Abstract

We present a design methodology and analysis of a cavity optomechanical system in which a localized GHz frequency mechanical mode of a nanobeam resonator is evanescently coupled to a high quality factor (Q > 106) optical mode of a separate nanobeam optical cavity. Using separate nanobeams provides flexibility, enabling the independent design and optimization of the optics and mechanics of the system. In addition, the small gap (≈25 nm) between the two resonators gives rise to a slot mode effect that enables a large zero-point optomechanical coupling strength to be achieved, with g/2π > 300 kHz in a Si3N4 system at 980 nm and g/2π ≈ 900 kHz in a Si system at 1550 nm. The fact that large coupling strengths to GHz mechanical oscillators can be achieved in Si3N4 is important, as this material has a broad optical transparency window, which allows operation throughout the visible and near-infrared. As an application of this platform, we consider wide-band optical frequency conversion between 1300 nm and 980 nm, using two optical nanobeam cavities coupled on either side to the breathing mode of a mechanical nanobeam resonator.

© 2012 OSA

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    [CrossRef]
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    [CrossRef]
  22. A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express17, 11366–11370 (2009).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  29. Q. Quan and M. Loncar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express19, 18529–18542 (2011).
    [CrossRef] [PubMed]
  30. Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys.Lett.96, 203102 (2010).
    [CrossRef]
  31. M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and-losses of localized optical andmechanical modes in optomechanicalcrystals,” Opt. Express17, 20078–20098 (2009).
    [CrossRef] [PubMed]
  32. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E65, 066611 (2002).
    [CrossRef]
  33. J. Chan, A. H. Safavi-Naeini, J. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” (2012), arXiv:1206.2099.
  34. P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X2, 011008 (2012).
    [CrossRef]
  35. M. Khan, T. Babinec, M. W. McCutcheon, P. Deotare, and M. Lončar, “Fabrication and characterization of high-quality-factor silicon nitride nanobeam cavities,” Opt. Lett.36, 421–423 (2011).
    [CrossRef] [PubMed]
  36. A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics1, 215–223 (2007).
    [CrossRef]
  37. R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics3, 696–705 (2009).
    [CrossRef]
  38. A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express18, 14926–14943 (2010).
    [CrossRef] [PubMed]
  39. R. M. Camacho, J. Chan, M. Eichenfield, and O. Painter, “Characterization of radiation pressure and thermal effects in a nanoscale optomechanical cavity,” Opt. Express17, 15726–15735 (2009).
    [CrossRef] [PubMed]
  40. K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express10, 670–684 (2002).
    [PubMed]
  41. H. J. Kimble, “The quantum internet,” Nature (London)453, 1023–1030 (2008).
    [CrossRef]
  42. M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
    [CrossRef]
  43. J. Hwang, M. Pototschnig, R. Lettow, G. Zumofen, A. Renn, S. Goetzinger, and V. Sandoghdar, “A single-molecule optical transistor,” Nature460, 76–80 (2009).
    [CrossRef] [PubMed]
  44. C. A. Regal, J. D. Teufel, and K. W. Lehnert, “Measuring nanomechanical motion with a microwave cavity interferometer,” Nat. Phys.4, 555–560 (2008).
    [CrossRef]
  45. J. Sulkko, M. A. Sillanpää, P. Häkkinen, 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]
  46. F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonators,” Nature (London)480, 351–354 (2011).
    [CrossRef]

2012 (6)

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity-optomechanics,” arXiv:1203.5730 (2012).

C. F.-V. K. M. C. Dong and L. W.-H. Tian, “A microchip optomechanical accelerometer,” arXiv:1205.2360 (2012).

J. Zheng, Y. Li, S. Aras, M. Stein, K. L. Shepard, and C. W. Wong, “Parametric optomechanical oscillations in two-dimensional slot-type high-Q photonic crystal cavities,” Appl. Phys. Lett.100, 211908 (2012).
[CrossRef]

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A microchip optomechanical accelerometer,” arXiv:1203.5730 (2012).

