Abstract

We fabricate and characterize a microscale silicon opto-electromechanical system whose mechanical motion is coupled capacitively to an electrical circuit and optically via radiation pressure to a photonic crystal cavity. To achieve large electromechanical interaction strength, we implement an inverse shadow mask fabrication scheme which obtains capacitor gaps as small as 30 nm while maintaining a silicon surface quality necessary for minimizing optical loss. Using the sensitive optical read-out of the photonic crystal cavity, we characterize the linear and nonlinear capacitive coupling to the fundamental ωm/2π = 63 MHz in-plane flexural motion of the structure, showing that the large electromechanical coupling in such devices may be suitable for realizing efficient microwave-to-optical signal conversion.

© 2015 Optical Society of America

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References

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  1. N. Yazdi, F. Avazi, and K. Najafi, “Micromachined inertial sensors,” Proc. IEEE 86, 1640–1659 (1998).
    [Crossref]
  2. T. Tajima, T. Nishiguchi, S. Chiba, A. Morita, M. Abe, K. Tanioka, N. Saito, and M. Esashi, “High-performance ultra-small single crystalline silicon microphone of an integrated structure,” Microelectron. Eng. 67–68, 508–519 (2003).
    [Crossref]
  3. W. P. Eatony and J. H. Smith, “Micromachined pressure sensors: review and recent developments,” Smart Mater. Struct. 6, 530–539 (1997).
    [Crossref]
  4. K. A. Cook-Chennault, N. Thambi, and A. M. Sastry, “Powering MEMS portable devices: a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems,” Smart Mater. Struct. 17, 043001 (2008).
    [Crossref]
  5. M. S. Hanay, S. Kelber, A. K. Naik, D. Chi, S. Hentz, E. C. Bullard, E. Colinet, L. Duraffourg, and M. L. Roukes, “Single-protein nanomechanical mass spectrometry in real time,” Nature Nanotech. 7, 602–608 (2012).
    [Crossref]
  6. A. Manz, N. Graber, and H. M. Widmer, “Miniaturized total chemical analysis systems: a novel concept for chemical sensing,” Sens. Actuat. B: Chem. 1, 244–248 (1990).
    [Crossref]
  7. M. Eichenfield, R. M. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometer-scale photonic crystal opto-mechanical cavity,” Nature 459, 550–555 (2009).
    [Crossref] [PubMed]
  8. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
    [Crossref] [PubMed]
  9. J. D. Cohen and S. M. Meenehan, “Optical coupling to nanoscale optomechanical cavities for near quantum-limited motion transduction,” Opt. Express 21, 11227 (2013).
    [Crossref] [PubMed]
  10. G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, and T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
    [Crossref]
  11. J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
    [Crossref] [PubMed]
  12. K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical Transducers for Long-Distance Quantum Communication,” Phys. Rev. Lett. 105, 220501 (2010).
    [Crossref]
  13. A. H. Safavi-Naeini and O. Painter, “Proposal for an optomechanical traveling wave phononphoton translator,” New J. Phys. 13, 013017 (2011).
    [Crossref]
  14. C. A. Regal and K. W. Lehnert, “From cavity electromechanics to cavity optomechanics,” J. Phys.: Conf. Ser. 264, 012025 (2011).
  15. S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible Optical-to-Microwave Quantum Interface,” Phys. Rev. Lett. 109, 130503 (2012).
    [Crossref] [PubMed]
  16. Y.-D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14, 105010 (2012).
    [Crossref]
  17. T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, J. Zeuthen, E. Appel, J. M. Taylor, A. Srensen, K. Usami, A. Sorrenson, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
    [Crossref] [PubMed]
  18. R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
    [Crossref]
  19. J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
    [Crossref]
  20. M. Winger, T. D. Blasius, T. P. M. Alegre, A. H. Safavi-Naeini, S. Meenehan, J. Cohen, S. Stobbe, and O. Painter, “A chip-scale integrated cavity-electro-optomechanics platform,” Opt. Express 19, 24905–24921 (2011).
    [Crossref]
  21. K. Cicak, M. Allman, J. Strong, K. Osborn, and R. Simmonds, “Vacuum-Gap Capacitors for Low-Loss Super-conducting Resonant Circuits,” IEEE Trans. Appl. Supercond. 19, 948–952 (2009).
    [Crossref]
  22. J. Sulkko, M. A. Sillanpaa, P. Hakkinen, L. Lechner, M. Helle, A. Fefferman, J. Parpia, and P. J. Hakonen, “Strong Gate Coupling of High-Q Nanomechanical Resonators,” Nano Lett. 10, 4884–4889 (2010).
    [Crossref] [PubMed]
  23. J. Tian, W. Yan, Y. Liu, J. Luo, D. Zhang, Z. Li, and M. Qiu, “Optical quality improvement of Si photonic devices fabricated by focused-ion-beam milling,” J. Lightwave Technol. 27, 4306–4310 (2009).
    [Crossref]
  24. A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97, 181106 (2010).
    [Crossref]
  25. C. P. Michael, M. Borselli, T. J. Johnson, C. Chrystal, and O. Painter, “An optical fiber-taper probe for wafer-scale microphotonic device characterization,” Opt. Express 15, 4745–4752 (2007).
    [Crossref] [PubMed]
  26. S. S. Verbridge, H. G. Craighead, and J. M. Parpia, “A megahertz nanomechanical resonator with room temperature quality factor over a million,” Appl. Phys. Lett. 92, 013112 (2008).
    [Crossref]
  27. M. Borselli, High-Q microresonators as lasing elements for silicon photonics, Ph.D. thesis, California Institute of Technology (2006).
  28. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory and Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
    [Crossref]
  29. D. Rugar and P. Grütter, “Mechanical parametric amplification and thermomechanical noise squeezing,” Phys. Rev. Lett. 67, 699–702 (1991).
    [Crossref] [PubMed]
  30. R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, “Noise Squeezing in a Nanomechanical Duffing Resonator,” Phys. Rev. Lett. 98, 078103 (2007).
    [Crossref] [PubMed]
  31. M. Poot and H. X. Tang, “Phase shifting, strong coupling, and parametric feedback squeezing of an opto-electromechanical device,” in Proceedings of CLEO: 2013 p. CW3F.7 (2013).
  32. C. C. Wu and Z. Zhong, “Capacitive Spring Softening in Single-Walled Carbon Nanotube Nanoelectromechanical Resonators,” Nano Lett. 11, 1448–1451 (2011).
    [Crossref] [PubMed]
  33. A. Szorkovszky, A. A. Clerk, A. C. Doherty, and W. P. Bowen, “Detuned mechanical parametric amplification as a quantum non-demolition measurement,” New J. Phys. 16, 043023 (2014).
    [Crossref]
  34. I. Mahboob and H. Yamaguchi, “Bit storage and bit flip operations in an electromechanical oscillator,” Nat. Nano 3, 275–279 (2008).
    [Crossref]
  35. S. Rips and M. J. Hartmann, “Quantum Information Processing with Nanomechanical Qubits,” Phys. Rev. Lett. 110, 120503 (2013).
    [Crossref] [PubMed]
  36. Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458, 1001–1004 (2009).
    [Crossref] [PubMed]
  37. M. Agarwal, K.-K. Park, R. Candler, B. Kim, M. Hopcroft, S. A. Chandorkar, C. Jha, R. Melamud, T. Kenny, and B. Murmann, “Nonlinear Characterization of Electrostatic MEMS Resonators,” in International Frequency Control Symposium and Exposition, 2006 IEEE pp. 209–212 (2006).
    [Crossref]
  38. V. Kaajakari, T. Mattila, A. Lipsanen, and A. Oja, “Nonlinear mechanical effects in silicon longitudinal mode beam resonators,” Sens. Actua. A 120, 64–70 (2005).
    [Crossref]
  39. R. Lifshitz and M. C. Cross, “Response of parametrically driven nonlinear coupled oscillators with application to micromechanical and nanomechanical resonator arrays,” Phys. Rev. B 67, 134302 (2003).
    [Crossref]
  40. S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Circuit QED and engineering charge-based superconducting qubits,” Phys. Scr. T137, 014012 (2009).
    [Crossref]
  41. K. Cicak, D. Li, J. A. Strong, M. S. Allman, F. Altomare, A. J. Sirois, J. D. Whittaker, J. D. Teufel, and R. W. Simmonds, “Low-loss superconducting resonant circuits using vacuum-gap-based microwave components,” App. Phys. Lett. 96, 093502 (2010).
    [Crossref]
  42. J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
    [Crossref] [PubMed]
  43. S. M. Meenehan, J. D. Cohen, S. Groeblacher, J. T. Hill, A. H. Safavi-Naeini, M. Aspelmeyer, and O. Painter, “Thermalization properties at mK temperatures of a nanoscale optomechanical resonator with acoustic-bandgap shield,” http://arxiv.org/abs/1403.3703 (2014).
  44. A. H. Safavi-Naeini, S. Groeblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
    [Crossref] [PubMed]
  45. A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Neeley, H. Wang, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Microwave dielectric loss at single photon energies and millikelvin temperatures,” Appl. Phys. Lett. 92, 112903 (2008).
    [Crossref]
  46. Y. Shim, J.-P. Raskin, C. R. Neve, and M. Rais-Zadeh, “RF MEMS Passives on High-Resistivity Silicon Substrates,” IEEE Microw. Wirel. Compon. Lett. 23, 632–634 (2013).
    [Crossref]
  47. J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
    [Crossref]

