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.

  • Review Article
  • Published:

Optomechanics for quantum technologies

Nature Physics volume 18, pages 15–24 (2022)Cite this article

Subjects

Abstract

The ability to control the motion of mechanical systems through interaction with light has opened the door to a plethora of applications in fundamental and applied physics. With experiments routinely reaching the quantum regime, the focus has now turned towards creating and exploiting interesting non-classical states of motion and entanglement in optomechanical systems. Quantumness has also shifted from being the very reason why experiments are constructed to becoming a resource for the investigation of fundamental physics and the creation of quantum technologies. Here, by focusing on opto- and electromechanical platforms we review recent progress in quantum state preparation and entanglement of mechanical systems, together with applications to signal processing and transduction, quantum sensing and topological physics, as well as small-scale thermodynamics.

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: Platforms for studying optomechanical science.
Fig. 2: Non-classical correlations in and between mechanical resonators.
Fig. 3: Entanglement of massive mechanical resonators.
Fig. 4: Efficient and coherent transduction in optomechanical systems.
Fig. 5: Non-reciprocal effects in optomechanical systems.

Similar content being viewed by others

References

  1. Ashkin, A. The pressure of laser light. Sci. Am. 226, 62–71 (1972).

    Article  Google Scholar 

  2. Einstein, A. Zur Quantentheorie der Strahlung. Phys. Z. 18, 121–128 (1917).

    Google Scholar 

  3. Kepler, J. De Cometis Libelli Tres I. Astronomicus, Theoremata Continens de Novam… III. Astrologicus, de Significationibus Cometarum Annorum Motu Cometarum… II. Physicus, Continens Physiologiam Cometarum 1607 et 1618 (Mylii, 1619).

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Verhagen, E., Deléglise, S., Weis, S., Schliesser, A. & Kippenberg, T. J. Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode. Nature 482, 63–67 (2012).

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  MATH  ADS  Google Scholar 

  8. 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).

    Article  ADS  Google Scholar 

  9. Barzanjeh, S. et al. Stationary entangled radiation from micromechanical motion. Nature 570, 480–483 (2019).

    Article  ADS  Google Scholar 

  10. Dowling, J. P. & Milburn, G. J. Quantum technology: the second quantum revolution. Philos. Trans. R. Soc. A 361, 1655–1674 (2003).

    Article  MathSciNet  ADS  Google Scholar 

  11. Rogers, B., Lo Gullo, N., De Chiara, G., Palma, G. M. & Paternostro, M. Hybrid optomechanics for quantum technologies. Quantum Meas. Quantum Metrol. 2, 11–43 (2014).

    ADS  Google Scholar 

  12. Kurizki, G. et al. Quantum technologies with hybrid systems. Proc. Natl Acad. Sci. USA 112, 3866–3873 (2015).

    Article  ADS  Google Scholar 

  13. Braginskii, V. B. & Manukin, A. B. Measurement of Weak Forces in Physics Experiments (Univ. Chicago Press, 1977).

  14. 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).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  15. Hanbury Brown, R. & Twiss, R. Q. Correlation between photons in two coherent beams of light. Nature 177, 27–29 (1956).

    Article  ADS  Google Scholar 

  16. Horodecki, R., Horodecki, P., Horodecki, M. & Horodecki, K. Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  17. Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V. & Wehner, S. Bell nonlocality. Rev. Mod. Phys. 86, 419–478 (2014).

    Article  ADS  Google Scholar 

  18. Lauk, N. et al. Perspectives on quantum transduction. Quantum Sci. Technol. 5, 020501 (2020).

    Article  ADS  Google Scholar 

  19. Lambert, N. J., Rueda, A., Sedlmeir, F. & Schwefel, H. G. L. Coherent conversion between microwave and optical photons—an overview of physical implementations. Adv. Quantum Technol. 3, 1900077 (2020).

    Article  Google Scholar 

  20. Gemmer, J., Michel, M. & Mahler, G. Quantum Thermodynamics Vol. 784 (Springer, 2009).

  21. Vinjanampathy, S. & Anders, J. Quantum thermodynamics. Contemp. Phys. 57, 545–579 (2016).

    Article  ADS  Google Scholar 

  22. Bohr Brask, J., Haack, G., Brunner, N. & Huber, M. Autonomous quantum thermal machine for generating steady-state entanglement. New J. Phys. 17, 113029 (2015).

