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Slowing, advancing and switching of microwave signals using circuit nanoelectromechanics

Abstract

The parametric coupling of electromagnetic and mechanical degrees of freedom gives rise to a host of optomechanical phenomena. Examples include quantum-limited displacement measurements, sideband cooling or amplification of mechanical motion. Likewise, this interaction provides mechanically mediated functionality for the processing of electromagnetic signals, such as microwave amplification. Here, we couple a superconducting niobium coplanar waveguide cavity to a nanomechanical oscillator, and demonstrate all-microwave field-controlled tunable slowing and advancing of microwave signals, with millisecond distortion-free delay and negligible losses. This is realized by using electromechanically induced transparency, an effect analogous to electromagnetically induced transparency in atomic physics. Moreover, by temporally modulating the electromechanical coupling and correspondingly the transparency window, switching of microwave signals is demonstrated and its temporal dynamics investigated. The exquisite temporal control gained over the electromechanical coupling provides the basis for realizing advanced protocols for storage of both classical and quantum microwave signals.

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Figure 1: Superconducting circuit nanoelectromechanical system.
Figure 2: Electromechanical and nanomechanical response.
Figure 3: Delayed and advanced microwave pulse propagation in a circuit electromechanical system in the presence of electromechanically induced transparency at 200 mK.
Figure 4: Switching dynamics.

References

  1. Day, P. K., LeDuc, H. G., Mazin, B. A., Vayonakis, A. & Zmuidzinas, J. A broadband superconducting detector suitable for use in large arrays. Nature 425, 817–821 (2003).

    Article  ADS  Google Scholar 

  2. Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).

    Article  ADS  Google Scholar 

  3. Vion, D. et al. Manipulating the quantum state of an electrical circuit. Science 296, 886–889 (2002).

    Article  ADS  Google Scholar 

  4. Clarke, J. & Wilhelm, F. K. Superconducting quantum bits. Nature 453, 1031–1042 (2008).

    Article  ADS  Google Scholar 

  5. Houck, A. A. et al. Generating single microwave photons in a circuit. Nature 449, 328–331 (2007).

    Article  ADS  Google Scholar 

  6. Majer, J. et al. Coupling superconducting qubits via a cavity bus. Nature 449, 443–447 (2007).

    Article  ADS  Google Scholar 

  7. Schoelkopf, R. J. & Girvin, S. M. Wiring up quantum systems. Nature 451, 664–669 (2008).

    Article  ADS  Google Scholar 

  8. Mariantoni, M. et al. Implementing the quantum von Neumann architecture with superconducting circuits. Science 334, 61–65 (2011).

    Article  ADS  Google Scholar 

  9. Rabl, P. et al. Hybrid quantum processors: Molecular ensembles as quantum memory for solid state circuits. Phys. Rev. Lett. 97, 033003 (2006).

    Article  ADS  Google Scholar 

  10. André, A. et al. A coherent all-electrical interface between polar molecules and mesoscopic superconducting resonators. Nature Phys. 2, 636–642 (2006).

    Article  ADS  Google Scholar 

  11. Schuster, D. I. et al. High-cooperativity coupling of electron-spin ensembles to superconducting cavities. Phys. Rev. Lett. 105, 140501 (2010).

    Article  ADS  Google Scholar 

  12. Kubo, Y. et al. Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble. Phys. Rev. Lett. 107, 220501 (2011).

    Article  ADS  Google Scholar 

  13. Frey, T. et al. Dipole coupling of a double quantum dot to a microwave resonator. Phys. Rev. Lett. 108, 046807 (2012).

    Article  ADS  Google Scholar 

  14. Kippenberg, T. J. & Vahala, K. J. Cavity optomechanics: Back-action at the mesoscale. Science 321, 1172–1176 (2008).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  16. Regal, C. A., Teufel, J. D. & Lehnert, K. W. Measuring nanomechanical motion with a microwave cavity interferometer. Nature Phys. 4, 555–560 (2008).