2014 (3)

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, J. Zeuthen, E. Appel, J. M. Taylor, A. Srensen, K. Usami, A. Sorrenson, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref] [PubMed]

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
[Crossref]

A. Szorkovszky, A. A. Clerk, A. C. Doherty, and W. P. Bowen, “Detuned mechanical parametric amplification as a quantum non-demolition measurement,” New J. Phys. 16, 043023 (2014).
[Crossref]

2013 (5)

A. H. Safavi-Naeini, S. Groeblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

Y. Shim, J.-P. Raskin, C. R. Neve, and M. Rais-Zadeh, “RF MEMS Passives on High-Resistivity Silicon Substrates,” IEEE Microw. Wirel. Compon. Lett. 23, 632–634 (2013).
[Crossref]

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
[Crossref]

S. Rips and M. J. Hartmann, “Quantum Information Processing with Nanomechanical Qubits,” Phys. Rev. Lett. 110, 120503 (2013).
[Crossref] [PubMed]

J. D. Cohen and S. M. Meenehan, “Optical coupling to nanoscale optomechanical cavities for near quantum-limited motion transduction,” Opt. Express 21, 11227 (2013).
[Crossref] [PubMed]

2012 (4)

S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible Optical-to-Microwave Quantum Interface,” Phys. Rev. Lett. 109, 130503 (2012).
[Crossref] [PubMed]

Y.-D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14, 105010 (2012).
[Crossref]

M. S. Hanay, S. Kelber, A. K. Naik, D. Chi, S. Hentz, E. C. Bullard, E. Colinet, L. Duraffourg, and M. L. Roukes, “Single-protein nanomechanical mass spectrometry in real time,” Nature Nanotech. 7, 602–608 (2012).
[Crossref]

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
[Crossref]

2011 (6)

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

A. H. Safavi-Naeini and O. Painter, “Proposal for an optomechanical traveling wave phononphoton translator,” New J. Phys. 13, 013017 (2011).
[Crossref]

C. A. Regal and K. W. Lehnert, “From cavity electromechanics to cavity optomechanics,” J. Phys.: Conf. Ser. 264, 012025 (2011).

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

C. C. Wu and Z. Zhong, “Capacitive Spring Softening in Single-Walled Carbon Nanotube Nanoelectromechanical Resonators,” Nano Lett. 11, 1448–1451 (2011).
[Crossref] [PubMed]

M. Winger, T. D. Blasius, T. P. M. Alegre, A. H. Safavi-Naeini, S. Meenehan, J. Cohen, S. Stobbe, and O. Painter, “A chip-scale integrated cavity-electro-optomechanics platform,” Opt. Express 19, 24905–24921 (2011).
[Crossref]

2010 (5)

J. Sulkko, M. A. Sillanpaa, P. Hakkinen, L. Lechner, M. Helle, A. Fefferman, J. Parpia, and P. J. Hakonen, “Strong Gate Coupling of High-Q Nanomechanical Resonators,” Nano Lett. 10, 4884–4889 (2010).
[Crossref] [PubMed]

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97, 181106 (2010).
[Crossref]

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical Transducers for Long-Distance Quantum Communication,” Phys. Rev. Lett. 105, 220501 (2010).
[Crossref]

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, and T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
[Crossref]

K. Cicak, D. Li, J. A. Strong, M. S. Allman, F. Altomare, A. J. Sirois, J. D. Whittaker, J. D. Teufel, and R. W. Simmonds, “Low-loss superconducting resonant circuits using vacuum-gap-based microwave components,” App. Phys. Lett. 96, 093502 (2010).
[Crossref]

2009 (6)

S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Circuit QED and engineering charge-based superconducting qubits,” Phys. Scr. T137, 014012 (2009).
[Crossref]

M. Eichenfield, R. M. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometer-scale photonic crystal opto-mechanical cavity,” Nature 459, 550–555 (2009).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref] [PubMed]

J. Tian, W. Yan, Y. Liu, J. Luo, D. Zhang, Z. Li, and M. Qiu, “Optical quality improvement of Si photonic devices fabricated by focused-ion-beam milling,” J. Lightwave Technol. 27, 4306–4310 (2009).
[Crossref]

K. Cicak, M. Allman, J. Strong, K. Osborn, and R. Simmonds, “Vacuum-Gap Capacitors for Low-Loss Super-conducting Resonant Circuits,” IEEE Trans. Appl. Supercond. 19, 948–952 (2009).
[Crossref]

Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458, 1001–1004 (2009).
[Crossref] [PubMed]

2008 (4)

S. S. Verbridge, H. G. Craighead, and J. M. Parpia, “A megahertz nanomechanical resonator with room temperature quality factor over a million,” Appl. Phys. Lett. 92, 013112 (2008).
[Crossref]

K. A. Cook-Chennault, N. Thambi, and A. M. Sastry, “Powering MEMS portable devices: a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems,” Smart Mater. Struct. 17, 043001 (2008).
[Crossref]

I. Mahboob and H. Yamaguchi, “Bit storage and bit flip operations in an electromechanical oscillator,” Nat. Nano 3, 275–279 (2008).
[Crossref]

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Neeley, H. Wang, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Microwave dielectric loss at single photon energies and millikelvin temperatures,” Appl. Phys. Lett. 92, 112903 (2008).
[Crossref]

2007 (2)

2005 (1)

V. Kaajakari, T. Mattila, A. Lipsanen, and A. Oja, “Nonlinear mechanical effects in silicon longitudinal mode beam resonators,” Sens. Actua. A 120, 64–70 (2005).
[Crossref]

2003 (2)

R. Lifshitz and M. C. Cross, “Response of parametrically driven nonlinear coupled oscillators with application to micromechanical and nanomechanical resonator arrays,” Phys. Rev. B 67, 134302 (2003).
[Crossref]

T. Tajima, T. Nishiguchi, S. Chiba, A. Morita, M. Abe, K. Tanioka, N. Saito, and M. Esashi, “High-performance ultra-small single crystalline silicon microphone of an integrated structure,” Microelectron. Eng. 67–68, 508–519 (2003).
[Crossref]

2002 (1)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory and Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

1998 (1)

N. Yazdi, F. Avazi, and K. Najafi, “Micromachined inertial sensors,” Proc. IEEE 86, 1640–1659 (1998).
[Crossref]

1997 (1)

W. P. Eatony and J. H. Smith, “Micromachined pressure sensors: review and recent developments,” Smart Mater. Struct. 6, 530–539 (1997).
[Crossref]

1991 (1)

D. Rugar and P. Grütter, “Mechanical parametric amplification and thermomechanical noise squeezing,” Phys. Rev. Lett. 67, 699–702 (1991).
[Crossref] [PubMed]

1990 (1)

A. Manz, N. Graber, and H. M. Widmer, “Miniaturized total chemical analysis systems: a novel concept for chemical sensing,” Sens. Actuat. B: Chem. 1, 244–248 (1990).
[Crossref]

Abdi, M.

S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible Optical-to-Microwave Quantum Interface,” Phys. Rev. Lett. 109, 130503 (2012).
[Crossref] [PubMed]

Abe, M.

T. Tajima, T. Nishiguchi, S. Chiba, A. Morita, M. Abe, K. Tanioka, N. Saito, and M. Esashi, “High-performance ultra-small single crystalline silicon microphone of an integrated structure,” Microelectron. Eng. 67–68, 508–519 (2003).
[Crossref]

Agarwal, M.