    Article  MATH  ADS  Google Scholar 

  23. Karrai, K., Favero, I. & Metzger, C. Doppler optomechanics of a photonic crystal. Phys. Rev. Lett. 100, 240801 (2008).

    Article  ADS  Google Scholar 

  24. Xuereb, A., Domokos, P., Asbóth, J., Horak, P. & Freegarde, T. Scattering theory of cooling and heating in optomechanical systems. Phys. Rev. A 79, 053810 (2009).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  MATH  ADS  Google Scholar 

  27. 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 

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

    Article  ADS  Google Scholar 

  29. Peterson, R. W. et al. Laser cooling of a micromechanical membrane to the quantum backaction limit. Phys. Rev. Lett. 116, 063601 (2016).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. Clark, J. B., Lecocq, F., Simmonds, R. W., Aumentado, J. & Teufel, J. D. Sideband cooling beyond the quantum backaction limit with squeezed light. Nature 541, 191–195 (2017).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  33. Millen, J. & Stickler, B. A. Quantum experiments with microscale particles. Contemp. Phys. 61, 155–168 (2020).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  36. 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).

    Article  ADS  Google Scholar 

  37. Shkarin, A. B. et al. Quantum optomechanics in a liquid. Phys. Rev. Lett. 122, 153601 (2019).

    Article  ADS  Google Scholar 

  38. He, X. et al. Strong optical coupling through superfluid Brillouin lasing. Nat. Phys. 16, 417–421 (2020).

    Article  Google Scholar 

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

    Article  Google Scholar 

  40. Ferraro, A., Olivares, S. & Paris, M. Gaussian States in Quantum Information (Napoli Series on Physics and Astrophysics, Bibliopolis, 2005).

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

    Article  Google Scholar 

  42. Clerk, A. A. in Quantum Optomechanics and Nanomechanics (eds Cohadon, P.-F. et al.) 183–236 (Oxford Univ. Press, 2020).

  43. Vogel, W., Welsch, D.-G. & Wallentowitz, S. Quantum Optics: an Introduction (Wiley-VCH, 2005).

  44. 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 

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

    Article  ADS  Google Scholar 

  46. 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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  48. Manenti, R. et al. Circuit quantum acoustodynamics with surface acoustic waves. Nat. Commun. 8, 975 (2017).

    Article  ADS  Google Scholar 

  49. Moores, B. A., Sletten, L. R., Viennot, J. J. & Lehnert, K. W. Cavity quantum acoustic device in the multimode strong coupling regime. Phys. Rev. Lett. 120, 227701 (2018).

    Article  ADS  Google Scholar 

  50. Bienfait, A. et al. Quantum erasure using entangled surface acoustic phonons. Phys. Rev. X 10, 021055 (2020).

    Google Scholar 

  51. Viennot, J. J., Ma, X. & Lehnert, K. W. Phonon-number-sensitive electromechanics. Phys. Rev. Lett. 121, 183601 (2018).

    Article  ADS  Google Scholar 

  52. Arrangoiz-Arriola, P. et al. Resolving the energy levels of a nanomechanical oscillator. Nature 571, 537–540 (2019).

    Article  ADS  Google Scholar 

  53. Sletten, L. R., Moores, B. A., Viennot, J. J. & Lehnert, K. W. Resolving phonon Fock states in a multimode cavity with a double-slit qubit. Phys. Rev. X 9, 021056 (2019).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  55. Riedinger, R. et al. Non-classical correlations between single photons and phonons from a mechanical oscillator. Nature 530, 313–316 (2016).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  MATH  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  59. Riedinger, R. et al. Remote quantum entanglement between two micromechanical oscillators. Nature 556, 473–477 (2018).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  61. Mercier de Lépinay, L., Ockeloen-Korppi, C. F., Woolley, M. J. & Sillanpää, M. A. Quantum mechanics-free subsystem with mechanical oscillators. Science 372, 625–629 (2021).

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  63. Thomas, R. A. et al. Entanglement between distant macroscopic mechanical and spin systems. Nat. Phys. 17, 228–233 (2021).

    Article  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  65. Barzanjeh, S. et al. Microwave quantum illumination. Phys. Rev. Lett. 114, 080503 (2015).

    Article  ADS  Google Scholar 

  66. Barzanjeh, S., Pirandola, S., Vitali, D. & Fink, J. M. Microwave quantum illumination using a digital receiver. Sci. Adv. 6, eabb0451 (2020).