J. Chan, A. H. Safavi-Naeini, J. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” (2012), arXiv:1206.2099.

P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X2, 011008 (2012).
[CrossRef]

2011 (9)

M. Khan, T. Babinec, M. W. McCutcheon, P. Deotare, and M. Lončar, “Fabrication and characterization of high-quality-factor silicon nitride nanobeam cavities,” Opt. Lett.36, 421–423 (2011).
[CrossRef] [PubMed]

Q. Quan and M. Loncar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express19, 18529–18542 (2011).
[CrossRef] [PubMed]

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature (London)472, 69–73 (2011).
[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 (London)475, 359–363 (2011).
[CrossRef]

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

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

D. E. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys.13, 023003 (2011).
[CrossRef]

K. Stannigel, P. Rabl, A. S. Sørensen, M. D. Lukin, and P. Zoller, “Optomechanical transducers for quantum-information processing,” Phys. Rev. A84, 042341 (2011).
[CrossRef]

F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonators,” Nature (London)480, 351–354 (2011).
[CrossRef]

2010 (8)

J. Sulkko, M. A. Sillanpää, P. Häkkinen, 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]

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
[CrossRef]

A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express18, 14926–14943 (2010).
[CrossRef] [PubMed]

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science330, 1520–1523 (2010).
[CrossRef] [PubMed]

L. Tian and H. Wang, “Optical wavelength conversion of quantum states with optomechanics,” Phys. Rev. A82, 053806 (2010).
[CrossRef]

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B81, 121101 (2010).
[CrossRef]

Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys.Lett.96, 203102 (2010).
[CrossRef]

K. Y. Fong, W. H. P. Pernice, M. Li, and H. X. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett.97, 073112 (2010).
[CrossRef]

2009 (10)

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature459, 550–555 (2009).
[CrossRef] [PubMed]

A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express17, 11366–11370 (2009).
[CrossRef] [PubMed]

E. Shah Hosseini, S. Yegnanarayanan, A. H. Atabaki, M. Soltani, and A. Adibi, “High quality planar silicon nitride microdisk resonators for integrated photonics in the vsible wavelength range,” Opt. Express17, 14543–14551 (2009).
[CrossRef]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and-losses of localized optical andmechanical modes in optomechanicalcrystals,” Opt. Express17, 20078–20098 (2009).
[CrossRef] [PubMed]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett.103, 103601 (2009).
[CrossRef] [PubMed]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature462, 633–636 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462, 78–82 (2009).
[CrossRef] [PubMed]

R. M. Camacho, J. Chan, M. Eichenfield, and O. Painter, “Characterization of radiation pressure and thermal effects in a nanoscale optomechanical cavity,” Opt. Express17, 15726–15735 (2009).
[CrossRef] [PubMed]

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics3, 696–705 (2009).
[CrossRef]

J. Hwang, M. Pototschnig, R. Lettow, G. Zumofen, A. Renn, S. Goetzinger, and V. Sandoghdar, “A single-molecule optical transistor,” Nature460, 76–80 (2009).
[CrossRef] [PubMed]

2008 (4)

C. A. Regal, J. D. Teufel, and K. W. Lehnert, “Measuring nanomechanical motion with a microwave cavity interferometer,” Nat. Phys.4, 555–560 (2008).
[CrossRef]

H. J. Kimble, “The quantum internet,” Nature (London)453, 1023–1030 (2008).
[CrossRef]

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. Bleszynski Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett.92, 103125 (2008).
[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]

2007 (2)

A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics1, 215–223 (2007).
[CrossRef]

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express15, 17172–17205 (2007).
[CrossRef] [PubMed]

2006 (1)

P. E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, “Integration of fiber-coupled high-Q SiNx microdisks with magnetostatic atom chips,” Appl. Phys. Lett.89, 131108 (2006).
[CrossRef]

2005 (1)

2004 (1)

2002 (2)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E65, 066611 (2002).
[CrossRef]

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express10, 670–684 (2002).
[PubMed]

1811 (1)

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).

Adibi, A.

Alegre, T. P. M.

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature (London)472, 69–73 (2011).
[CrossRef]

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

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 (London)475, 359–363 (2011).
[CrossRef]

Almeida, V. R.

Aras, S.

J. Zheng, Y. Li, S. Aras, M. Stein, K. L. Shepard, and C. W. Wong, “Parametric optomechanical oscillations in two-dimensional slot-type high-Q photonic crystal cavities,” Appl. Phys. Lett.100, 211908 (2012).
[CrossRef]

Arcizet, O.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science330, 1520–1523 (2010).
[CrossRef] [PubMed]

Aspelmeyer, M.

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

Atabaki, A. H.

Babinec, T.

Barclay, P. E.

P. E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, “Integration of fiber-coupled high-Q SiNx microdisks with magnetostatic atom chips,” Appl. Phys. Lett.89, 131108 (2006).
[CrossRef]

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microcavities excited via an integrated waveguide and fiber taper,” Opt. Express13, 801–820 (2005).
[CrossRef] [PubMed]

Barrios, C. A.

Blasius, T. D.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A microchip optomechanical accelerometer,” arXiv:1203.5730 (2012).

Bleszynski Jayich, A. C.

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. Bleszynski Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett.92, 103125 (2008).
[CrossRef]

Camacho, R.