M. Agarwal, K.-K. Park, R. Candler, B. Kim, M. Hopcroft, S. A. Chandorkar, C. Jha, R. Melamud, T. Kenny, and B. Murmann, “Nonlinear Characterization of Electrostatic MEMS Resonators,” in International Frequency Control Symposium and Exposition, 2006 IEEE pp. 209–212 (2006).
[Crossref]

Alegre, T. P. M.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

M. Winger, T. D. Blasius, T. P. M. Alegre, A. H. Safavi-Naeini, S. Meenehan, J. Cohen, S. Stobbe, and O. Painter, “A chip-scale integrated cavity-electro-optomechanics platform,” Opt. Express 19, 24905–24921 (2011).
[Crossref]

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97, 181106 (2010).
[Crossref]

Allman, M.

K. Cicak, M. Allman, J. Strong, K. Osborn, and R. Simmonds, “Vacuum-Gap Capacitors for Low-Loss Super-conducting Resonant Circuits,” IEEE Trans. Appl. Supercond. 19, 948–952 (2009).
[Crossref]

Allman, M. S.

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

K. Cicak, D. Li, J. A. Strong, M. S. Allman, F. Altomare, A. J. Sirois, J. D. Whittaker, J. D. Teufel, and R. W. Simmonds, “Low-loss superconducting resonant circuits using vacuum-gap-based microwave components,” App. Phys. Lett. 96, 093502 (2010).
[Crossref]

Almog, R.

R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, “Noise Squeezing in a Nanomechanical Duffing Resonator,” Phys. Rev. Lett. 98, 078103 (2007).
[Crossref] [PubMed]

Altomare, F.

K. Cicak, D. Li, J. A. Strong, M. S. Allman, F. Altomare, A. J. Sirois, J. D. Whittaker, J. D. Teufel, and R. W. Simmonds, “Low-loss superconducting resonant circuits using vacuum-gap-based microwave components,” App. Phys. Lett. 96, 093502 (2010).
[Crossref]

Andrews, R. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
[Crossref]

Anetsberger, G.

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, and T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
[Crossref]

Ansmann, M.

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Neeley, H. Wang, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Microwave dielectric loss at single photon energies and millikelvin temperatures,” Appl. Phys. Lett. 92, 112903 (2008).
[Crossref]

Appel, E.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, J. Zeuthen, E. Appel, J. M. Taylor, A. Srensen, K. Usami, A. Sorrenson, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref] [PubMed]

Arcizet, O.

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, and T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
[Crossref]

Aspelmeyer, M.

A. H. Safavi-Naeini, S. Groeblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

Avazi, F.

N. Yazdi, F. Avazi, and K. Najafi, “Micromachined inertial sensors,” Proc. IEEE 86, 1640–1659 (1998).
[Crossref]

Awschalom, D. D.

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
[Crossref]

Bagci, T.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, J. Zeuthen, E. Appel, J. M. Taylor, A. Srensen, K. Usami, A. Sorrenson, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref] [PubMed]

Barzanjeh, S.

S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible Optical-to-Microwave Quantum Interface,” Phys. Rev. Lett. 109, 130503 (2012).
[Crossref] [PubMed]

Bialczak, R. C.

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Neeley, H. Wang, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Microwave dielectric loss at single photon energies and millikelvin temperatures,” Appl. Phys. Lett. 92, 112903 (2008).
[Crossref]

Blasius, T. D.

Bochmann, J.

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
[Crossref]

Borselli, M.

Bowen, W. P.

A. Szorkovszky, A. A. Clerk, A. C. Doherty, and W. P. Bowen, “Detuned mechanical parametric amplification as a quantum non-demolition measurement,” New J. Phys. 16, 043023 (2014).
[Crossref]

Buks, E.

R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, “Noise Squeezing in a Nanomechanical Duffing Resonator,” Phys. Rev. Lett. 98, 078103 (2007).
[Crossref] [PubMed]

Bullard, E. C.

M. S. Hanay, S. Kelber, A. K. Naik, D. Chi, S. Hentz, E. C. Bullard, E. Colinet, L. Duraffourg, and M. L. Roukes, “Single-protein nanomechanical mass spectrometry in real time,” Nature Nanotech. 7, 602–608 (2012).
[Crossref]

Camacho, R. M.

M. Eichenfield, R. M. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometer-scale photonic crystal opto-mechanical cavity,” Nature 459, 550–555 (2009).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref] [PubMed]

Candler, R.

M. Agarwal, K.-K. Park, R. Candler, B. Kim, M. Hopcroft, S. A. Chandorkar, C. Jha, R. Melamud, T. Kenny, and B. Murmann, “Nonlinear Characterization of Electrostatic MEMS Resonators,” in International Frequency Control Symposium and Exposition, 2006 IEEE pp. 209–212 (2006).
[Crossref]

Chan, J.

A. H. Safavi-Naeini, S. Groeblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

M. Eichenfield, R. M. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometer-scale photonic crystal opto-mechanical cavity,” Nature 459, 550–555 (2009).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref] [PubMed]

Chandorkar, S. A.

M. Agarwal, K.-K. Park, R. Candler, B. Kim, M. Hopcroft, S. A. Chandorkar, C. Jha, R. Melamud, T. Kenny, and B. Murmann, “Nonlinear Characterization of Electrostatic MEMS Resonators,” in International Frequency Control Symposium and Exposition, 2006 IEEE pp. 209–212 (2006).
[Crossref]

Chi, D.

M. S. Hanay, S. Kelber, A. K. Naik, D. Chi, S. Hentz, E. C. Bullard, E. Colinet, L. Duraffourg, and M. L. Roukes, “Single-protein nanomechanical mass spectrometry in real time,” Nature Nanotech. 7, 602–608 (2012).
[Crossref]

Chiba, S.

T. Tajima, T. Nishiguchi, S. Chiba, A. Morita, M. Abe, K. Tanioka, N. Saito, and M. Esashi, “High-performance ultra-small single crystalline silicon microphone of an integrated structure,” Microelectron. Eng. 67–68, 508–519 (2003).
[Crossref]

Chrystal, C.

Cicak, K.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
[Crossref]

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

K. Cicak, D. Li, J. A. Strong, M. S. Allman, F. Altomare, A. J. Sirois, J. D. Whittaker, J. D. Teufel, and R. W. Simmonds, “Low-loss superconducting resonant circuits using vacuum-gap-based microwave components,” App. Phys. Lett. 96, 093502 (2010).
[Crossref]

K. Cicak, M. Allman, J. Strong, K. Osborn, and R. Simmonds, “Vacuum-Gap Capacitors for Low-Loss Super-conducting Resonant Circuits,” IEEE Trans. Appl. Supercond. 19, 948–952 (2009).
[Crossref]

Cleland, A. N.

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
[Crossref]

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Neeley, H. Wang, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Microwave dielectric loss at single photon energies and millikelvin temperatures,” Appl. Phys. Lett. 92, 112903 (2008).
[Crossref]

Clerk, A. A.

A. Szorkovszky, A. A. Clerk, A. C. Doherty, and W. P. Bowen, “Detuned mechanical parametric amplification as a quantum non-demolition measurement,” New J. Phys. 16, 043023 (2014).
[Crossref]

Y.-D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14, 105010 (2012).
[Crossref]

Cohen, J.

Cohen, J. D.

Colinet, E.

M. S. Hanay, S. Kelber, A. K. Naik, D. Chi, S. Hentz, E. C. Bullard, E. Colinet, L. Duraffourg, and M. L. Roukes, “Single-protein nanomechanical mass spectrometry in real time,” Nature Nanotech. 7, 602–608 (2012).
[Crossref]

Cook-Chennault, K. A.

K. A. Cook-Chennault, N. Thambi, and A. M. Sastry, “Powering MEMS portable devices: a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems,” Smart Mater. Struct. 17, 043001 (2008).
[Crossref]

Craighead, H. G.

S. S. Verbridge, H. G. Craighead, and J. M. Parpia, “A megahertz nanomechanical resonator with room temperature quality factor over a million,” Appl. Phys. Lett. 92, 013112 (2008).
[Crossref]

Cross, M. C.

R. Lifshitz and M. C. Cross, “Response of parametrically driven nonlinear coupled oscillators with application to micromechanical and nanomechanical resonator arrays,” Phys. Rev. B 67, 134302 (2003).
[Crossref]

Devoret, M. H.

S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Circuit QED and engineering charge-based superconducting qubits,” Phys. Scr. T137, 014012 (2009).
[Crossref]

Doherty, A. C.

A. Szorkovszky, A. A. Clerk, A. C. Doherty, and W. P. Bowen, “Detuned mechanical parametric amplification as a quantum non-demolition measurement,” New J. Phys. 16, 043023 (2014).
[Crossref]

Donner, T.

