonreciprocal phononic devices3,4,5,6,7,8,9,10,11 have not simultaneously combined the features necessary for robust operation: strong nonreciprocity, in situ tunability, compact integration and continuous operation. Furthermore, they have been applied only to coherent signals (rather than fluctuations or noise), and have been realized exclusively in travelling-wave systems (rather than resonators). Here we describe a scheme that uses the standard cavity-optomechanical interaction to produce robust nonreciprocal coupling between phononic resonators. This scheme provides about 30 decibels of isolation in continuous operation and can be tuned in situ simply via the phases of the drive tones applied to the cavity. In addition, by directly monitoring the dynamics of the resonators we show that this nonreciprocity can control thermal fluctuations, and that this control represents a way to cool phononic resonators.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Optically induced mechanical nonreciprocity.
Fig. 2: Nonreciprocal phonon transmission.
Fig. 3: Isolation between phononic resonators.
Fig. 4: Cooling by nonreciprocity.

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

References

  1. 1.

    Jalas, D. et al. What is—and what is not—an optical isolator. Nat. Photon. 7, 579–582 (2013).

    ADS  CAS  Article  Google Scholar 

  2. 2.

    Fleury, R., Sounas, D., Haberman, M. R. & Alù, A. Nonreciprocal acoustics. Acoust. Today 11, 14–21 (2015).

    Google Scholar 

  3. 3.

    Lewis, M. F. & Patterson, E. Acoustic-surface-wave isolator. Appl. Phys. Lett. 20, 276–278 (1972).

    ADS  CAS  Article  Google Scholar 

  4. 4.

    Camley, R. E. Nonreciprocal surface waves. Surf. Sci. Rep. 7, 103–187 (1987).

    ADS  CAS  Article  Google Scholar 

  5. 5.

    Sasaki, R., Nii, Y., Iguchi, Y. & Onose, Y. Nonreciprocal propagation of surface acoustic wave in Ni/LiNbO3. Phys. Rev. B 95, 020407 (2017).

    ADS  Article  Google Scholar 

  6. 6.

    Liang, B., Guo, X. S., Tu, J., Zhang, D. & Cheng, J. C. An acoustic rectifier. Nat. Mater. 9, 989–992 (2010).

    ADS  CAS  Article  Google Scholar 

  7. 7.

    Boechler, N., Theocharis, G. & Daraio, C. Bifurcation-based acoustic switching and rectification. Nat. Mater. 10, 665–668 (2011).

    ADS  CAS  Article  Google Scholar 

  8. 8.

    Popa, B.-I. & Cummer, S. A. Non-reciprocal and highly nonlinear active acoustic metamaterials. Nat. Commun. 5, 3398 (2014).

    Article  Google Scholar 

  9. 9.

    Fleury, R., Sounas, D. L., Sieck, C. F., Haberman, M. R. & Alù, A. Sound isolation and giant linear nonreciprocity in a compact acoustic circulator. Science 343, 516–519 (2014).

    ADS  CAS  Article  Google Scholar 

  10. 10.

    Xu, H., Mason, D., Jiang, L. & Harris, J. G. E. Topological energy transfer in an optomechanical system with an exceptional point. Nature 537, 80–83 (2016).

    ADS  CAS  Article  Google Scholar 

  11. 11.

    Xu, H., Mason, D., Jiang, L. & Harris, J. G. E. Topological dynamics in an optomechanical system with highly non-degenerate modes. Preprint at https://arxiv.org/abs/1703.07374 (2017).

  12. 12.

    Ruesink, F., Miri, M.-A., Alù, A. & Verhagen, E. Nonreciprocity and magnetic-free isolation based on optomechanical interactions. Nat. Commun. 7, 13662 (2016).

    ADS  CAS  Article  Google Scholar 

  13. 13.

    Huang, P. et al. Nonreciprocal radio frequency transduction in a parametric mechanical artificial lattice. Phys. Rev. Lett. 117, 017701 (2016).

    ADS  Article  Google Scholar 

  14. 14.

    Sounas, D. L. & Alù, A. Non-reciprocal photonics based on time modulation. Nat. Photon. 11, 774–783 (2017).

    ADS  CAS  Article  Google Scholar 

  15. 15.

    Peterson, G. A. et al. Demonstration of efficient nonreciprocity in a microwave optomechanical circuit. Phys. Rev. X 7, 031001 (2017).

    Google Scholar 

  16. 16.

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

    ADS  CAS  Article  Google Scholar 

  17. 17.

    Barzanjeh, S. et al. Mechanical on-chip microwave circulator. Nat. Commun. 8, 953 (2017).

    ADS  CAS  Article  Google Scholar 

  18. 18.