P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X2, 011008 (2012).
[CrossRef]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature459, 550–555 (2009).
[CrossRef] [PubMed]

Camacho, R. M.

Chan, J.

J. Chan, A. H. Safavi-Naeini, J. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” (2012), arXiv:1206.2099.

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity-optomechanics,” arXiv:1203.5730 (2012).

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature (London)472, 69–73 (2011).
[CrossRef]

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

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462, 78–82 (2009).
[CrossRef] [PubMed]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature459, 550–555 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and-losses of localized optical andmechanical modes in optomechanicalcrystals,” Opt. Express17, 20078–20098 (2009).
[CrossRef] [PubMed]

R. M. Camacho, J. Chan, M. Eichenfield, and O. Painter, “Characterization of radiation pressure and thermal effects in a nanoscale optomechanical cavity,” Opt. Express17, 15726–15735 (2009).
[CrossRef] [PubMed]

Chang, D. E.

D. E. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys.13, 023003 (2011).
[CrossRef]

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature (London)472, 69–73 (2011).
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G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature462, 633–636 (2009).
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F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonators,” Nature (London)480, 351–354 (2011).
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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 (London)475, 359–363 (2011).
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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).
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P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X2, 011008 (2012).
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S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science330, 1520–1523 (2010).
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Deotare, P. B.

Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys.Lett.96, 203102 (2010).
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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 (London)475, 359–363 (2011).
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A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature (London)472, 69–73 (2011).
[CrossRef]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462, 78–82 (2009).
[CrossRef] [PubMed]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature459, 550–555 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and-losses of localized optical andmechanical modes in optomechanicalcrystals,” Opt. Express17, 20078–20098 (2009).
[CrossRef] [PubMed]

R. M. Camacho, J. Chan, M. Eichenfield, and O. Painter, “Characterization of radiation pressure and thermal effects in a nanoscale optomechanical cavity,” Opt. Express17, 15726–15735 (2009).
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C. F.-V. K. M. C. Dong and L. W.-H. Tian, “A microchip optomechanical accelerometer,” arXiv:1205.2360 (2012).

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J. Sulkko, M. A. Sillanpää, P. Häkkinen, 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).
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S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E65, 066611 (2002).
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K. Y. Fong, W. H. P. Pernice, M. Li, and H. X. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett.97, 073112 (2010).
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Gavartin, E.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science330, 1520–1523 (2010).
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J. Hwang, M. Pototschnig, R. Lettow, G. Zumofen, A. Renn, S. Goetzinger, and V. Sandoghdar, “A single-molecule optical transistor,” Nature460, 76–80 (2009).
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A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express17, 11366–11370 (2009).
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G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature462, 633–636 (2009).
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J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature (London)478, 89–92 (2011).
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R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics3, 696–705 (2009).
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D. E. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys.13, 023003 (2011).
[CrossRef]

Häkkinen, P.

J. Sulkko, M. A. Sillanpää, P. Häkkinen, 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]

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F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonators,” Nature (London)480, 351–354 (2011).
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J. Sulkko, M. A. Sillanpää, P. Häkkinen, 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).
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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 (London)475, 359–363 (2011).
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B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. Bleszynski Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett.92, 103125 (2008).
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F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonators,” Nature (London)480, 351–354 (2011).
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J. Sulkko, M. A. Sillanpää, P. Häkkinen, 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).
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J. Chan, A. H. Safavi-Naeini, J. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” (2012), arXiv:1206.2099.

Hill, J. T.

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity-optomechanics,” arXiv:1203.5730 (2012).

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature (London)472, 69–73 (2011).
[CrossRef]

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

Hwang, J.

J. Hwang, M. Pototschnig, R. Lettow, G. Zumofen, A. Renn, S. Goetzinger, and V. Sandoghdar, “A single-molecule optical transistor,” Nature460, 76–80 (2009).
[CrossRef] [PubMed]

Ibanescu, M.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E65, 066611 (2002).
[CrossRef]

Jayich, A. M.

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. Bleszynski Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett.92, 103125 (2008).
[CrossRef]

Jiang, X.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett.103, 103601 (2009).
[CrossRef] [PubMed]

Joannopoulos, J. D.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E65, 066611 (2002).
[CrossRef]

Johnson, S. G.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E65, 066611 (2002).
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Kimble, H. J.

H. J. Kimble, “The quantum internet,” Nature (London)453, 1023–1030 (2008).
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S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science330, 1520–1523 (2010).
[CrossRef] [PubMed]

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express15, 17172–17205 (2007).
[CrossRef] [PubMed]

Krause, A.