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

Duraffourg, L.

M. S. Hanay, S. Kelber, A. K. Naik, D. Chi, S. Hentz, E. C. Bullard, E. Colinet, L. Duraffourg, and M. L. Roukes, “Single-protein nanomechanical mass spectrometry in real time,” Nature Nanotech. 7, 602–608 (2012).
[Crossref]

Eatony, W. P.

W. P. Eatony and J. H. Smith, “Micromachined pressure sensors: review and recent developments,” Smart Mater. Struct. 6, 530–539 (1997).
[Crossref]

Eichenfield, M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref] [PubMed]

M. Eichenfield, R. M. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometer-scale photonic crystal opto-mechanical cavity,” Nature 459, 550–555 (2009).
[Crossref] [PubMed]

Esashi, M.

T. Tajima, T. Nishiguchi, S. Chiba, A. Morita, M. Abe, K. Tanioka, N. Saito, and M. Esashi, “High-performance ultra-small single crystalline silicon microphone of an integrated structure,” Microelectron. Eng. 67–68, 508–519 (2003).
[Crossref]

Fefferman, A.

J. Sulkko, M. A. Sillanpaa, P. Hakkinen, L. Lechner, M. Helle, A. Fefferman, J. Parpia, and P. J. Hakonen, “Strong Gate Coupling of High-Q Nanomechanical Resonators,” Nano Lett. 10, 4884–4889 (2010).
[Crossref] [PubMed]

Fink, Y.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory and Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

Gavartin, E.

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, and T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
[Crossref]

Girvin, S. M.

S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Circuit QED and engineering charge-based superconducting qubits,” Phys. Scr. T137, 014012 (2009).
[Crossref]

Gorodetsky, M. L.

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, and T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
[Crossref]

Graber, N.

A. Manz, N. Graber, and H. M. Widmer, “Miniaturized total chemical analysis systems: a novel concept for chemical sensing,” Sens. Actuat. B: Chem. 1, 244–248 (1990).
[Crossref]

Groblacher, S.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

Groeblacher, S.

A. H. Safavi-Naeini, S. Groeblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

Grütter, P.

D. Rugar and P. Grütter, “Mechanical parametric amplification and thermomechanical noise squeezing,” Phys. Rev. Lett. 67, 699–702 (1991).
[Crossref] [PubMed]

Hakkinen, P.

J. Sulkko, M. A. Sillanpaa, P. Hakkinen, L. Lechner, M. Helle, A. Fefferman, J. Parpia, and P. J. Hakonen, “Strong Gate Coupling of High-Q Nanomechanical Resonators,” Nano Lett. 10, 4884–4889 (2010).
[Crossref] [PubMed]

Hakonen, P. J.

J. Sulkko, M. A. Sillanpaa, P. Hakkinen, L. Lechner, M. Helle, A. Fefferman, J. Parpia, and P. J. Hakonen, “Strong Gate Coupling of High-Q Nanomechanical Resonators,” Nano Lett. 10, 4884–4889 (2010).
[Crossref] [PubMed]

Hanay, M. S.

M. S. Hanay, S. Kelber, A. K. Naik, D. Chi, S. Hentz, E. C. Bullard, E. Colinet, L. Duraffourg, and M. L. Roukes, “Single-protein nanomechanical mass spectrometry in real time,” Nature Nanotech. 7, 602–608 (2012).
[Crossref]

Harlow, J. W.

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

Hartmann, M. J.

S. Rips and M. J. Hartmann, “Quantum Information Processing with Nanomechanical Qubits,” Phys. Rev. Lett. 110, 120503 (2013).
[Crossref] [PubMed]

Helle, M.

J. Sulkko, M. A. Sillanpaa, P. Hakkinen, L. Lechner, M. Helle, A. Fefferman, J. Parpia, and P. J. Hakonen, “Strong Gate Coupling of High-Q Nanomechanical Resonators,” Nano Lett. 10, 4884–4889 (2010).
[Crossref] [PubMed]

Hentz, S.

M. S. Hanay, S. Kelber, A. K. Naik, D. Chi, S. Hentz, E. C. Bullard, E. Colinet, L. Duraffourg, and M. L. Roukes, “Single-protein nanomechanical mass spectrometry in real time,” Nature Nanotech. 7, 602–608 (2012).
[Crossref]

Hill, J. T.

A. H. Safavi-Naeini, S. Groeblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

Hofheinz, M.

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Neeley, H. Wang, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Microwave dielectric loss at single photon energies and millikelvin temperatures,” Appl. Phys. Lett. 92, 112903 (2008).
[Crossref]

Hopcroft, M.

M. Agarwal, K.-K. Park, R. Candler, B. Kim, M. Hopcroft, S. A. Chandorkar, C. Jha, R. Melamud, T. Kenny, and B. Murmann, “Nonlinear Characterization of Electrostatic MEMS Resonators,” in International Frequency Control Symposium and Exposition, 2006 IEEE pp. 209–212 (2006).
[Crossref]

Ibanescu, M.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory and Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

Jha, C.

M. Agarwal, K.-K. Park, R. Candler, B. Kim, M. Hopcroft, S. A. Chandorkar, C. Jha, R. Melamud, T. Kenny, and B. Murmann, “Nonlinear Characterization of Electrostatic MEMS Resonators,” in International Frequency Control Symposium and Exposition, 2006 IEEE pp. 209–212 (2006).
[Crossref]

Joannopoulos, J. D.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory and Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

Johnson, S. G.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory and Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

Johnson, T. J.

Kaajakari, V.

V. Kaajakari, T. Mattila, A. Lipsanen, and A. Oja, “Nonlinear mechanical effects in silicon longitudinal mode beam resonators,” Sens. Actua. A 120, 64–70 (2005).
[Crossref]

Katz, N.

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Neeley, H. Wang, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Microwave dielectric loss at single photon energies and millikelvin temperatures,” Appl. Phys. Lett. 92, 112903 (2008).
[Crossref]

Kelber, S.

M. S. Hanay, S. Kelber, A. K. Naik, D. Chi, S. Hentz, E. C. Bullard, E. Colinet, L. Duraffourg, and M. L. Roukes, “Single-protein nanomechanical mass spectrometry in real time,” Nature Nanotech. 7, 602–608 (2012).
[Crossref]

Kenny, T.

M. Agarwal, K.-K. Park, R. Candler, B. Kim, M. Hopcroft, S. A. Chandorkar, C. Jha, R. Melamud, T. Kenny, and B. Murmann, “Nonlinear Characterization of Electrostatic MEMS Resonators,” in International Frequency Control Symposium and Exposition, 2006 IEEE pp. 209–212 (2006).
[Crossref]

Kim, B.

M. Agarwal, K.-K. Park, R. Candler, B. Kim, M. Hopcroft, S. A. Chandorkar, C. Jha, R. Melamud, T. Kenny, and B. Murmann, “Nonlinear Characterization of Electrostatic MEMS Resonators,” in International Frequency Control Symposium and Exposition, 2006 IEEE pp. 209–212 (2006).
[Crossref]

Kippenberg, T. J.

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, and T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
[Crossref]

Kotthaus, J. P.

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, and T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
[Crossref]

Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458, 1001–1004 (2009).
[Crossref] [PubMed]

Krause, A.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

Lechner, L.

J. Sulkko, M. A. Sillanpaa, P. Hakkinen, L. Lechner, M. Helle, A. Fefferman, J. Parpia, and P. J. Hakonen, “Strong Gate Coupling of High-Q Nanomechanical Resonators,” Nano Lett. 10, 4884–4889 (2010).
[Crossref] [PubMed]

Lehnert, K. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
[Crossref]

C. A. Regal and K. W. Lehnert, “From cavity electromechanics to cavity optomechanics,” J. Phys.: Conf. Ser. 264, 012025 (2011).

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

Li, D.

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

K. Cicak, D. Li, J. A. Strong, M. S. Allman, F. Altomare, A. J. Sirois, J. D. Whittaker, J. D. Teufel, and R. W. Simmonds, “Low-loss superconducting resonant circuits using vacuum-gap-based microwave components,” App. Phys. Lett. 96, 093502 (2010).
[Crossref]

Li, Z.

Lifshitz, R.

R. Lifshitz and M. C. Cross, “Response of parametrically driven nonlinear coupled oscillators with application to micromechanical and nanomechanical resonator arrays,” Phys. Rev. B 67, 134302 (2003).
[Crossref]

Lipsanen, A.