    Article  Google Scholar 

  17. Rocheleau, T. et al. Preparation and detection of a mechanical resonator near the ground state of motion. Nature 463, 72–75 (2010).

    Article  ADS  Google Scholar 

  18. Teufel, J. D., Donner, R., Castellanos-Beltran, M. A., Harlow, J. W. & Lehnert, K. W. Nanomechanical motion measured with precision beyond the standard quantum limit. Nature Nanotechnol. 4, 820–823 (2009).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Massel, F. et al. Microwave amplification with nanomechanical resonators. Nature 480, 351–354 (2011).

    Article  ADS  Google Scholar 

  21. Weis, S. et al. Optomechanically induced transparency. Science 330, 1520–1523 (2010).

    Article  ADS  Google Scholar 

  22. Safavi-Naeini, A. H. et al. Electromagnetically induced transparency and slow light with optomechanics. Nature 472, 69–73 (2011).

    Article  ADS  Google Scholar 

  23. 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 

  24. Romero-Isart, O. et al. Optically levitating dielectrics in the quantum regime: Theory and protocols. Phys. Rev. A 83, 013803 (2011).

    Article  ADS  Google Scholar 

  25. Wang, X., Vinjanampathy, S., Strauch, F. W. & Jacobs, K. Ultraefficient cooling of resonators: Beating sideband cooling with quantum control. Phys. Rev. Lett. 107, 177204 (2011).

    Article  ADS  Google Scholar 

  26. Gorodetsky, M., Schliesser, A., Anetsberger, G., Deleglise, S. & Kippenberg, T. J. Determination of the vacuum optomechanical coupling rate using frequency noise calibration. Opt. Express 18, 23236–23246 (2010).

    Article  ADS  Google Scholar 

  27. Agarwal, G. S. & Huang, S. Electromagnetically induced transparency in mechanical effects of light. Phys. Rev. A 81, 041803 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  29. Teufel, J. D., Harlow, J. D., Regal, C. A. & Lehnert, K. W. Dynamical backaction of microwave fields on a nanomechanical oscillator. Phys. Rev. Lett. 101, 197203 (2008).

    Article  ADS  Google Scholar 

  30. Kippenberg, T. J., Rokhsari, H., Carmon, T., Scherer, A. & Vahala, K. J. Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity. Phys. Rev. Lett. 95, 033901 (2005).

    Article  ADS  Google Scholar 

  31. Schliesser, A., Del’Haye, P., Nooshi, N., Vahala, K. & Kippenberg, T. Radiation pressure cooling of a micromechanical oscillator using dynamical backaction. Phys. Rev. Lett. 97, 243905 (2006).

    Article  ADS  Google Scholar 

  32. Gigan, S. et al. Self-cooling of a micromirror by radiation pressure. Nature 444, 67–70 (2006).

    Article  ADS  Google Scholar 

  33. Arcizet, O., Cohadon, P-F., Briant, T., Pinard, M. & Heidmann, A. Radiation-pressure cooling and optomechanical instability of a micromirror. Nature 444, 71–74 (2006).

    Article  ADS  Google Scholar 

  34. Nayfeh, A. H. & Mook, D. T. Nonlinear Oscillations (Wiley, 1979).

    MATH  Google Scholar 

  35. Kozinsky, I., Postma, H. W. C., Bargatin, I. & Roukes, M. L. Tuning nonlinearity, dynamic range, and frequency of nanomechanical resonators. Appl. Phys. Lett. 88, 253101 (2006).

    Article  ADS  Google Scholar 

  36. Unterreithmeier, Q. P., Faust, T. & Kotthaus, J. P. Nonlinear switching dynamics in a nanomechanical resonator. Phys. Rev. B 81, 241405 (2010).

    Article  ADS  Google Scholar 

  37. Metcalfe, M. et al. Measuring the decoherence of a quantronium qubit with the cavity bifurcation amplifier. Phys. Rev. B 76, 174516 (2007).