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

Krause, A. G.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A microchip optomechanical accelerometer,” arXiv:1203.5730 (2012).

Kuramochi, E.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B81, 121101 (2010).
[CrossRef]

Lechner, L.

J. Sulkko, M. A. Sillanpää, P. Häkkinen, 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]

Lehnert, K. 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 (London)475, 359–363 (2011).
[CrossRef]

C. A. Regal, J. D. Teufel, and K. W. Lehnert, “Measuring nanomechanical motion with a microwave cavity interferometer,” Nat. Phys.4, 555–560 (2008).
[CrossRef]

Lettow, R.

J. Hwang, M. Pototschnig, R. Lettow, G. Zumofen, A. Renn, S. Goetzinger, and V. Sandoghdar, “A single-molecule optical transistor,” Nature460, 76–80 (2009).
[CrossRef] [PubMed]

Lev, B.

P. E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, “Integration of fiber-coupled high-Q SiNx microdisks with magnetostatic atom chips,” Appl. Phys. Lett.89, 131108 (2006).
[CrossRef]

Levy, J. S.

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 (London)475, 359–363 (2011).
[CrossRef]

Li, M.

K. Y. Fong, W. H. P. Pernice, M. Li, and H. X. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett.97, 073112 (2010).
[CrossRef]

Li, Y.

J. Zheng, Y. Li, S. Aras, M. Stein, K. L. Shepard, and C. W. Wong, “Parametric optomechanical oscillations in two-dimensional slot-type high-Q photonic crystal cavities,” Appl. Phys. Lett.100, 211908 (2012).
[CrossRef]

Lin, Q.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A microchip optomechanical accelerometer,” arXiv:1203.5730 (2012).

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature (London)472, 69–73 (2011).
[CrossRef]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett.103, 103601 (2009).
[CrossRef] [PubMed]

Lipson, M.

Loncar, M.

Ludwig, M.

M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquadt, “Optomechanical photon detection and enhanced dispersive phonon readout,” arXiv:1202.0532 (2012).

Lukin, M. D.

K. Stannigel, P. Rabl, A. S. Sørensen, M. D. Lukin, and P. Zoller, “Optomechanical transducers for quantum-information processing,” Phys. Rev. A84, 042341 (2011).
[CrossRef]

Ma, L.

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
[CrossRef]

Mabuchi, H.

P. E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, “Integration of fiber-coupled high-Q SiNx microdisks with magnetostatic atom chips,” Appl. Phys. Lett.89, 131108 (2006).
[CrossRef]

Marquadt, F.

M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquadt, “Optomechanical photon detection and enhanced dispersive phonon readout,” arXiv:1202.0532 (2012).

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F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonators,” Nature (London)480, 351–354 (2011).
[CrossRef]

Matsuo, S.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B81, 121101 (2010).
[CrossRef]

McCutcheon, M. W.

Meenehan, S.

J. Chan, A. H. Safavi-Naeini, J. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” (2012), arXiv:1206.2099.

Notomi, M.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B81, 121101 (2010).
[CrossRef]

Painter, O.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A microchip optomechanical accelerometer,” arXiv:1203.5730 (2012).

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity-optomechanics,” arXiv:1203.5730 (2012).

J. Chan, A. H. Safavi-Naeini, J. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” (2012), arXiv:1206.2099.

D. E. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys.13, 023003 (2011).
[CrossRef]

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

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

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature (London)472, 69–73 (2011).
[CrossRef]

A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express18, 14926–14943 (2010).
[CrossRef] [PubMed]

R. M. Camacho, J. Chan, M. Eichenfield, and O. Painter, “Characterization of radiation pressure and thermal effects in a nanoscale optomechanical cavity,” Opt. Express17, 15726–15735 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and-losses of localized optical andmechanical modes in optomechanicalcrystals,” Opt. Express17, 20078–20098 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462, 78–82 (2009).
[CrossRef] [PubMed]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett.103, 103601 (2009).
[CrossRef] [PubMed]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature459, 550–555 (2009).
[CrossRef] [PubMed]

P. E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, “Integration of fiber-coupled high-Q SiNx microdisks with magnetostatic atom chips,” Appl. Phys. Lett.89, 131108 (2006).
[CrossRef]

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microcavities excited via an integrated waveguide and fiber taper,” Opt. Express13, 801–820 (2005).
[CrossRef] [PubMed]

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express10, 670–684 (2002).
[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).

M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquadt, “Optomechanical photon detection and enhanced dispersive phonon readout,” arXiv:1202.0532 (2012).

Parpia, J.

J. Sulkko, M. A. Sillanpää, P. Häkkinen, 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]

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]

Pernice, W. H. P.