    Article  ADS  Google Scholar 

  67. Deffner, S. & Campbell, S. Quantum Thermodynamics: an Introduction to the Thermodynamics of Quantum Information (Morgan & Claypool, 2019).

  68. Tian, L. & Wang, H. Optical wavelength conversion of quantum states with optomechanics. Phys. Rev. A 82, 053806 (2010).

    Article  ADS  Google Scholar 

  69. Barzanjeh, S., Abdi, M., Milburn, G. J., Tombesi, P. & Vitali, D. Reversible optical-to-microwave quantum interface. Phys. Rev. Lett. 109, 130503 (2012).

    Article  ADS  Google Scholar 

  70. Habraken, S. J. M., Stannigel, K., Lukin, M. D., Zoller, P. & Rabl, P. Continuous mode cooling and phonon routers for phononic quantum networks. New J. Phys. 14, 115004 (2012).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  71. Vermersch, B., Guimond, P. O., Pichler, H. & Zoller, P. Quantum state transfer via noisy photonic and phononic waveguides. Phys. Rev. Lett. 118, 133601 (2017).

    Article  ADS  Google Scholar 

  72. Patel, R. N. et al. Single-mode phononic wire. Phys. Rev. Lett. 121, 040501 (2018).

    Article  ADS  Google Scholar 

  73. Rueda, A. et al. Efficient microwave to optical photon conversion: an electro-optical realization. Optica 3, 597–604 (2016).

    Article  ADS  Google Scholar 

  74. Rueda, A., Hease, W., Barzanjeh, S. & Fink, J. M. Electro-optic entanglement source for microwave to telecom quantum state transfer. npj Quantum Inf. 5, 108 (2019).

    Article  ADS  Google Scholar 

  75. McKenna, T. P. et al. Cryogenic microwave-to-optical conversion using a triply resonant lithium-niobate-on-sapphire transducer. Optica 7, 1737–1745 (2020).

    Article  ADS  Google Scholar 

  76. Hease, W. et al. Bidirectional electro-optic wavelength conversion in the quantum ground state. PRX Quantum 1, 020315 (2020).

    Article  Google Scholar 

  77. Han, X. et al. Cavity piezo-mechanics for superconducting–nanophotonic quantum interface. Nat. Commun. 11, 3237 (2020).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  79. Forsch, M. et al. Microwave-to-optics conversion using a mechanical oscillator in its quantum ground state. Nat. Phys. 16, 69–74 (2019).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  82. Higginbotham, A. P. et al. Harnessing electro-optic correlations in an efficient mechanical converter. Nat. Phys. 14, 1038–1042 (2018).

    Article  Google Scholar 

  83. Arnold, G. et al. Converting microwave and telecom photons with a silicon photonic nanomechanical interface. Nat. Commun. 11, 4460 (2020).

    Article  ADS  Google Scholar 

  84. Caves, C. M., Thorne, K. S., Drever, R. W., Sandberg, V. D. & Zimmermann, M. On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I. Issues of principle. Rev. Mod. Phys. 52, 341 (1980).

    Article  ADS  Google Scholar 

  85. Braginsky, V. B., Vorontsov, Y. I. & Thorne, K. S. Quantum nondemolition measurements. Science 209, 547–557 (1980).

    Article  ADS  Google Scholar 

  86. Hertzberg, J. et al. Back-action-evading measurements of nanomechanical motion. Nat. Phys. 6, 213–217 (2010).

    Article  Google Scholar 

  87. Ockeloen-Korppi, C. et al. Quantum backaction evading measurement of collective mechanical modes. Phys. Rev. Lett. 117, 140401 (2016).

    Article  ADS  Google Scholar 

  88. Tsang, M. & Caves, C. M. Evading quantum mechanics: engineering a classical subsystem within a quantum environment. Phys. Rev. X 2, 031016 (2012).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  90. Tse, M. E. et al. Quantum-enhanced advanced LIGO detectors in the era of gravitational-wave astronomy. Phys. Rev. Lett. 123, 231107 (2019).

    Article  ADS  Google Scholar 

  91. Purdy, T. P., Peterson, R. W. & Regal, C. A. Observation of radiation pressure shot noise on a macroscopic object. Science 339, 801–804 (2013).

    Article  ADS  Google Scholar 

  92. Cripe, J. et al. Measurement of quantum back action in the audio band at room temperature. Nature 568, 364–367 (2019).

