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Bulk crystalline optomechanics

Nature Physics volume 14, pages 601–607 (2018)Cite this article

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Abstract

Control of long-lived, high-frequency phonons using light offers a path towards creating robust quantum links, and could lead to tools for precision metrology with applications to quantum information processing. Optomechanical systems based on bulk acoustic-wave resonators are well suited for this goal in light of their high quality factors, and because they do not suffer from surface interactions as much as their microscale counterparts. However, so far these phonons have been accessible only electromechanically, using piezoelectric interactions. Here, we demonstrate customizable optomechanical coupling to macroscopic phonon modes of a bulk acoustic-wave resonator at cryogenic temperatures. These phonon modes, which are formed by shaping the surfaces of a crystal into a plano-convex phononic resonator, yield appreciable optomechanical coupling rates, providing access to high acoustic quality factors (4.2 × 107) at high phonon frequencies (13 GHz). This simple approach, which uses bulk properties rather than nanostructural control, is appealing for the ability to engineer optomechanical systems at high frequencies that are robust against thermal decoherence. Moreover, we show that this optomechanical system yields a unique form of dispersive symmetry-breaking that enables phonon heating or cooling without an optical cavity.

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Fig. 1: The bulk crystalline optomechanical system.
Fig. 2: The anatomy of the Stokes signatures produced by the bulk crystalline system.
Fig. 3: Phonon-mode spectroscopy of the bulk crystalline device.
Fig. 4: Dispersive symmetry-breaking in bulk crystalline optomechanics.

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References

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

    ADS  Google Scholar 

  2. Meystre, P. A short walk through quantum optomechanics. Ann. Phys. 525, 215–233 (2013).

    MATH  Google Scholar 

  3. Marquardt, F. & Girvin, S. Optomechanics. Physics 2, 40 (2009).

    Google Scholar 

  4. Favero, I. & Karrai, K. Optomechanics of deformable optical cavities. Nat. Photon. 3, 201–205 (2009).

    ADS  Google Scholar 

  5. De Lorenzo, L. & Schwab, K. Superfluid optomechanics: coupling of a superfluid to a superconducting condensate. New. J. Phys. 16, 113020 (2014).

    Google Scholar 

  6. Lee, H. et al. Chemically etched ultrahigh-q wedge-resonator on a silicon chip. Nat. Photon. 6, 369–373 (2012).

    ADS  Google Scholar 

  7. Safavi-Naeini, A. H. et al. Observation of quantum motion of a nanomechanical resonator. Phys. Rev. Lett. 108, 033602 (2012).

    ADS  Google Scholar 

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

    Google Scholar 

  9. Wilson, D. et al. Measurement-based control of a mechanical oscillator at its thermal decoherence rate. Nature 524, 325–329 (2015).

    ADS  Google Scholar 

  10. Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011).

    ADS  Google Scholar 

  11. Jayich, A. et al. Dispersive optomechanics: a membrane inside a cavity. New. J. Phys. 10, 095008 (2008).

    ADS  Google Scholar 

  12. Bahl, G., Zehnpfennig, J., Tomes, M. & Carmon, T. Stimulated optomechanical excitation of surface acoustic waves in a microdevice. Nat. Commun. 2, 403 (2011).

    ADS  Google Scholar 

  13. Cohen, J. D. et al. Phonon counting and intensity interferometry of a nanomechanical resonator. Nature 520, 522–525 (2015).

    ADS  Google Scholar 

  14. Ekinci, K. & Roukes, M. Nanoelectromechanical systems. Rev. Sci. Instrum. 76, 061101 (2005).

    ADS  Google Scholar 

  15. Regal, C., Teufel, J. & Lehnert, K. Measuring nanomechanical motion with a microwave cavity interferometer. Nat. Phys. 4, 555–560 (2008).

    Google Scholar 

  16. Bochmann, J., Vainsencher, A., Awschalom, D. D. & Cleland, A. N. Nanomechanical coupling between microwave and optical photons. Nat. Phys. 9, 712–716 (2013).

    Google Scholar 

  17. Mahboob, I., Nishiguchi, K., Fujiwara, A. & Yamaguchi, H. Phonon lasing in an electromechanical resonator. Phys. Rev. Lett. 110, 127202 (2013).