K. Y. Fong, W. H. P. Pernice, M. Li, and H. X. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett.97, 073112 (2010).
[CrossRef]

Pirkkalainen, J.-M.

F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonators,” Nature (London)480, 351–354 (2011).
[CrossRef]

Pototschnig, M.

J. Hwang, M. Pototschnig, R. Lettow, G. Zumofen, A. Renn, S. Goetzinger, and V. Sandoghdar, “A single-molecule optical transistor,” Nature460, 76–80 (2009).
[CrossRef] [PubMed]

Quan, Q.

Q. Quan and M. Loncar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express19, 18529–18542 (2011).
[CrossRef] [PubMed]

Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys.Lett.96, 203102 (2010).
[CrossRef]

Rabl, P.

K. Stannigel, P. Rabl, A. S. Sørensen, M. D. Lukin, and P. Zoller, “Optomechanical transducers for quantum-information processing,” Phys. Rev. A84, 042341 (2011).
[CrossRef]

Rakher, M. T.

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
[CrossRef]

Rakich, P. T.

P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X2, 011008 (2012).
[CrossRef]

Regal, C. A.

C. A. Regal, J. D. Teufel, and K. W. Lehnert, “Measuring nanomechanical motion with a microwave cavity interferometer,” Nat. Phys.4, 555–560 (2008).
[CrossRef]

Reinke, C.

P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X2, 011008 (2012).
[CrossRef]

Renn, A.

J. Hwang, M. Pototschnig, R. Lettow, G. Zumofen, A. Renn, S. Goetzinger, and V. Sandoghdar, “A single-molecule optical transistor,” Nature460, 76–80 (2009).
[CrossRef] [PubMed]

Rivière, R.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science330, 1520–1523 (2010).
[CrossRef] [PubMed]

Roh, Y.-G.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B81, 121101 (2010).
[CrossRef]

Rosenberg, J.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett.103, 103601 (2009).
[CrossRef] [PubMed]

Safavi-Naeini, A. H.

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity-optomechanics,” arXiv:1203.5730 (2012).

J. Chan, A. H. Safavi-Naeini, J. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” (2012), arXiv:1206.2099.

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

D. E. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys.13, 023003 (2011).
[CrossRef]

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature (London)472, 69–73 (2011).
[CrossRef]

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

A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express18, 14926–14943 (2010).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and-losses of localized optical andmechanical modes in optomechanicalcrystals,” Opt. Express17, 20078–20098 (2009).
[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).

M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquadt, “Optomechanical photon detection and enhanced dispersive phonon readout,” arXiv:1202.0532 (2012).

Saloniemi, H.

F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonators,” Nature (London)480, 351–354 (2011).
[CrossRef]

Sandoghdar, V.

J. Hwang, M. Pototschnig, R. Lettow, G. Zumofen, A. Renn, S. Goetzinger, and V. Sandoghdar, “A single-molecule optical transistor,” Nature460, 76–80 (2009).
[CrossRef] [PubMed]

Sato, T.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B81, 121101 (2010).
[CrossRef]

Schliesser, A.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science330, 1520–1523 (2010).
[CrossRef] [PubMed]

Shah Hosseini, E.

Shanks, W. E.

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. Bleszynski Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett.92, 103125 (2008).
[CrossRef]

Shepard, K. L.

J. Zheng, Y. Li, S. Aras, M. Stein, K. L. Shepard, and C. W. Wong, “Parametric optomechanical oscillations in two-dimensional slot-type high-Q photonic crystal cavities,” Appl. Phys. Lett.100, 211908 (2012).
[CrossRef]

Shields, A. J.

A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics1, 215–223 (2007).
[CrossRef]

Shinya, A.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B81, 121101 (2010).
[CrossRef]

Sillanpää, M. A.

F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonators,” Nature (London)480, 351–354 (2011).
[CrossRef]

J. Sulkko, M. A. Sillanpää, P. Häkkinen, 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]

Simmonds, R. 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 (London)475, 359–363 (2011).
[CrossRef]

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 (London)475, 359–363 (2011).
[CrossRef]

Skorobogatiy, M. A.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E65, 066611 (2002).
[CrossRef]

Slattery, O.

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
[CrossRef]

Soltani, M.

Sørensen, A. S.

K. Stannigel, P. Rabl, A. S. Sørensen, M. D. Lukin, and P. Zoller, “Optomechanical transducers for quantum-information processing,” Phys. Rev. A84, 042341 (2011).
[CrossRef]

Srinivasan, K.