V. Kaajakari, T. Mattila, A. Lipsanen, and A. Oja, “Nonlinear mechanical effects in silicon longitudinal mode beam resonators,” Sens. Actua. A 120, 64–70 (2005).
[Crossref]

Liu, Y.

Lucero, E.

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Neeley, H. Wang, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Microwave dielectric loss at single photon energies and millikelvin temperatures,” Appl. Phys. Lett. 92, 112903 (2008).
[Crossref]

Lukin, M. D.

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical Transducers for Long-Distance Quantum Communication,” Phys. Rev. Lett. 105, 220501 (2010).
[Crossref]

Luo, J.

Mahboob, I.

I. Mahboob and H. Yamaguchi, “Bit storage and bit flip operations in an electromechanical oscillator,” Nat. Nano 3, 275–279 (2008).
[Crossref]

Manz, A.

A. Manz, N. Graber, and H. M. Widmer, “Miniaturized total chemical analysis systems: a novel concept for chemical sensing,” Sens. Actuat. B: Chem. 1, 244–248 (1990).
[Crossref]

Martinis, J. M.

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Neeley, H. Wang, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Microwave dielectric loss at single photon energies and millikelvin temperatures,” Appl. Phys. Lett. 92, 112903 (2008).
[Crossref]

Mattila, T.

V. Kaajakari, T. Mattila, A. Lipsanen, and A. Oja, “Nonlinear mechanical effects in silicon longitudinal mode beam resonators,” Sens. Actua. A 120, 64–70 (2005).
[Crossref]

McKenney, C.

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Neeley, H. Wang, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Microwave dielectric loss at single photon energies and millikelvin temperatures,” Appl. Phys. Lett. 92, 112903 (2008).
[Crossref]

Meenehan, S.

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
[Crossref]

M. Winger, T. D. Blasius, T. P. M. Alegre, A. H. Safavi-Naeini, S. Meenehan, J. Cohen, S. Stobbe, and O. Painter, “A chip-scale integrated cavity-electro-optomechanics platform,” Opt. Express 19, 24905–24921 (2011).
[Crossref]

Meenehan, S. M.

Melamud, R.

M. Agarwal, K.-K. Park, R. Candler, B. Kim, M. Hopcroft, S. A. Chandorkar, C. Jha, R. Melamud, T. Kenny, and B. Murmann, “Nonlinear Characterization of Electrostatic MEMS Resonators,” in International Frequency Control Symposium and Exposition, 2006 IEEE pp. 209–212 (2006).
[Crossref]

Michael, C. P.

Milburn, G. J.

S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible Optical-to-Microwave Quantum Interface,” Phys. Rev. Lett. 109, 130503 (2012).
[Crossref] [PubMed]

Morita, A.

T. Tajima, T. Nishiguchi, S. Chiba, A. Morita, M. Abe, K. Tanioka, N. Saito, and M. Esashi, “High-performance ultra-small single crystalline silicon microphone of an integrated structure,” Microelectron. Eng. 67–68, 508–519 (2003).
[Crossref]

Murmann, B.

M. Agarwal, K.-K. Park, R. Candler, B. Kim, M. Hopcroft, S. A. Chandorkar, C. Jha, R. Melamud, T. Kenny, and B. Murmann, “Nonlinear Characterization of Electrostatic MEMS Resonators,” in International Frequency Control Symposium and Exposition, 2006 IEEE pp. 209–212 (2006).
[Crossref]

Naik, A. K.

M. S. Hanay, S. Kelber, A. K. Naik, D. Chi, S. Hentz, E. C. Bullard, E. Colinet, L. Duraffourg, and M. L. Roukes, “Single-protein nanomechanical mass spectrometry in real time,” Nature Nanotech. 7, 602–608 (2012).
[Crossref]

Najafi, K.

N. Yazdi, F. Avazi, and K. Najafi, “Micromachined inertial sensors,” Proc. IEEE 86, 1640–1659 (1998).
[Crossref]

Neeley, M.

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Neeley, H. Wang, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Microwave dielectric loss at single photon energies and millikelvin temperatures,” Appl. Phys. Lett. 92, 112903 (2008).
[Crossref]

Neve, C. R.

Y. Shim, J.-P. Raskin, C. R. Neve, and M. Rais-Zadeh, “RF MEMS Passives on High-Resistivity Silicon Substrates,” IEEE Microw. Wirel. Compon. Lett. 23, 632–634 (2013).
[Crossref]

Nishiguchi, T.

T. Tajima, T. Nishiguchi, S. Chiba, A. Morita, M. Abe, K. Tanioka, N. Saito, and M. Esashi, “High-performance ultra-small single crystalline silicon microphone of an integrated structure,” Microelectron. Eng. 67–68, 508–519 (2003).
[Crossref]

O’Connell, A. D.

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Neeley, H. Wang, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Microwave dielectric loss at single photon energies and millikelvin temperatures,” Appl. Phys. Lett. 92, 112903 (2008).
[Crossref]

Oja, A.

V. Kaajakari, T. Mattila, A. Lipsanen, and A. Oja, “Nonlinear mechanical effects in silicon longitudinal mode beam resonators,” Sens. Actua. A 120, 64–70 (2005).
[Crossref]

Osborn, K.

K. Cicak, M. Allman, J. Strong, K. Osborn, and R. Simmonds, “Vacuum-Gap Capacitors for Low-Loss Super-conducting Resonant Circuits,” IEEE Trans. Appl. Supercond. 19, 948–952 (2009).
[Crossref]

Painter, O.

A. H. Safavi-Naeini, S. Groeblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
[Crossref]

M. Winger, T. D. Blasius, T. P. M. Alegre, A. H. Safavi-Naeini, S. Meenehan, J. Cohen, S. Stobbe, and O. Painter, “A chip-scale integrated cavity-electro-optomechanics platform,” Opt. Express 19, 24905–24921 (2011).
[Crossref]

A. H. Safavi-Naeini and O. Painter, “Proposal for an optomechanical traveling wave phononphoton translator,” New J. Phys. 13, 013017 (2011).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97, 181106 (2010).
[Crossref]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref] [PubMed]

M. Eichenfield, R. M. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometer-scale photonic crystal opto-mechanical cavity,” Nature 459, 550–555 (2009).
[Crossref] [PubMed]

C. P. Michael, M. Borselli, T. J. Johnson, C. Chrystal, and O. Painter, “An optical fiber-taper probe for wafer-scale microphotonic device characterization,” Opt. Express 15, 4745–4752 (2007).
[Crossref] [PubMed]

Park, K.-K.

M. Agarwal, K.-K. Park, R. Candler, B. Kim, M. Hopcroft, S. A. Chandorkar, C. Jha, R. Melamud, T. Kenny, and B. Murmann, “Nonlinear Characterization of Electrostatic MEMS Resonators,” in International Frequency Control Symposium and Exposition, 2006 IEEE pp. 209–212 (2006).
[Crossref]

Parpia, J.

J. Sulkko, M. A. Sillanpaa, P. Hakkinen, L. Lechner, M. Helle, A. Fefferman, J. Parpia, and P. J. Hakonen, “Strong Gate Coupling of High-Q Nanomechanical Resonators,” Nano Lett. 10, 4884–4889 (2010).
[Crossref] [PubMed]

Parpia, J. M.

S. S. Verbridge, H. G. Craighead, and J. M. Parpia, “A megahertz nanomechanical resonator with room temperature quality factor over a million,” Appl. Phys. Lett. 92, 013112 (2008).
[Crossref]

Peterson, R. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
[Crossref]

Polzik, E. S.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, J. Zeuthen, E. Appel, J. M. Taylor, A. Srensen, K. Usami, A. Sorrenson, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref] [PubMed]

Poot, M.

M. Poot and H. X. Tang, “Phase shifting, strong coupling, and parametric feedback squeezing of an opto-electromechanical device,” in Proceedings of CLEO: 2013 p. CW3F.7 (2013).

Purdy, T. P.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
[Crossref]

Qiu, M.

Rabl, P.

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical Transducers for Long-Distance Quantum Communication,” Phys. Rev. Lett. 105, 220501 (2010).
[Crossref]

Rais-Zadeh, M.

Y. Shim, J.-P. Raskin, C. R. Neve, and M. Rais-Zadeh, “RF MEMS Passives on High-Resistivity Silicon Substrates,” IEEE Microw. Wirel. Compon. Lett. 23, 632–634 (2013).
[Crossref]

Raskin, J.-P.