    ADS  Google Scholar 

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

    Google Scholar 

  19. Bagci, T. et al. Optical detection of radio waves through a nanomechanical transducer. Nature 507, 81–85 (2014).

    ADS  Google Scholar 

  20. O'Connell, A. D. et al. Quantum ground state and single-phonon control of a mechanical resonator. Nature 464, 697–703 (2010).

    ADS  Google Scholar 

  21. Chu, Y. et al. Quantum acoustics with superconducting qubits. Science 358, 199–202 (2017).

    ADS  MathSciNet  MATH  Google Scholar 

  22. Schuetz, M. J. A. et al. Universal quantum transducers based on surface acoustic waves. Phys. Rev. X 5, 031031 (2015).

    Google Scholar 

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

    ADS  Google Scholar 

  24. Gustafsson, M. V. et al. Propagating phonons coupled to an artificial atom. Science 346, 207–211 (2014).

    ADS  Google Scholar 

  25. Thaxter, J. & Tannenwald, P. Phonon generation, propagation, and attenuation at 70 GHz. IEEE Trans. Sonics Ultrason. 13, 61–68 (1966).

    Google Scholar 

  26. Blair, M. & Jacobsen, E. Very low attenuation of 9.3 Gc elastic waves in quartz at 4.2°K. Phys. Lett. 23, 647–648 (1966).

    ADS  Google Scholar 

  27. Safavi-Naeini, A. H. et al. Squeezed light from a silicon micromechanical resonator. Nature 500, 185–189 (2013).

    ADS  Google Scholar 

  28. Pitanti, A. et al. Strong opto-electro-mechanical coupling in a silicon photonic crystal cavity. Opt. Express 23, 3196–3208 (2015).

    ADS  Google Scholar 

  29. Balram, K. C., Davanço, M. I., Song, J. D. & Srinivasan, K. Coherent coupling between radiofrequency, optical and acoustic waves in piezo-optomechanical circuits. Nat. Photon. 10, 346–352 (2016).

    ADS  Google Scholar 

  30. Schliesser, A., Rivière, R., Anetsberger, G., Arcizet, O. & Kippenberg, T. J. Resolved-sideband cooling of a micromechanical oscillator. Nat. Phys. 4, 415–419 (2008).

    Google Scholar 

  31. Eichenfield, M., Chan, J., Camacho, R. M., Vahala, K. J. & Painter, O. Optomechanical crystals. Nature 462, 78–82 (2009).

    ADS  Google Scholar 

  32. Chan, J., Safavi-Naeini, A. H., Hill, J. T., Meenehan, S. & Painter, O. Optimized optomechanical crystal cavity with acoustic radiation shield. Appl. Phys. Lett. 101, 081115 (2012).

    ADS  Google Scholar 

  33. Hong, S. et al. Hanbury Brown and Twiss interferometry of single phonons from an optomechanical resonator. Science 358, 203–206 (2017).

    ADS  MathSciNet  MATH  Google Scholar 

  34. Galliou, S. et al. Extremely low loss phonon-trapping cryogenic acoustic cavities for future physical experiments. Sci. Rep. 3, 2132 (2013).

    Google Scholar 

  35. Goryachev, M., Creedon, D. L., Galliou, S. & Tobar, M. E. Observation of Rayleigh phonon scattering through excitation of extremely high overtones in low-loss cryogenic acoustic cavities for hybrid quantum systems. Phys. Rev. Lett. 111, 085502 (2013).

    ADS  Google Scholar 

  36. Goryachev, M., Farr, W. G., Galliou, S. & Tobar, M. E. Jump chaotic behaviour of ultra low loss bulk acoustic wave cavities. Appl. Phys. Lett. 105, 063501 (2014).

    ADS  Google Scholar 

  37. Lo, A. et al. Acoustic tests of Lorentz symmetry using quartz oscillators. Phys. Rev. X 6, 011018 (2016).

    Google Scholar 

  38. Goryachev, M. & Tobar, M. E. Gravitational wave detection with high frequency phonon trapping acoustic cavities. Phys. Rev. D 90, 102005 (2014).