    Article  ADS  Google Scholar 

  93. Brooks, D. W. et al. Non-classical light generated by quantum-noise-driven cavity optomechanics. Nature 488, 476–480 (2012).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  95. Purdy, T. P., Yu, P. L., Peterson, R. W., Kampel, N. S. & Regal, C. A. Strong optomechanical squeezing of light. Phys. Rev. X 3, 031012 (2013).

    Google Scholar 

  96. Clark, J. B., Lecocq, F., Simmonds, R. W., Aumentado, J. & Teufel, J. D. Observation of strong radiation pressure forces from squeezed light on a mechanical oscillator. Nat. Phys. 12, 683–687 (2016).

    Article  Google Scholar 

  97. Vyatchanin, S. & Zubova, E. Quantum variation measurement of a force. Phys. Lett. A 201, 269–274 (1995).

    Article  ADS  Google Scholar 

  98. Kampel, N. S. et al. Improving broadband displacement detection with quantum correlations. Phys. Rev. X 7, 021008 (2017).

    Google Scholar 

  99. 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).

    Article  Google Scholar 

  100. Li, Y. L. & Barker, P. F. Characterization and testing of a micro-g whispering gallery mode optomechanical accelerometer. J. Lightwave Technol. 36, 3919–3926 (2018).

    Article  ADS  Google Scholar 

  101. Yap, M. J. et al. Broadband reduction of quantum radiation pressure noise via squeezed light injection. Nat. Photon. 14, 19–23 (2020).

    Article  Google Scholar 

  102. McCuller, L. et al. Frequency-dependent squeezing for advanced LIGO. Phys. Rev. Lett. 124, 171102 (2020).

    Article  ADS  Google Scholar 

  103. Zhang, K., Bariani, F. & Meystre, P. Quantum optomechanical heat engine. Phys. Rev. Lett. 112, 150602 (2014).

    Article  ADS  Google Scholar 

  104. Zhang, K., Bariani, F. & Meystre, P. Theory of an optomechanical quantum heat engine. Phys. Rev. A 90, 023819 (2014).

    Article  ADS  Google Scholar 

  105. Dong, Y., Zhang, K., Bariani, F. & Meystre, P. Work measurement in an optomechanical quantum heat engine. Phys. Rev. A 92, 033854 (2015).

    Article  ADS  Google Scholar 

  106. Abari, N. E., Angelis, G. V. D., Zippilli, S. & Vitali, D. An optomechanical heat engine with feedback-controlled in-loop light. New J. Phys. 21, 093051 (2019).

    Article  ADS  Google Scholar 

  107. Mari, A., Farace, A. & Giovannetti, V. Quantum optomechanical piston engines powered by heat. J. Phys. B 48, 175501 (2015).

    Article  ADS  Google Scholar 

  108. Gelbwaser-Klimovsky, D. & Kurizki, G. Work extraction from heat-powered quantized optomechanical setups. Sci. Rep. 5, 7809 (2015).

    Article  ADS  Google Scholar 

  109. Dechant, A., Kiesel, N. & Lutz, E. All-optical nanomechanical heat engine. Phys. Rev. Lett. 114, 183602 (2015).

    Article  ADS  Google Scholar 

  110. Landi, G. T. & Paternostro, M. Irreversible entropy production, from quantum to classical. Rev. Mod. Phys. 93, 035008 (2021).

    Article  ADS  Google Scholar 

  111. Brunelli, M. et al. Experimental determination of irreversible entropy production in out-of-equilibrium mesoscopic quantum systems. Phys. Rev. Lett. 121, 160604 (2018).

    Article  ADS  Google Scholar 

  112. Belenchia, A., Mancino, L., Landi, G. T. & Paternostro, M. Entropy production in continuously measured quantum systems. npj Quant. Inf. 6, 97 (2020).

    Article  ADS  Google Scholar 

  113. Millen, J., Deesuwan, T., Barker, P. & Anders, J. Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere. Nat. Nanotechnol. 9, 425–429 (2014).

    Article  ADS  Google Scholar 

  114. Hafezi, M. & Rabl, P. Optomechanically induced non-reciprocity in microring resonators. Opt. Express 20, 7672 (2012).

    Article  ADS  Google Scholar 

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

    Google Scholar 

  116. Miri, M.-A., Ruesink, F., Verhagen, E. & Alù, A. Optical nonreciprocity based on optomechanical coupling. Phys. Rev. Appl. 7, 064014 (2017).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  122. Xu, X.-W. & Li, Y. Optical nonreciprocity and optomechanical circulator in three-mode optomechanical systems. Phys. Rev. A 91, 053854 (2015).

