Demonstrating and exploiting the quantum nature of macroscopic mechanical objects would help us to investigate directly the limitations of quantum-based measurements and quantum information protocols, as well as to test long-standing questions about macroscopic quantum coherence1,2,3. Central to this effort is the necessity of long-lived mechanical states. Previous efforts have witnessed quantum behaviour4, but for a low-quality-factor mechanical system. The field of cavity optomechanics and electromechanics5,6, in which a high-quality-factor mechanical oscillator is parametrically coupled to an electromagnetic cavity resonance, provides a practical architecture for cooling, manipulation and detection of motion at the quantum level1. One requirement is strong coupling7,8,9, in which the interaction between the two systems is faster than the dissipation of energy from either system. Here, by incorporating a free-standing, flexible aluminium membrane into a lumped-element superconducting resonant cavity, we have increased the single-photon coupling strength between these two systems by more than two orders of magnitude, compared to previously obtained coupling strengths. A parametric drive tone at the difference frequency between the mechanical oscillator and the cavity resonance dramatically increases the overall coupling strength, allowing us to completely enter the quantum-enabled, strong-coupling regime. This is evidenced by a maximum normal-mode splitting of nearly six bare cavity linewidths. Spectroscopic measurements of these ‘dressed states’ are in excellent quantitative agreement with recent theoretical predictions10,11. The basic circuit architecture presented here provides a feasible path to ground-state cooling and subsequent coherent control and measurement of long-lived quantum states of mechanical motion.
This is a preview of subscription content
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Braginsky, V. B. & Khalili, F. Y. Quantum Measurement (Cambridge Univ. Press, 1992)
Mancini, S., Man'ko, V. I. & Tombesi, P. Ponderomotive control of quantum macroscopic coherence. Phys. Rev. A 55, 3042–3050 (1997)
Bose, S., Jacobs, K. & Knight, P. L. Preparation of nonclassical states in cavities with a moving mirror. Phys. Rev. A 56, 4175–4186 (1997)
O'Connell, A. D. et al. Quantum ground state and single-phonon control of a mechanical resonator. Nature 464, 697–703 (2010)
Kippenberg, T. J. & Vahala, K. J. Cavity optomechanics: back-action at the mesoscale. Science 321, 1172–1176 (2008)
Marquardt, F. & Girvin, S. M. Optomechanics. Physics 2, 40 (2009)
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)
Wilson-Rae, I., Nooshi, N., Zwerger, W. & Kippenberg, T. J. Theory of ground state cooling of a mechanical oscillator using dynamical backaction. Phys. Rev. Lett. 99, 093901 (2007)
Dobrindt, J. M., Wilson-Rae, I. & Kippenberg, T. J. Parametric normal-mode splitting in cavity optomechanics. Phys. Rev. Lett. 101, 263602 (2008)
Agarwal, G. S. & Huang, S. Electromagnetically induced transparency in mechanical effects of light. Phys. Rev. A 81, 041803 (2010)
Weis, S. et al. Optomechanically induced transparency. Science 330, 1520–1523 (2010)
Ekinci, K. L. & Roukes, M. L. Nanoelectromechanical systems. Rev. Sci. Instrum. 76, 061101 (2005)
Diedrich, F., Bergquist, J. C., Itano, W. M. & Wineland, D. J. Laser cooling to the zero-point energy of motion. Phys. Rev. Lett. 62, 403–406 (1989)
Gröblacher, S., Hammerer, K., Vanner, M. R. & Aspelmeyer, M. Observation of strong coupling between a micromechanical resonator and an optical cavity field. Nature 460, 724–727 (2009)
Thompson, J. D. et al. Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature 452, 72–75 (2008)
Braginsky, V. B., Manukin, A. B. & Tikhonov, M. Y. Investigation of dissipative ponderomotive effects of electromagnetic radiation. Sov. Phys. JETP 31, 829–830 (1970)
Linthorne, N. P., Veitch, P. J. & Blair, D. G. Interaction of a parametric transducer with a resonant bar gravitational radiation detector. J. Phys. D 23, 1–6 (1990)
Regal, C. A., Teufel, J. D. & Lehnert, K. W. Measuring nanomechanical motion with a microwave cavity interferometer. Nature Phys. 4, 555–560 (2008)
Teufel, J. D., Harlow, J. W., Regal, C. A. & Lehnert, K. W. Dynamical backaction of microwave fields on a nanomechanical oscillator. Phys. Rev. Lett. 101, 197203 (2008)
Rocheleau, T. et al. Preparation and detection of a mechanical resonator near the ground state of motion. Nature 463, 72–75 (2010)
Teufel, J. D., Donner, T., Castellanos-Beltran, M. A., Harlow, J. W. & Lehnert, K. W. Nanomechanical motion measured with an imprecision below that at the standard quantum limit. Nature Nanotechnol. 4, 820–823 (2009)
Hertzberg, J. B. et al. Back-action-evading measurements of nanomechanical motion. Nature Phys. 6, 213–217 (2010)
Cicak, K. et al. Low-loss superconducting resonant circuits using vacuum-gap-based microwave components. Appl. Phys. Lett. 96, 093502 (2010)
Blencowe, M. P. & Buks, E. Quantum analysis of a linear dc squid mechanical displacement detector. Phys. Rev. B 76, 014511 (2007)
Boller, K.-J., Imamolu, A. & Harris, S. E. Observation of electromagnetically induced transparency. Phys. Rev. Lett. 66, 2593–2596 (1991)
Hofheinz, M. et al. Synthesizing arbitrary quantum states in a superconducting resonator. Nature 459, 546–549 (2009)
Marshall, W., Simon, C., Penrose, R. & Bouwmeester, D. Towards quantum superpositions of a mirror. Phys. Rev. Lett. 91, 130401 (2003)
Castellanos-Beltran, M. A., Irwin, K. D., Hilton, G. C., Vale, L. R. & Lehnert, K. W. Amplification and squeezing of quantum noise with a tunable Josephson metamaterial. Nature Phys. 4, 929–931 (2008)
Akram, U., Kiesel, N., Aspelmeyer, M. & Milburn, G. J. Single-photon opto-mechanics in the strong coupling regime. N. J. Phys. 12, 083030 (2010)
Regal, C. A. & Lehnert, K. W. From cavity electromechanics to cavity optomechanics. J. Phys. Conf. Ser. 264, 012025 (2011)
We thank A. W. Sanders for taking the micrograph in Fig. 1b, and acknowledge discussions with T. Donner, J. H. Harlow and K. W. Lehnert. This paper is a contribution by the National Institute of Standards and Technology and not subject to US copyright.
The authors declare no competing financial interests.
About this article
Cite this article
Teufel, J., Li, D., Allman, M. et al. Circuit cavity electromechanics in the strong-coupling regime. Nature 471, 204–208 (2011). https://doi.org/10.1038/nature09898
Scientific Reports (2022)
Applied Physics B (2022)
Journal of Low Temperature Physics (2022)
Phase dependence of the dynamical behaviours and photon entanglement induced by two-fold modulations in optomechanical interfaces
Nature Electronics (2021)