    ADS  Google Scholar 

  39. Boyd, R. W. Nonlinear Optics (Academic, San Diego, CA, 2003).

  40. Braginsky, V. B., Mitrofanov, V. & Panov, V. I. Systems with Small Dissipation (Univ. of Chicago Press, Chicago, 1985).

  41. Cleland, A. N. Foundations of Nanomechanics: From Solid-State Theory to Device Applications (Springer, Berlin, 2013).

  42. Ohno, S., Sonehara, T., Tatsu, E., Koreeda, A. & Saikan, S. kHz stimulated Brillouin spectroscopy. Rev. Sci. Instrum. 77, 123104 (2006).

    ADS  Google Scholar 

  43. Ohno, S., Sonehara, T., Tatsu, E., Koreeda, A. & Saikan, S. Spectral shape of stimulated Brillouin scattering in crystals. Phys. Rev. B 92, 214105 (2015).

    ADS  Google Scholar 

  44. Sonehara, T., Konno, Y., Kaminaga, H., Saikan, S. & Ohno, S. Frequency-modulated stimulated Brillouin spectroscopy in crystals. J. Opt. Soc. Am. B24, 1193–1198 (2007).

    ADS  Google Scholar 

  45. Ohmachi, Y. & Uchida, N. Temperature dependence of elastic, dielectric, and piezoelectric constants in TeO2 single crystals. J. Appl. Phys. 41, 2307–2311 (1970).

    ADS  Google Scholar 

  46. McSkimin, H., Andreatch, P. Jr & Thurston, R. Elastic moduli of quartz versus hydrostatic pressure at 25° and- 195.8°C. J. Appl. Phys. 36, 1624–1632 (1965).

    ADS  Google Scholar 

  47. Goryachev, M. et al. Extremely low-loss acoustic phonons in a quartz bulk acoustic wave resonator at millikelvin temperature. Appl. Phys. Lett. 100, 243504 (2012).

    ADS  Google Scholar 

  48. Tamura, S., Shields, J. & Wolfe, J. Lattice dynamics and elastic phonon scattering in silicon. Phys. Rev. B 44, 3001–3011 (1991).

    ADS  Google Scholar 

  49. Tamura, S.-i Isotope scattering of large-wave-vector phonons in GaAs and InSb: Deformation-dipole and overlap-shell models. Phys. Rev. B 30, 849–854 (1984).

    ADS  Google Scholar 

  50. Vahala, K. J. Back-action limit of linewidth in an optomechanical oscillator. Phys. Rev. A 78, 023832 (2008).

    ADS  Google Scholar 

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Acknowledgements

Primary support for this work was provided by NSF MRSEC DMR-1119826. This work was supported in part by the Packard Fellowship for Science and Engineering and Yale University. The authors thank P. Fleury, Y. Chu, E. Kittlaus, N. Otterstrom, J. Harris, K. Johnson, A. Shkarin, A. Kashkanova and G. Harris for valuable feedback and discussions.

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  1. These authors contributed equally: W. H. Renninger, P. Kharel.

Authors and Affiliations

  1. Department of Applied Physics, Yale University, New Haven, CT, USA

    W. H. Renninger, P. Kharel, R. O. Behunin & P. T. Rakich

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  1. W. H. Renninger
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Contributions

W.H.R. and P.T.R. conceived the device and spectroscopy approach. W.H.R. conducted experiments to produce the initial results. W.H.R. and P.K. jointly advanced these techniques to produce the final results under the guidance of P.T.R. W.H.R. and P.K. developed simulation methods with input from R.O.B. and P.T.R. P.K. and R.O.B. developed the analytical theory with guidance from W.H.R. and P.T.R. All authors participated in the writing of this manuscript.

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Correspondence to W. H. Renninger or P. T. Rakich.

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Supplementary notes, Supplementary Figures 1–18, Supplementary notes

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Renninger, W.H., Kharel, P., Behunin, R.O. et al. Bulk crystalline optomechanics. Nature Phys 14, 601–607 (2018). https://doi.org/10.1038/s41567-018-0090-3

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