    Article  ADS  Google Scholar 

  123. Brendel, C., Peano, V., Painter, O. J. & Marquardt, F. Pseudomagnetic fields for sound at the nanoscale. Proc. Natl Acad. Sci. USA 114, E3390–E3395 (2017).

    Article  ADS  Google Scholar 

  124. Peano, V., Brendel, C., Schmidt, M. & Marquardt, F. Topological phases of sound and light. Phys. Rev. X 5, 031011 (2015).

    Google Scholar 

  125. Cha, J., Kim, K. W. & Daraio, C. Experimental realization of on-chip topological nanoelectromechanical metamaterials. Nature 564, 229–233 (2018).

    Article  ADS  Google Scholar 

  126. Ren, H. et al. Topological phonon transport in an optomechanical system. Preprint at https://arxiv.org/abs/2009.06174 (2020).

  127. Heinrich, G., Ludwig, M., Qian, J., Kubala, B. & Marquardt, F. Collective dynamics in optomechanical arrays. Phys. Rev. Lett. 107, 043603 (2011).

    Article  ADS  Google Scholar 

  128. Schmidt, M., Peano, V. & Marquardt, F. Optomechanical Dirac physics. New J. Phys. 17, 023025 (2015).

    Article  ADS  Google Scholar 

  129. Sanavio, C., Peano, V. & Xuereb, A. Nonreciprocal topological phononics in optomechanical arrays. Phys. Rev. B 101, 085108 (2020).

    Article  ADS  Google Scholar 

  130. Gan, J.-H., Xiong, H., Si, L.-G., Lü, X.-Y. & Wu, Y. Solitons in optomechanical arrays. Opt. Lett. 41, 2676 (2016).

    Article  ADS  Google Scholar 

  131. Hafezi, M., Mittal, S., Fan, J., Migdall, A. & Taylor, J. M. Imaging topological edge states in silicon photonics. Nat. Photon. 7, 1001–1005 (2013).

    Article  ADS  Google Scholar 

  132. Mousavi, S. H., Khanikaev, A. B. & Wang, Z. Topologically protected elastic waves in phononic metamaterials. Nat. Commun. 6, 8682 (2015).

    Article  ADS  Google Scholar 

  133. Brendel, C., Peano, V., Painter, O. & Marquardt, F. Snowflake phononic topological insulator at the nanoscale. Phys. Rev. B 97, 020102 (2018).

    Article  ADS  Google Scholar 

  134. Bassi, A., Lochan, K., Satin, S., Singh, T. P. & Ulbricht, H. Models of wave-function collapse, underlying theories, and experimental tests. Rev. Mod. Phys. 85, 471–527 (2013).

    Article  ADS  Google Scholar 

  135. Schlosshauer, M. Decoherence, the measurement problem, and interpretations of quantum mechanics. Rev. Mod. Phys. 76, 1267–1305 (2004).

    Article  ADS  Google Scholar 

  136. Bassi, A., Großardt, A. & Ulbricht, H. Gravitational decoherence. Class. Quantum Gravity 34, 193002 (2017).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  137. Moore, G. T. Quantum theory of the electromagnetic field in a variable-length one-dimensional cavity. J. Math. Phys. 11, 2679–2691 (1970).

    Article  ADS  Google Scholar 

  138. Sanz, M., Wieczorek, W., Gröblacher, S. & Solano, E. Electro-mechanical Casimir effect. Quantum 2, 91 (2018).

    Article  Google Scholar 

  139. Macrì, V. et al. Nonperturbative dynamical Casimir effect in optomechanical systems: vacuum Casimir–Rabi splittings. Phys. Rev. X 8, 011031 (2018).

    Google Scholar 

  140. 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 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  143. Fang, K., Matheny, M. H., Luan, X. & Painter, O. Optical transduction and routing of microwave phonons in cavity–optomechanical circuits. Nat. Photon. 10, 489–496 (2016).

    Article  ADS  Google Scholar 

  144. Zivari, A., Stockill, R., Fiaschi, N. & Gröblacher, S. Non-classical mechanical states guided in a phononic waveguide. Preprint at https://arxiv.org/abs/2108.06248 (2021).