Y. Shim, J.-P. Raskin, C. R. Neve, and M. Rais-Zadeh, “RF MEMS Passives on High-Resistivity Silicon Substrates,” IEEE Microw. Wirel. Compon. Lett. 23, 632–634 (2013).
[Crossref]

Regal, C. A.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
[Crossref]

C. A. Regal and K. W. Lehnert, “From cavity electromechanics to cavity optomechanics,” J. Phys.: Conf. Ser. 264, 012025 (2011).

Rips, S.

S. Rips and M. J. Hartmann, “Quantum Information Processing with Nanomechanical Qubits,” Phys. Rev. Lett. 110, 120503 (2013).
[Crossref] [PubMed]

Roukes, M. L.

M. S. Hanay, S. Kelber, A. K. Naik, D. Chi, S. Hentz, E. C. Bullard, E. Colinet, L. Duraffourg, and M. L. Roukes, “Single-protein nanomechanical mass spectrometry in real time,” Nature Nanotech. 7, 602–608 (2012).
[Crossref]

Rugar, D.

D. Rugar and P. Grütter, “Mechanical parametric amplification and thermomechanical noise squeezing,” Phys. Rev. Lett. 67, 699–702 (1991).
[Crossref] [PubMed]

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, S. Groeblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
[Crossref]

M. Winger, T. D. Blasius, T. P. M. Alegre, A. H. Safavi-Naeini, S. Meenehan, J. Cohen, S. Stobbe, and O. Painter, “A chip-scale integrated cavity-electro-optomechanics platform,” Opt. Express 19, 24905–24921 (2011).
[Crossref]

A. H. Safavi-Naeini and O. Painter, “Proposal for an optomechanical traveling wave phononphoton translator,” New J. Phys. 13, 013017 (2011).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97, 181106 (2010).
[Crossref]

Saito, N.

T. Tajima, T. Nishiguchi, S. Chiba, A. Morita, M. Abe, K. Tanioka, N. Saito, and M. Esashi, “High-performance ultra-small single crystalline silicon microphone of an integrated structure,” Microelectron. Eng. 67–68, 508–519 (2003).
[Crossref]

Sastry, A. M.

K. A. Cook-Chennault, N. Thambi, and A. M. Sastry, “Powering MEMS portable devices: a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems,” Smart Mater. Struct. 17, 043001 (2008).
[Crossref]

Schmid, S.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, J. Zeuthen, E. Appel, J. M. Taylor, A. Srensen, K. Usami, A. Sorrenson, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref] [PubMed]

Schoelkopf, R. J.

S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Circuit QED and engineering charge-based superconducting qubits,” Phys. Scr. T137, 014012 (2009).
[Crossref]

Shim, Y.

Y. Shim, J.-P. Raskin, C. R. Neve, and M. Rais-Zadeh, “RF MEMS Passives on High-Resistivity Silicon Substrates,” IEEE Microw. Wirel. Compon. Lett. 23, 632–634 (2013).
[Crossref]

Shtempluck, O.

R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, “Noise Squeezing in a Nanomechanical Duffing Resonator,” Phys. Rev. Lett. 98, 078103 (2007).
[Crossref] [PubMed]

Sillanpaa, M. A.

J. Sulkko, M. A. Sillanpaa, P. Hakkinen, L. Lechner, M. Helle, A. Fefferman, J. Parpia, and P. J. Hakonen, “Strong Gate Coupling of High-Q Nanomechanical Resonators,” Nano Lett. 10, 4884–4889 (2010).
[Crossref] [PubMed]

Simmonds, R.

K. Cicak, M. Allman, J. Strong, K. Osborn, and R. Simmonds, “Vacuum-Gap Capacitors for Low-Loss Super-conducting Resonant Circuits,” IEEE Trans. Appl. Supercond. 19, 948–952 (2009).
[Crossref]

Simmonds, R. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
[Crossref]

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

K. Cicak, D. Li, J. A. Strong, M. S. Allman, F. Altomare, A. J. Sirois, J. D. Whittaker, J. D. Teufel, and R. W. Simmonds, “Low-loss superconducting resonant circuits using vacuum-gap-based microwave components,” App. Phys. Lett. 96, 093502 (2010).
[Crossref]

Simonsen, A.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, J. Zeuthen, E. Appel, J. M. Taylor, A. Srensen, K. Usami, A. Sorrenson, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref] [PubMed]

Sirois, A. J.

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

K. Cicak, D. Li, J. A. Strong, M. S. Allman, F. Altomare, A. J. Sirois, J. D. Whittaker, J. D. Teufel, and R. W. Simmonds, “Low-loss superconducting resonant circuits using vacuum-gap-based microwave components,” App. Phys. Lett. 96, 093502 (2010).
[Crossref]

Skorobogatiy, M. A.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory and Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

Smith, J. H.

W. P. Eatony and J. H. Smith, “Micromachined pressure sensors: review and recent developments,” Smart Mater. Struct. 6, 530–539 (1997).
[Crossref]

Sørensen, A. S.

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical Transducers for Long-Distance Quantum Communication,” Phys. Rev. Lett. 105, 220501 (2010).
[Crossref]

Sorrenson, A.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, J. Zeuthen, E. Appel, J. M. Taylor, A. Srensen, K. Usami, A. Sorrenson, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref] [PubMed]

Srensen, A.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, J. Zeuthen, E. Appel, J. M. Taylor, A. Srensen, K. Usami, A. Sorrenson, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref] [PubMed]

Stannigel, K.

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical Transducers for Long-Distance Quantum Communication,” Phys. Rev. Lett. 105, 220501 (2010).
[Crossref]

Stobbe, S.

Strong, J.

K. Cicak, M. Allman, J. Strong, K. Osborn, and R. Simmonds, “Vacuum-Gap Capacitors for Low-Loss Super-conducting Resonant Circuits,” IEEE Trans. Appl. Supercond. 19, 948–952 (2009).
[Crossref]

Strong, J. A.

K. Cicak, D. Li, J. A. Strong, M. S. Allman, F. Altomare, A. J. Sirois, J. D. Whittaker, J. D. Teufel, and R. W. Simmonds, “Low-loss superconducting resonant circuits using vacuum-gap-based microwave components,” App. Phys. Lett. 96, 093502 (2010).
[Crossref]

Sulkko, J.

J. Sulkko, M. A. Sillanpaa, P. Hakkinen, L. Lechner, M. Helle, A. Fefferman, J. Parpia, and P. J. Hakonen, “Strong Gate Coupling of High-Q Nanomechanical Resonators,” Nano Lett. 10, 4884–4889 (2010).
[Crossref] [PubMed]

Szorkovszky, A.

A. Szorkovszky, A. A. Clerk, A. C. Doherty, and W. P. Bowen, “Detuned mechanical parametric amplification as a quantum non-demolition measurement,” New J. Phys. 16, 043023 (2014).
[Crossref]

Tajima, T.

T. Tajima, T. Nishiguchi, S. Chiba, A. Morita, M. Abe, K. Tanioka, N. Saito, and M. Esashi, “High-performance ultra-small single crystalline silicon microphone of an integrated structure,” Microelectron. Eng. 67–68, 508–519 (2003).
[Crossref]

Tang, H. X.

M. Poot and H. X. Tang, “Phase shifting, strong coupling, and parametric feedback squeezing of an opto-electromechanical device,” in Proceedings of CLEO: 2013 p. CW3F.7 (2013).

Tanioka, K.

T. Tajima, T. Nishiguchi, S. Chiba, A. Morita, M. Abe, K. Tanioka, N. Saito, and M. Esashi, “High-performance ultra-small single crystalline silicon microphone of an integrated structure,” Microelectron. Eng. 67–68, 508–519 (2003).
[Crossref]

Taylor, J. M.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, J. Zeuthen, E. Appel, J. M. Taylor, A. Srensen, K. Usami, A. Sorrenson, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref] [PubMed]

Teufel, J. D.

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

K. Cicak, D. Li, J. A. Strong, M. S. Allman, F. Altomare, A. J. Sirois, J. D. Whittaker, J. D. Teufel, and R. W. Simmonds, “Low-loss superconducting resonant circuits using vacuum-gap-based microwave components,” App. Phys. Lett. 96, 093502 (2010).
[Crossref]

Thambi, N.

K. A. Cook-Chennault, N. Thambi, and A. M. Sastry, “Powering MEMS portable devices: a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems,” Smart Mater. Struct. 17, 043001 (2008).
[Crossref]

Tian, J.

Tombesi, P.

S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible Optical-to-Microwave Quantum Interface,” Phys. Rev. Lett. 109, 130503 (2012).
[Crossref] [PubMed]

Unterreithmeier, Q. P.