    Ruesink, F., Mathew, J. P., Miri, M.-A., Alù, A. & Verhagen, E. Optical circulation in a multimode optomechanical resonator. Nat. Commun. 9, 1798 (2018).

    ADS  Article  Google Scholar 

  19. 19.

    Aspelmeyer, M., Kippenberg, T. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).

    ADS  Article  Google Scholar 

  20. 20.

    Zwickl, B. M. et al. High quality mechanical and optical properties of commercial silicon nitride membranes. Appl. Phys. Lett. 92, 103125 (2008).

    ADS  Article  Google Scholar 

  21. 21.

    Buchmann, L. F. & Stamper-Kurn, D. M. Nondegenerate multimode optomechanics. Phys. Rev. A 92, 013851 (2015).

    ADS  Article  Google Scholar 

  22. 22.

    Weaver, M. J. et al. Coherent optomechanical state transfer between disparate mechanical resonators. Nat. Commun. 8, 824 (2017).

    ADS  Article  Google Scholar 

  23. 23.

    Metelmann, A. & Clerk, A. A. Nonreciprocal photon transmission and amplification via reservoir engineering. Phys. Rev. X 5, 021025 (2015).

    Google Scholar 

  24. 24.

    Ranzani, L. & Aumentado, J. Graph-based analysis of nonreciprocity in coupled-mode systems. New J. Phys. 17, 023024 (2015).

    ADS  Article  Google Scholar 

  25. 25.

    Fang, K. et al. Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering. Nat. Phys. 13, 465–471 (2017).

    CAS  Article  Google Scholar 

  26. 26.

    Malz, D. et al. Quantum-limited directional amplifiers with optomechanics. Phys. Rev. Lett. 120, 023601 (2018).

    ADS  CAS  Article  Google Scholar 

  27. 27.

    Barzanjeh, S., Aquilina, M. & Xuereb, A. Manipulating the flow of thermal noise in quantum devices. Phys. Rev. Lett. 120, 060601 (2018).

    ADS  CAS  Article  Google Scholar 

  28. 28.

    Clerk, A. A., Devoret, M. H., Girvin, S. M., Marquardt, F. & Schoelkopf, R. J. Introduction to quantum noise, measurement, and amplification. Rev. Mod. Phys. 82, 1155–1208 (2010).

    ADS  MathSciNet  Article  Google Scholar 

  29. 29.

    Yamamoto, K., Otsuka, S., Ando, M., Kawabe, K. & Tsubono, K. Experimental study of thermal noise caused by an inhomogeneously distributed loss. Phys. Lett. A 280, 289–296 (2001).

    ADS  CAS  Article  Google Scholar 

  30. 30.

    Schwarz, C. et al. Deviation from the normal mode expansion in a coupled graphene-nanomechanical system. Phys. Rev. Appl. 6, 064021 (2016).

    ADS  Article  Google Scholar 

  31. 31.

    Unterreithmeier, Q. P., Weig, E. M. & Kotthaus, J. P. Universal transduction scheme for nanomechanical systems based on dielectric forces. Nature 458, 1001–1004 (2009).

    ADS  CAS  Article  Google Scholar 

  32. 32.

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

    ADS  CAS  Article  Google Scholar 

  33. 33.

    Okamoto, H. et al. Coherent phonon manipulation in coupled mechanical resonators. Nat. Phys. 9, 480–484 (2013).

    CAS  Article  Google Scholar 

  34. 34.

    Shkarin, A. B. et al. Optically mediated hybridization between two mechanical modes. Phys. Rev. Lett. 112, 013602 (2014).

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the Air Force Office of Scientific Research grant number FA9550-15-1-0270, the Air Force Office of Scientific Research Multidisciplinary University Research Initiative grant number FA9550-15-1-0029, the Office of Naval Research Multidisciplinary University Research Initiative grant number N00014-15-1-2761 and the Simons Foundation (award number 505450).

Reviewer information

Nature thanks Claudiu Genes, Andre Xuereb and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information

Affiliations

Authors

Contributions

H.X., A.A.C. and J.G.E.H. designed the study. H.X. and L.J. carried out the measurements. H.X. and L.J. analysed the data. All authors contributed to the writing of the manuscript.

Corresponding author

Correspondence to J. G. E. Harris.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Extended data figures and tables

Extended Data Fig. 1 Temperature of each phononic mode as a function of the control tone phase.

This data was used to calculate the normalized temperature ratio shown in Fig. 4b. The error bars show the standard error of the mean.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Xu, H., Jiang, L., Clerk, A.A. et al. Nonreciprocal control and cooling of phonon modes in an optomechanical system. Nature 568, 65–69 (2019). https://doi.org/10.1038/s41586-019-1061-2

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

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