  145. Marquardt, F., Chen, J. P., Clerk, A. A. & Girvin, S. M. Quantum theory of cavity-assisted sideband cooling of mechanical motion. Phys. Rev. Lett. 99, 093902 (2007).

    Article  ADS  Google Scholar 

  146. Thompson, J. D. et al. Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature 452, 72–75 (2008).

    Article  ADS  Google Scholar 

  147. Law, C. K. Interaction between a moving mirror and radiation pressure: a Hamiltonian formulation. Phys. Rev. A 51, 2537–2541 (1995).

    Article  ADS  Google Scholar 

  148. Nunnenkamp, A., Børkje, K. & Girvin, S. M. Single-photon optomechanics. Phys. Rev. Lett. 107, 063602 (2011).

    Article  ADS  Google Scholar 

  149. Rabl, P. Photon blockade effect in optomechanical systems. Phys. Rev. Lett. 107, 063601 (2011).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

S.B. acknowledges funding by the Natural Sciences and Engineering Research Council of Canada (NSERC) through its Discovery Grant, funding and advisory support provided by Alberta Innovates through the Accelerating Innovations into CarE (AICE)—Concepts Program, and support from Alberta Innovates and NSERC through an Advance Grant. A.X. acknowledges funding by the European Union’s Horizon 2020 research and innovation programme under grant agreement 732894 (FET Proactive HOT) and by the Julian Schwinger Foundation project grant JSF-16-03-0000 (TOM). S.G. is supported by the European Research Council (ERC Starting Grant Strong-Q, 676842; and ERC Consolidator Grant Q-ECHOS, 101001005) and by the Netherlands Organization for Scientific Research (NWO/OCW) as part of the Frontiers of Nanoscience program, as well as through Vidi (680-47-541/994) and Vrij Programma (680-92-18-04) grants. M.P. is supported by the H2020/FETOPEN/2018/2020 project TEQ (766900), the DfE-SFI Investigator Programme (15/IA/2864), COST Action CA15220, the Royal Society Wolfson Research Fellowship (RSWF\R3\183013), the Royal Society International Exchanges Programme (IEC\R2\192220), the Leverhulme Trust Research Project Grant (RGP/2018/266), the UK EPSRC (project QuamNESS, grant EP/T028106/1) and the CNR/RS (London) project “Testing fundamental theories with ultracold atoms”. C.A.R. acknowledges funding by the US National Science Foundation under grant 1125844 and a Cottrell FRED Award from the Research Corporation for Science Advancement under grant 27321. E.M.W. acknowledges funding by the European Union’s Horizon 2020 research and innovation program under grant agreement 732894 (FET Proactive HOT), the German Federal Ministry of Education and Research (contract 13N14777) within the European QuantERA co-fund project QuaSeRT, and project QT-6 SPOC of the Baden-Württemberg Foundation.

Author information

Authors and Affiliations

  1. Institute for Quantum Science and Technology, University of Calgary, Calgary, Alberta, Canada

    Shabir Barzanjeh

  2. Department of Physics, University of Malta, Msida, Malta

    André Xuereb

  3. Kavli Institute of Nanoscience, Department of Quantum Nanoscience, Delft University of Technology, Delft, The Netherlands

    Simon Gröblacher

  4. Centre for Theoretical Atomic, Molecular, and Optical Physics (CTAMOP), School of Mathematics and Physics, Queen’s University, Belfast, UK

    Mauro Paternostro

  5. JILA, University of Colorado and National Institute of Standards and Technology, Boulder, CO, USA

    Cindy A. Regal

  6. Department of Physics, University of Colorado, Boulder, CO, USA

    Cindy A. Regal

  7. Department of Physics, University of Konstanz, Konstanz, Germany

    Eva M. Weig

  8. Department of Electrical and Computer Engineering, Technical University of Munich, Munich, Germany

    Eva M. Weig

  9. Munich Center for Quantum Science and Technology (MCQST), Munich, Germany

    Eva M. Weig

Authors
  1. Shabir Barzanjeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. André Xuereb
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Simon Gröblacher
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mauro Paternostro
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Cindy A. Regal
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Eva M. Weig
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the writing, editing, and revision of the manuscript.

Corresponding authors

Correspondence to Shabir Barzanjeh or André Xuereb.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks James Millen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barzanjeh, S., Xuereb, A., Gröblacher, S. et al. Optomechanics for quantum technologies. Nat. Phys. 18, 15–24 (2022). https://doi.org/10.1038/s41567-021-01402-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-021-01402-0

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