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, and T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
[Crossref]

Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458, 1001–1004 (2009).
[Crossref] [PubMed]

Usami, K.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, J. Zeuthen, E. Appel, J. M. Taylor, A. Srensen, K. Usami, A. Sorrenson, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref] [PubMed]

Vahala, K. J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref] [PubMed]

M. Eichenfield, R. M. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometer-scale photonic crystal opto-mechanical cavity,” Nature 459, 550–555 (2009).
[Crossref] [PubMed]

Vainsencher, A.

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
[Crossref]

Verbridge, S. S.

S. S. Verbridge, H. G. Craighead, and J. M. Parpia, “A megahertz nanomechanical resonator with room temperature quality factor over a million,” Appl. Phys. Lett. 92, 013112 (2008).
[Crossref]

Villanueva, L. G.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, J. Zeuthen, E. Appel, J. M. Taylor, A. Srensen, K. Usami, A. Sorrenson, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref] [PubMed]

Vitali, D.

S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible Optical-to-Microwave Quantum Interface,” Phys. Rev. Lett. 109, 130503 (2012).
[Crossref] [PubMed]

Wang, H.

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Neeley, H. Wang, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Microwave dielectric loss at single photon energies and millikelvin temperatures,” Appl. Phys. Lett. 92, 112903 (2008).
[Crossref]

Wang, Y.-D.

Y.-D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14, 105010 (2012).
[Crossref]

Weig, E. M.

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, and T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
[Crossref]

Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458, 1001–1004 (2009).
[Crossref] [PubMed]

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Neeley, H. Wang, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Microwave dielectric loss at single photon energies and millikelvin temperatures,” Appl. Phys. Lett. 92, 112903 (2008).
[Crossref]

Weisberg, O.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory and Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

Whittaker, J. D.

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

K. Cicak, D. Li, J. A. Strong, M. S. Allman, F. Altomare, A. J. Sirois, J. D. Whittaker, J. D. Teufel, and R. W. Simmonds, “Low-loss superconducting resonant circuits using vacuum-gap-based microwave components,” App. Phys. Lett. 96, 093502 (2010).
[Crossref]

Widmer, H. M.

A. Manz, N. Graber, and H. M. Widmer, “Miniaturized total chemical analysis systems: a novel concept for chemical sensing,” Sens. Actuat. B: Chem. 1, 244–248 (1990).
[Crossref]

Winger, M.

M. Winger, T. D. Blasius, T. P. M. Alegre, A. H. Safavi-Naeini, S. Meenehan, J. Cohen, S. Stobbe, and O. Painter, “A chip-scale integrated cavity-electro-optomechanics platform,” Opt. Express 19, 24905–24921 (2011).
[Crossref]

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97, 181106 (2010).
[Crossref]

Wu, C. C.

C. C. Wu and Z. Zhong, “Capacitive Spring Softening in Single-Walled Carbon Nanotube Nanoelectromechanical Resonators,” Nano Lett. 11, 1448–1451 (2011).
[Crossref] [PubMed]

Yamaguchi, H.

I. Mahboob and H. Yamaguchi, “Bit storage and bit flip operations in an electromechanical oscillator,” Nat. Nano 3, 275–279 (2008).
[Crossref]

Yan, W.

Yazdi, N.

N. Yazdi, F. Avazi, and K. Najafi, “Micromachined inertial sensors,” Proc. IEEE 86, 1640–1659 (1998).
[Crossref]

Zaitsev, S.

R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, “Noise Squeezing in a Nanomechanical Duffing Resonator,” Phys. Rev. Lett. 98, 078103 (2007).
[Crossref] [PubMed]

Zeuthen, J.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, J. Zeuthen, E. Appel, J. M. Taylor, A. Srensen, K. Usami, A. Sorrenson, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref] [PubMed]

Zhang, D.

Zhong, Z.

C. C. Wu and Z. Zhong, “Capacitive Spring Softening in Single-Walled Carbon Nanotube Nanoelectromechanical Resonators,” Nano Lett. 11, 1448–1451 (2011).
[Crossref] [PubMed]

Zoller, P.

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical Transducers for Long-Distance Quantum Communication,” Phys. Rev. Lett. 105, 220501 (2010).
[Crossref]

App. Phys. Lett. (1)

K. Cicak, D. Li, J. A. Strong, M. S. Allman, F. Altomare, A. J. Sirois, J. D. Whittaker, J. D. Teufel, and R. W. Simmonds, “Low-loss superconducting resonant circuits using vacuum-gap-based microwave components,” App. Phys. Lett. 96, 093502 (2010).
[Crossref]

Appl. Phys. Lett. (4)

A. D. O’Connell, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, C. McKenney, M. Neeley, H. Wang, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Microwave dielectric loss at single photon energies and millikelvin temperatures,” Appl. Phys. Lett. 92, 112903 (2008).
[Crossref]

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
[Crossref]

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97, 181106 (2010).
[Crossref]

S. S. Verbridge, H. G. Craighead, and J. M. Parpia, “A megahertz nanomechanical resonator with room temperature quality factor over a million,” Appl. Phys. Lett. 92, 013112 (2008).
[Crossref]

IEEE Microw. Wirel. Compon. Lett. (1)

Y. Shim, J.-P. Raskin, C. R. Neve, and M. Rais-Zadeh, “RF MEMS Passives on High-Resistivity Silicon Substrates,” IEEE Microw. Wirel. Compon. Lett. 23, 632–634 (2013).
[Crossref]

IEEE Trans. Appl. Supercond. (1)

K. Cicak, M. Allman, J. Strong, K. Osborn, and R. Simmonds, “Vacuum-Gap Capacitors for Low-Loss Super-conducting Resonant Circuits,” IEEE Trans. Appl. Supercond. 19, 948–952 (2009).
[Crossref]

J. Lightwave Technol. (1)

J. Phys.: Conf. Ser. (1)

C. A. Regal and K. W. Lehnert, “From cavity electromechanics to cavity optomechanics,” J. Phys.: Conf. Ser. 264, 012025 (2011).

Microelectron. Eng. (1)

T. Tajima, T. Nishiguchi, S. Chiba, A. Morita, M. Abe, K. Tanioka, N. Saito, and M. Esashi, “High-performance ultra-small single crystalline silicon microphone of an integrated structure,” Microelectron. Eng. 67–68, 508–519 (2003).
[Crossref]

Nano Lett. (2)

J. Sulkko, M. A. Sillanpaa, P. Hakkinen, L. Lechner, M. Helle, A. Fefferman, J. Parpia, and P. J. Hakonen, “Strong Gate Coupling of High-Q Nanomechanical Resonators,” Nano Lett. 10, 4884–4889 (2010).
[Crossref] [PubMed]

C. C. Wu and Z. Zhong, “Capacitive Spring Softening in Single-Walled Carbon Nanotube Nanoelectromechanical Resonators,” Nano Lett. 11, 1448–1451 (2011).
[Crossref] [PubMed]

Nat. Nano (1)

I. Mahboob and H. Yamaguchi, “Bit storage and bit flip operations in an electromechanical oscillator,” Nat. Nano 3, 275–279 (2008).
[Crossref]

Nat. Phys. (2)

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
[Crossref]

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
[Crossref]

Nature (7)

M. Eichenfield, R. M. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometer-scale photonic crystal opto-mechanical cavity,” Nature 459, 550–555 (2009).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref] [PubMed]

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, J. Zeuthen, E. Appel, J. M. Taylor, A. Srensen, K. Usami, A. Sorrenson, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref] [PubMed]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458, 1001–1004 (2009).
[Crossref] [PubMed]

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

A. H. Safavi-Naeini, S. Groeblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500, 185–189 (2013).
[Crossref] [PubMed]

Nature Nanotech. (1)

M. S. Hanay, S. Kelber, A. K. Naik, D. Chi, S. Hentz, E. C. Bullard, E. Colinet, L. Duraffourg, and M. L. Roukes, “Single-protein nanomechanical mass spectrometry in real time,” Nature Nanotech. 7, 602–608 (2012).
[Crossref]

New J. Phys. (3)

A. H. Safavi-Naeini and O. Painter, “Proposal for an optomechanical traveling wave phononphoton translator,” New J. Phys. 13, 013017 (2011).
[Crossref]

Y.-D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14, 105010 (2012).
[Crossref]

A. Szorkovszky, A. A. Clerk, A. C. Doherty, and W. P. Bowen, “Detuned mechanical parametric amplification as a quantum non-demolition measurement,” New J. Phys. 16, 043023 (2014).
[Crossref]

Opt. Express (3)

Phys. Rev. A (1)

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, and T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
[Crossref]

