Abstract
Hybrid quantum systems with inherently distinct degrees of freedom have a key role in many physical phenomena. Well-known examples include cavity quantum electrodynamics1, trapped ions2, and electrons and phonons in the solid state. In those systems, strong coupling makes the constituents lose their individual character and form dressed states, which represent a collective form of dynamics. As well as having fundamental importance, hybrid systems also have practical applications, notably in the emerging field of quantum information control. A promising approach is to combine long-lived atomic states2,3 with the accessible electrical degrees of freedom in superconducting cavities and quantum bits4,5 (qubits). Here we integrate circuit cavity quantum electrodynamics6,7 with phonons. Apart from coupling to a microwave cavity, our superconducting transmon qubit8, consisting of tunnel junctions and a capacitor, interacts with a phonon mode in a micromechanical resonator, and thus acts like an atom coupled to two different cavities. We measure the phonon Stark shift, as well as the splitting of the qubit spectral line into motional sidebands, which feature transitions between the dressed electromechanical states. In the time domain, we observe coherent conversion of qubit excitation to phonons as sideband Rabi oscillations. This is a model system with potential for a quantum interface, which may allow for storage of quantum information in long-lived phonon states, coupling to optical photons or for investigations of strongly coupled quantum systems near the classical limit.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Raimond, J. M., Brune, M. & Haroche, S. Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565–582 (2001)
Leibfried, D., Blatt, R., Monroe, C. & Wineland, D. Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75, 281–324 (2003)
André, A. et al. A coherent all-electrical interface between polar molecules and mesoscopic superconducting resonators. Nature Phys. 2, 636–642 (2006)
Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999)
Clarke, J. & Wilhelm, F. K. Superconducting quantum bits. Nature 453, 1031–1042 (2008)
Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004)
Chiorescu, I. et al. Coherent dynamics of a flux qubit coupled to a harmonic oscillator. Nature 431, 159–162 (2004)
Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007)
Mariantoni, M. et al. Implementing the quantum von Neumann architecture with superconducting circuits. Science 334, 61–65 (2011)
Reed, M. D. et al. Realization of three-qubit quantum error correction with superconducting circuits. Nature 482, 382–385 (2012)
Fedorov, A., Steffen, L., Baur, M., da Silva, M. P. & Wallraff, A. Implementation of a Toffoli gate with superconducting circuits. Nature 481, 170–172 (2012)
Dewes, A. et al. Quantum speeding-up of computation demonstrated in a superconducting two-qubit processor. Phys. Rev. B 85, 140503 (2012)
Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Phys. Rev. Lett. 107, 240501 (2011)
Ursin, R. et al. Entanglement-based quantum communication over 144 km. Nature Phys. 3, 481–486 (2007)
Zhu, X. et al. Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond. Nature 478, 221–224 (2011)
Kubo, Y. et al. Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble. Phys. Rev. Lett. 107, 220501 (2011)
Teufel, J. D. et al. Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359–363 (2011)
Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011)
Armour, A. D., Blencowe, M. P. & Schwab, K. C. Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper-pair box. Phys. Rev. Lett. 88, 148301 (2002)
Tian, L. Entanglement from a nanomechanical resonator weakly coupled to a single Cooper-pair box. Phys. Rev. B 72, 195411 (2005)
Etaki, S. et al. Motion detection of a micromechanical resonator embedded in a d.c. SQUID. Nature Phys. 4, 785–788 (2008)
LaHaye, M. D., Suh, J., Echternach, P. M., Schwab, K. C. & Roukes, M. L. Nanomechanical measurements of a superconducting qubit. Nature 459, 960–964 (2009)
O’Connell, A. D. et al. Quantum ground state and single-phonon control of a mechanical resonator. Nature 464, 697–703 (2010)
Blais, A., Huang, R.-S., Wallraff, A., Girvin, S. M. & Schoelkopf, R. J. Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 (2004)
Li, T. F. et al. High-frequency metallic nanomechanical resonators. Appl. Phys. Lett. 92, 043112 (2008)
Monroe, C., Meekhof, D. M., King, B. E. & Wineland, D. J. A Schrödinger cat superposition state of an atom. Science 272, 1131–1136 (1996)
Roos, C. et al. Quantum state engineering on an optical transition and decoherence in a Paul trap. Phys. Rev. Lett. 83, 4713–4716 (1999)
Niemczyk, T. et al. Circuit quantum electrodynamics in the ultrastrong-coupling regime. Nature Phys. 6, 772–776 (2010)
Tuorila, J. et al. Stark effect and generalized Bloch–Siegert shift in a strongly driven two-level system. Phys. Rev. Lett. 105, 257003 (2010)
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)
Acknowledgements
We thank M. Silveri, E. Thuneberg and T. Heikkilä for discussions. This work was supported by the Academy of Finland under CoE in Low Temperature Quantum Phenomena and Devices and project 141559, and by the European Research Council (grant number 240387-NEMSQED) and EU-FP7-NMP-246026. The work benefited from the facilities at the Micronova Nanofabrication Center. J.-M.P. acknowledges support from the Väisälä Foundation, the Emil Aaltonen Foundation and the Kaute Foundation, and J.L. acknowledges support from NGSMP.
Author information
Authors and Affiliations
Contributions
M.A.S. conceived the experiment and designed the experimental set-up with P.J.H. J.L., J.-M.P. and G.S.P. designed the circuit layout. S.U.C. and J.-M.P. fabricated the samples. J.-M.P. conducted the measurements, developed the theory and wrote the manuscript. S.U.C. helped with the measurements. All authors commented on the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary Information
This file contains Supplementary Figures 1–14, Supplementary Methods, Supplementary Discussion, Supplementary Equations, and additional references. The file contains a detailed discussion of device fabrication, various calibrations in the experiment, theoretical modeling using different approaches and discussion of additional data not covered in the main text. (PDF 1717 kb)
Rights and permissions
About this article
Cite this article
Pirkkalainen, JM., Cho, S., Li, J. et al. Hybrid circuit cavity quantum electrodynamics with a micromechanical resonator. Nature 494, 211–215 (2013). https://doi.org/10.1038/nature11821
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nature11821
This article is cited by
-
Nonlinear optical response in multiple-mode coupling nanomechanical system
Nonlinear Dynamics (2024)
-
Phononic bath engineering of a superconducting qubit
Nature Communications (2023)
-
Nonlinear nanomechanical resonators approaching the quantum ground state
Nature Physics (2023)
-
Hybrid quantum systems with high-T\(_c\) superconducting resonators
Scientific Reports (2023)
-
Bidirectional field-steering and atomic steering induced by a magnon mode in a qubit-photon system
Scientific Reports (2023)
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.