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
[CrossRef]

P. E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, “Integration of fiber-coupled high-Q SiNx microdisks with magnetostatic atom chips,” Appl. Phys. Lett.89, 131108 (2006).
[CrossRef]

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microcavities excited via an integrated waveguide and fiber taper,” Opt. Express13, 801–820 (2005).
[CrossRef] [PubMed]

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express10, 670–684 (2002).
[PubMed]

Stannigel, K.

K. Stannigel, P. Rabl, A. S. Sørensen, M. D. Lukin, and P. Zoller, “Optomechanical transducers for quantum-information processing,” Phys. Rev. A84, 042341 (2011).
[CrossRef]

Stein, M.

J. Zheng, Y. Li, S. Aras, M. Stein, K. L. Shepard, and C. W. Wong, “Parametric optomechanical oscillations in two-dimensional slot-type high-Q photonic crystal cavities,” Appl. Phys. Lett.100, 211908 (2012).
[CrossRef]

Sulkko, J.

J. Sulkko, M. A. Sillanpää, P. Häkkinen, 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]

Tanabe, T.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B81, 121101 (2010).
[CrossRef]

Tang, H. X.

K. Y. Fong, W. H. P. Pernice, M. Li, and H. X. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett.97, 073112 (2010).
[CrossRef]

Tang, X.

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
[CrossRef]

Taniyama, H.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B81, 121101 (2010).
[CrossRef]

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 (London)475, 359–363 (2011).
[CrossRef]

C. A. Regal, J. D. Teufel, and K. W. Lehnert, “Measuring nanomechanical motion with a microwave cavity interferometer,” Nat. Phys.4, 555–560 (2008).
[CrossRef]

Thompson, J. D.

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. Bleszynski Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett.92, 103125 (2008).
[CrossRef]

Tian, L.

L. Tian and H. Wang, “Optical wavelength conversion of quantum states with optomechanics,” Phys. Rev. A82, 053806 (2010).
[CrossRef]

Vahala, K. J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462, 78–82 (2009).
[CrossRef] [PubMed]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature459, 550–555 (2009).
[CrossRef] [PubMed]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett.103, 103601 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and-losses of localized optical andmechanical modes in optomechanicalcrystals,” Opt. Express17, 20078–20098 (2009).
[CrossRef] [PubMed]

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express15, 17172–17205 (2007).
[CrossRef] [PubMed]

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]

W.-H. Tian, L.

C. F.-V. K. M. C. Dong and L. W.-H. Tian, “A microchip optomechanical accelerometer,” arXiv:1205.2360 (2012).

Wang, H.

L. Tian and H. Wang, “Optical wavelength conversion of quantum states with optomechanics,” Phys. Rev. A82, 053806 (2010).
[CrossRef]

Wang, Z.

P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X2, 011008 (2012).
[CrossRef]

Weis, S.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science330, 1520–1523 (2010).
[CrossRef] [PubMed]

Weisberg, O.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E65, 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 (London)475, 359–363 (2011).
[CrossRef]

Wiederhecker, G. S.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature462, 633–636 (2009).
[CrossRef] [PubMed]

Winger, M.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A microchip optomechanical accelerometer,” arXiv:1203.5730 (2012).

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature (London)472, 69–73 (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).

Wong, C. W.

J. Zheng, Y. Li, S. Aras, M. Stein, K. L. Shepard, and C. W. Wong, “Parametric optomechanical oscillations in two-dimensional slot-type high-Q photonic crystal cavities,” Appl. Phys. Lett.100, 211908 (2012).
[CrossRef]

Xu, Q.

Yang, C.

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. Bleszynski Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett.92, 103125 (2008).
[CrossRef]

Yegnanarayanan, S.

Zheng, J.

J. Zheng, Y. Li, S. Aras, M. Stein, K. L. Shepard, and C. W. Wong, “Parametric optomechanical oscillations in two-dimensional slot-type high-Q photonic crystal cavities,” Appl. Phys. Lett.100, 211908 (2012).
[CrossRef]

Zoller, P.

K. Stannigel, P. Rabl, A. S. Sørensen, M. D. Lukin, and P. Zoller, “Optomechanical transducers for quantum-information processing,” Phys. Rev. A84, 042341 (2011).
[CrossRef]

Zumofen, G.

J. Hwang, M. Pototschnig, R. Lettow, G. Zumofen, A. Renn, S. Goetzinger, and V. Sandoghdar, “A single-molecule optical transistor,” Nature460, 76–80 (2009).
[CrossRef] [PubMed]

Zwickl, B. M.

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. Bleszynski Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett.92, 103125 (2008).
[CrossRef]

Appl. Phys. Lett. (6)

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).