Phys. Rev. B (1)

R. Lifshitz and M. C. Cross, “Response of parametrically driven nonlinear coupled oscillators with application to micromechanical and nanomechanical resonator arrays,” Phys. Rev. B 67, 134302 (2003).
[Crossref]

Phys. Rev. E (1)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory and Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[Crossref]

Phys. Rev. Lett. (5)

D. Rugar and P. Grütter, “Mechanical parametric amplification and thermomechanical noise squeezing,” Phys. Rev. Lett. 67, 699–702 (1991).
[Crossref] [PubMed]

R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, “Noise Squeezing in a Nanomechanical Duffing Resonator,” Phys. Rev. Lett. 98, 078103 (2007).
[Crossref] [PubMed]

S. Rips and M. J. Hartmann, “Quantum Information Processing with Nanomechanical Qubits,” Phys. Rev. Lett. 110, 120503 (2013).
[Crossref] [PubMed]

S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible Optical-to-Microwave Quantum Interface,” Phys. Rev. Lett. 109, 130503 (2012).
[Crossref] [PubMed]

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical Transducers for Long-Distance Quantum Communication,” Phys. Rev. Lett. 105, 220501 (2010).
[Crossref]

Phys. Scr. (1)

S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Circuit QED and engineering charge-based superconducting qubits,” Phys. Scr. T137, 014012 (2009).
[Crossref]

Proc. IEEE (1)

N. Yazdi, F. Avazi, and K. Najafi, “Micromachined inertial sensors,” Proc. IEEE 86, 1640–1659 (1998).
[Crossref]

Sens. Actua. A (1)

V. Kaajakari, T. Mattila, A. Lipsanen, and A. Oja, “Nonlinear mechanical effects in silicon longitudinal mode beam resonators,” Sens. Actua. A 120, 64–70 (2005).
[Crossref]

Sens. Actuat. B: Chem. (1)

A. Manz, N. Graber, and H. M. Widmer, “Miniaturized total chemical analysis systems: a novel concept for chemical sensing,” Sens. Actuat. B: Chem. 1, 244–248 (1990).
[Crossref]

Smart Mater. Struct. (2)

W. P. Eatony and J. H. Smith, “Micromachined pressure sensors: review and recent developments,” Smart Mater. Struct. 6, 530–539 (1997).
[Crossref]

K. A. Cook-Chennault, N. Thambi, and A. M. Sastry, “Powering MEMS portable devices: a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems,” Smart Mater. Struct. 17, 043001 (2008).
[Crossref]

Other (4)

M. Poot and H. X. Tang, “Phase shifting, strong coupling, and parametric feedback squeezing of an opto-electromechanical device,” in Proceedings of CLEO: 2013 p. CW3F.7 (2013).

M. Borselli, High-Q microresonators as lasing elements for silicon photonics, Ph.D. thesis, California Institute of Technology (2006).

M. Agarwal, K.-K. Park, R. Candler, B. Kim, M. Hopcroft, S. A. Chandorkar, C. Jha, R. Melamud, T. Kenny, and B. Murmann, “Nonlinear Characterization of Electrostatic MEMS Resonators,” in International Frequency Control Symposium and Exposition, 2006 IEEE pp. 209–212 (2006).
[Crossref]

S. M. Meenehan, J. D. Cohen, S. Groeblacher, J. T. Hill, A. H. Safavi-Naeini, M. Aspelmeyer, and O. Painter, “Thermalization properties at mK temperatures of a nanoscale optomechanical resonator with acoustic-bandgap shield,” http://arxiv.org/abs/1403.3703 (2014).

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Figures (4)

Fig. 1
Fig. 1 (a) Simulated Ey(r) electric field component of the optical mode. (b) Total deformation |Q(r)| of the fundamental planar flexural mode of the Si slab. (c) Scanning electron microscope (SEM) image of the top-view of a typical realized device. The scale bar is 5 μm. The zoomed-in view to the right depicts the electrode gap, whose size is d < 30 nm. (d) Illustration of the inverse shadow mask technique. A mask is created with ZEP resist to define the electrical contacts, while the capacitor electrodes are defined using the etched Si edges. After lift-off and full release, the metal within the gap is removed together with the SiO2 buffer layer. The scale bar is 5 μm. The purpose of the small trench on the top of the picture is to redistribute the residual silicon stress in order to avoid out-of-plane bending of the device.
Fig. 2
Fig. 2 (a) Experimental setup for sample characterization. The tunable diode laser is calibrated with a high-finesse Mach Zender interferometer (MZ) [27] and can be locked using a wavemeter (WM) for feedback. After being attenuated (VOA) and polarization controlled (FPC), the evanescent field of a tapered optical fiber is used to couple light into the photonic crystal cavity (PCC). The optical transmission is then measured with a low bandwidth photodetector (D1) in the case of optical spectroscopy, or via a high-speed photodetector (D2) connected to a Spectrum Analyzer (SA) for analysis of the mechanical spectrum. In addition, voltage sources (VDC), a signal generator (VAC) or a Network analyzer (NA) were used to measure the electric response of the device. (b) Measured normalized optical transmission through the photonic crystal of device A. The red line is the best Lorentzian fit of the resonance, showing an intrinsic optical Q-factor of Qc ∼ 9 × 104. (c) Power spectral density of the optically transduced thermal Brownian motion of the structure of device A. The strong resonance peak at ωm/2π = 63 MHz is the fundamental in-plane mechanical mode of the slab structure, whereas the smaller peaks represent weakly coupled (predominantly) out-of-plane modes of the slab. The red line is a multi-Lorentzian fit to the transduced mechanical spectrum. (d) Simulated capacitance as a function of gap size, d, for the capacitor on one side of the slab structure. The data fits with a power law (red line) Cm = [6.933/d0.533] fF, with d in units of nanometers. Inset: simulated Ey electrostatic field amplitude within the capacitor. The field isolines are shown in black.
Fig. 3
Fig. 3 (a) Waterfall plot of the optical transmission spectra for the fundamental optical cavity resonance as a function of DC voltage (VDC = 0 to 5.6 V, 0.2 V steps). The x-axis has been normalized according to the optical center wavelength at zero applied bias, λc,0. (b) Measured optical resonance wavelength (open circles) versus V DC 2. Solid black curve corresponds to a linear fit to the measured data. (c) Linear coupling parameter extracted from different experiments (DC (circles), AC (triangles)) and for different samples (A (red) and B (blue)). The solid black line is the numerically simulated linear electromechanical coupling using eq. (1). The dashed green line is the linear electromechanical coupling calculated using the functional dependence of the capacitance versus gap d shown in Fig. 2(d).
Fig. 4
Fig. 4 Nonlinear electromechanical response of device B. (a) Measured amplitude response (|S21|) for a weak AC voltage probe (V0 <1 mVrms) and DC bias ranging from 0.2 V (blue curve) to 6 V (red curve) in 0.2 V steps. Successive spectra are offset from the VDC = 0.2 V spectrum in 1 dB increments. (b) Measured amplitude response (|S21|) of the optically transduced mechanical motion to a strong near-resonant electric drive (ωAC ∼ ωm) with fixed VDC=6 V and V0 ranging from 277–870 mVrms. Increasing the drive amplitude, the mechanical Lorentzian peak (red) starts to assume the form of a Duffing oscillator (green). After an instability threshold, the mechanics enters a frequency entrainment regime in which it is completely in phase with the AC drive (blue). (c) Measured relative phase response (ϕ(S21)) of the optically transduced mechanical motion for the same drive conditions as in (b). Note that the phase slope is about the same inside and outside the frequency entrainment region indicating that the phase of the mechanical response is locked to the phase of the drive. Successive spectra in (b) and (c) are offset from the VAC = 277 mVrms spectrum in 1 dB increments.

Equations (8)

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δ U ¯ E = V ( Q ˜ ( r ) n ) ( Δ ε | E | 2 Δ ε 1 | D | 2 ) d 2 r V ε | E | 2 d 3 r ,
F cap = 1 2 C m V 2 G e , 1 ,
m eff = Q * ( r ) ρ ( r ) Q ( r ) d 3 r max ( | Q | 2 ) ,
Δ ω c , DC ( V ) = g OM C m G e , 1 2 k eff V DC 2 = α V DC 2 ,
Δ ω c , AC = α Q m V 0 2 .
Δ ω m = ( ω m C m G e , 2 4 k eff ) V 2 = β V 2 ,
F cap V 2 = V DC 2 + V AC 2 + 2 V DC V AC .
V 0 , th = 2 k eff Q m 1 / 2 C m G e , 2 V DC .

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