    Article  ADS  Google Scholar 

  38. Mahboob, I. & Yamaguchi, H. Bit storage and bit flip operations in an electromechanical oscillator. Nature Nanotechnol. 3, 275–279 (2008).

    Article  Google Scholar 

  39. Schliesser, A. & Kippenberg, T. J. in Advances in Atomic, Molecular and Optical Physics Vol. 58 (eds Arimondo, E., Berman, P. & Lin, C. C.) Ch. 5, 207–323 (Elsevier Academic, 2010).

    Google Scholar 

  40. Jiang, C., Chen, B. & Zhu, K. Tunable pulse delay and advancement device based on a cavity electromechanical system. Europhys. Lett. 94, 38002 (2011).

    Article  ADS  Google Scholar 

  41. Fleischhauer, M., Imamoglu, A. & Marangos, J. P. Electromagnetically induced transparency: Optics in coherent media. Rev. Mod. Phys. 77, 633–673 (2005).

    Article  ADS  Google Scholar 

  42. Longdell, J. J., Fraval, E., Sellars, M. J. & Manson, N. B. Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid. Phys. Rev. Lett. 95, 063601 (2005).

    Article  ADS  Google Scholar 

  43. 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).

    Article  ADS  Google Scholar 

  44. Wang, Y-D. & Clerk, A. A. Using interference for high fidelity quantum state transfer in optomechanics. Phys. Rev. Lett. 108, 153603 (2012).

    Article  ADS  Google Scholar 

  45. Zhang, J., Peng, K. & Braunstein, S. L. Quantum-state transfer from light to macroscopic oscillators. Phys. Rev. A 68, 013808 (2003).

    Article  ADS  Google Scholar 

  46. Tian, L. Adiabatic state conversion and pulse transmission in optomechanical systems. Phys. Rev. Lett. 108, 153604 (2012).

    Article  ADS  Google Scholar 

  47. Phillips, D. F., Fleischhauer, A., Mair, A., Walsworth, R. L. & Lukin, M. D. Storage of light in atomic vapour. Phys. Rev. Lett. 86, 783–786 (2001).

    Article  ADS  Google Scholar 

  48. Palomaki, T. A. et al. State transfer between a mechanical oscillator and microwave fields in the quantum regime. Preprint at http://arxiv.org/abs/1206.5562 (2012).

  49. Fiore, V. et al. Storing optical information as a mechanical excitation in a silica optomechanical resonator. Phys. Rev. Lett. 107, 133601 (2011).

    Article  ADS  Google Scholar 

  50. Hoi, I. et al. Demonstration of a single-photon router in the microwave regime. Phys. Rev. Lett. 107, 073601 (2011).

    Article  ADS  Google Scholar 

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Acknowledgements

T.J.K. acknowledges support by the NCCR of Quantum Engineering, an ERC Starting Grant (SiMP) and the Swiss National Science Foundation (SNF). Financial support from the German Excellence Initiative through the Nanosystems Initiative Munich (NIM) is gratefully acknowledged. Samples were grown and fabricated at the Center of MicroNanotechnology (CMi) at EPFL. The authors acknowledge the assistance of S. Weis, T. Niemczyk and H. Chibani in fabrication, and P. Hakonen and P. Lähteenmäki for measurement in the early phase of the project.

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Contributions

X.Z. designed and fabricated the samples. The cryogenic measurement set-up was implemented by F.H. and H.H. F.H., X.Z., H.H. and A.S. performed the experiments. X.Z. and A.S. performed theoretical modelling and analysis of the data. X.Z. wrote the paper with guidance from A.S. and T.J.K. All authors discussed the results and contributed to the final version of the manuscript.

Corresponding authors

Correspondence to H. Huebl or T. J. Kippenberg.

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Zhou, X., Hocke, F., Schliesser, A. et al. Slowing, advancing and switching of microwave signals using circuit nanoelectromechanics. Nature Phys 9, 179–184 (2013). https://doi.org/10.1038/nphys2527

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