J. Zheng, Y. Li, S. Aras, M. Stein, K. L. Shepard, and C. W. Wong, “Parametric optomechanical oscillations in two-dimensional slot-type high-Q photonic crystal cavities,” Appl. Phys. Lett.100, 211908 (2012).
[CrossRef]

P. E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, “Integration of fiber-coupled high-Q SiNx microdisks with magnetostatic atom chips,” Appl. Phys. Lett.89, 131108 (2006).
[CrossRef]

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. Bleszynski Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett.92, 103125 (2008).
[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]

K. Y. Fong, W. H. P. Pernice, M. Li, and H. X. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett.97, 073112 (2010).
[CrossRef]

Appl. Phys.Lett. (1)

Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys.Lett.96, 203102 (2010).
[CrossRef]

Nano Lett. (1)

J. Sulkko, M. A. Sillanpää, P. Häkkinen, 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]

Nat. Photonics (3)

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
[CrossRef]

A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics1, 215–223 (2007).
[CrossRef]

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics3, 696–705 (2009).
[CrossRef]

Nat. Phys. (1)

C. A. Regal, J. D. Teufel, and K. W. Lehnert, “Measuring nanomechanical motion with a microwave cavity interferometer,” Nat. Phys.4, 555–560 (2008).
[CrossRef]

Nature (4)

J. Hwang, M. Pototschnig, R. Lettow, G. Zumofen, A. Renn, S. Goetzinger, and V. Sandoghdar, “A single-molecule optical transistor,” Nature460, 76–80 (2009).
[CrossRef] [PubMed]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature462, 633–636 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462, 78–82 (2009).
[CrossRef] [PubMed]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature459, 550–555 (2009).
[CrossRef] [PubMed]

Nature (London) (5)

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature (London)472, 69–73 (2011).
[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 (London)475, 359–363 (2011).
[CrossRef]

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

H. J. Kimble, “The quantum internet,” Nature (London)453, 1023–1030 (2008).
[CrossRef]

F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonators,” Nature (London)480, 351–354 (2011).
[CrossRef]

New J. Phys. (2)

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

D. E. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys.13, 023003 (2011).
[CrossRef]

Opt. Express (9)

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express15, 17172–17205 (2007).
[CrossRef] [PubMed]

A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express17, 11366–11370 (2009).
[CrossRef] [PubMed]

E. Shah Hosseini, S. Yegnanarayanan, A. H. Atabaki, M. Soltani, and A. Adibi, “High quality planar silicon nitride microdisk resonators for integrated photonics in the vsible wavelength range,” Opt. Express17, 14543–14551 (2009).
[CrossRef]

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microcavities excited via an integrated waveguide and fiber taper,” Opt. Express13, 801–820 (2005).
[CrossRef] [PubMed]

Q. Quan and M. Loncar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express19, 18529–18542 (2011).
[CrossRef] [PubMed]

A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express18, 14926–14943 (2010).
[CrossRef] [PubMed]

R. M. Camacho, J. Chan, M. Eichenfield, and O. Painter, “Characterization of radiation pressure and thermal effects in a nanoscale optomechanical cavity,” Opt. Express17, 15726–15735 (2009).
[CrossRef] [PubMed]

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express10, 670–684 (2002).
[PubMed]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and-losses of localized optical andmechanical modes in optomechanicalcrystals,” Opt. Express17, 20078–20098 (2009).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (2)

K. Stannigel, P. Rabl, A. S. Sørensen, M. D. Lukin, and P. Zoller, “Optomechanical transducers for quantum-information processing,” Phys. Rev. A84, 042341 (2011).
[CrossRef]

L. Tian and H. Wang, “Optical wavelength conversion of quantum states with optomechanics,” Phys. Rev. A82, 053806 (2010).
[CrossRef]

Phys. Rev. B (1)

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B81, 121101 (2010).
[CrossRef]

Phys. Rev. E (1)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E65, 066611 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett.103, 103601 (2009).
[CrossRef] [PubMed]

Phys. Rev. X (1)

P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X2, 011008 (2012).
[CrossRef]

Science (1)

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science330, 1520–1523 (2010).
[CrossRef] [PubMed]

Other (5)

M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquadt, “Optomechanical photon detection and enhanced dispersive phonon readout,” arXiv:1202.0532 (2012).

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity-optomechanics,” arXiv:1203.5730 (2012).

C. F.-V. K. M. C. Dong and L. W.-H. Tian, “A microchip optomechanical accelerometer,” arXiv:1205.2360 (2012).

J. Chan, A. H. Safavi-Naeini, J. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” (2012), arXiv:1206.2099.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A microchip optomechanical accelerometer,” arXiv:1203.5730 (2012).

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Figures (9)

Fig. 1
Fig. 1

Schematic of double beam optomechanical resonator.

Fig. 2
Fig. 2

(a) Si3N4 nanobeam optomechanical crystal. (b)–(d): first, second, and third order optical resonances. (e) Mechanical resonance.

Fig. 3
Fig. 3

(a) Simplified nanobeam geometry with only the optical arm of the mechanical resonator. (b) Photonic bands for the TE mode (Ey = 0 at the y = 0 plane) of the unit cell indicated in (a), for WA/WO = 0.25 and WA/WO = 0.65. (c) Normalized electric field amplitude for the fundamental TE mode band at the X point (open circle in (b)). (d) Normalized frequency bands for the first four TE photonic Bloch modes at the X-point, and (e) normalized effective length for the fundamental TE mode, as functions of WA/WO.

Fig. 4
Fig. 4

(a) Photonic lattice constant, (b) optical arm (WA) over optical beam (WO) width ratio, (c) frequency (at the X-point) of the first two TE photonic bands, and (d) photonic mirror strength, as functions of the distance from the cavity center (z = 0). (e) Squared electric field amplitude for the photonic mode generated with the parameters in (a)–(d).

Fig. 5
Fig. 5

(a) Phononic crystal geometry. (b) Mechanical Bloch mode band structure for a phononic crystal with WA/WO = 0.25. The inset shapes show a top view of the unit cell, with exaggerated boundary displacements for modes on bands A, B and C. (c) Evolution of the Γ-point eigenfrequency for band C, as a function of the ratio between the optical arm (WA) and optical beam (WO) widths.

Fig. 6
Fig. 6

(a) and (b): Mechanical beam breathing modes for (a) WM/WO = 2.6 and (b) WM/WO = 2.8. (c) Fundamental optical slot mode for the complete geometry. (d) Mechanical frequency, (e) normalized displacement Dx, (f) motional mass m, and (g) optomechanical coupling parameter gOM and zero-point motion optomechanical coupling rate g for the fundamental breathing mode as a function of WM/WO. As a function of gap width: (h) fundamental optical resonance wavelength, (i) quality factor, and (j) gOM and g of the fundamental mechanical breathing mode for WM/WO = 2.8, as in (b). Note that the geometry that produced (h)–(j) was optimized for a 25 nm gap. Improved values of gOM, g, and Q over those plotted can be obtained by optimization for different gap widths (see text). (k) Optical mode frequency and (l) optical quality factor as a function of rib width, for the geometry shown in (c), with a gap width of 25 nm and WM/WO = 2.8.

Fig. 7
Fig. 7

(a) Double optical cavity optomechanical crystal geometry. (b) 1310 nm optical mode. (c) Mechanical resonator breathing mode. (c) 980 nm optical mode. Green arrows indicate simultaneous coupling between the optical resonances and the mechanical mode.

Fig. 8
Fig. 8

Optical mode splitting for the symmetric double optical beam resonator in the inset. The dotted line in the inset indicates the symmetry plane that defines splits the original optical resonance into symmetric (blue) and anti-symmetric (red) modes. Parameters for the optical and mechanical resonators are as in Section 4, with WM/WO = 2.8.

Fig. 9
Fig. 9

Schematic for possible optomechanical microwave-to-optical wavelength converter. The RF cavity resonance frequency is modulated by the gap capacitance Cg, which depends on the gap width, and therefore on the displacement of the mechanical resonator. The latter is coupled to the slot optical mode formed with the optical beam.

Tables (2)

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Table 1 Silicon Based Optical Resonator Optomechanical Crystal Parameters. A slot width of 10 nm was assumed.

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Table 2 Double Optical Resonator Optomechanical Crystal Parameters. Both slots are assumed to be 25 nm wide.

Equations (6)

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L OM = 2 d V ε | E | 2 d A ( | Q n | ) ( Δ ε | E | | | 2 Δ ( ε 1 ) | D | 2 ) .
γ = ( ω 2 ω 1 ω 1 + ω 2 ) 2 ( ω ω 0 ω 0 ) 2 ,
D x = d A Q n d A | Q n | ,
[ α 1 β α 2 ] = [ κ 1 / 2 i G 1 0 i G 1 i γ i / 2 i G 2 0 i G 2 κ 2 / 2 ] 1 [ κ ex , 1 2 α in ; 1 0 0 ] ,
α out ; 2 = η 1 η 2 γ OM ; 1 γ OM ; 2 γ / 2 α in , 1 ,
η = | α out , 2 α in , 1 | 2 = η 1 η 2 4 C 1 C 2 ( 1 + C 1 + C 2 ) 2 ,

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