Abstract

We present a silicon optomechanical nanobeam design with a dynamically tunable acoustic mode at 10.2 GHz. The resonance frequency can be shifted by 90 kHz/V2 with an on-chip capacitor that was optimized to exert forces up to 1 µN at 10 V operation voltage. Optical resonance frequencies around 190 THz with Q-factors up to 2.2 × 106 place the structure in the well-resolved sideband regime with vacuum optomechanical coupling rates up to g0/2π = 353 kHz. Tuning can be used, for instance, to overcome variation in the device-to-device acoustic resonance frequency due to fabrication errors, paving the way for optomechanical circuits consisting of arrays of optomechanical cavities.

© 2016 Optical Society of America

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    [Crossref]
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2016 (2)

R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gröblacher, “Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530(7590), 313–316 (2016).
[Crossref] [PubMed]

T. Weiss, A. Kronwald, and F. Marquardt, “Noise-induced transitions in optomechanical synchronization,” New J. Phys. 18(1), 013043 (2016).
[Crossref]

2015 (6)

E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab, “Quantum squeezing of motion in a mechanical resonator,” Science 349(6251), 952–955 (2015).
[Crossref] [PubMed]

J.-M. Pirkkalainen, E. Damskägg, M. Brandt, F. Massel, and M. A. Sillanpää, “Squeezing of quantum noise of motion in a micromechanical resonator,” Phys. Rev. Lett. 115(24), 243601 (2015).
[Crossref] [PubMed]

M. Schmidt, S. Kessler, V. Peano, O. Painter, and F. Marquardt, “Optomechanical creation of magnetic fields for photons on a lattice,” Optica 2(7), 635–641 (2015).
[Crossref]

R. Lauter, C. Brendel, S. J. M. Habraken, and F. Marquardt, “Pattern phase diagram for two-dimensional arrays of coupled limit-cycle oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 92(1), 012902 (2015).
[Crossref] [PubMed]

V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” Phys. Rev. X 5(3), 031011 (2015).
[Crossref]

T. K. Paraïso, M. Kalaee, L. Zang, H. Pfeifer, F. Marquardt, and O. Painter, “Position-squared coupling in a tunable photonic crystal optomechanical cavity,” Phys. Rev. X 5(4), 041024 (2015).
[Crossref]

2014 (1)

M. Aspelmeyer, T. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

2013 (5)

T. A. Palomaki, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Entangling mechanical motion with microwave fields,” Science 342(6159), 710–713 (2013).
[Crossref] [PubMed]

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
[Crossref] [PubMed]

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3(3), 031012 (2013).
[Crossref]

M. Ludwig and F. Marquardt, “Quantum many-body dynamics in optomechanical arrays,” Phys. Rev. Lett. 111(7), 073603 (2013).
[Crossref] [PubMed]

Y. Wang, T. Li, and H. Yang, “Nanofabrication, effects and sensors based on micro-electro-mechanical systems technology,” Philos. Trans. A Math. Phys. Eng. Sci. 371(2000), 20120315 (2013).
[Crossref] [PubMed]

2012 (5)

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(8), 081115 (2012).
[Crossref]

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6(11), 768–772 (2012).
[Crossref]

I. Pikovski, M. R. Vanner, M. Aspelmeyer, M. S. Kim, and Č. Brukner, “Probing Planck-scale physics with quantum optics,” Nat. Phys. 8(5), 393–397 (2012).
[Crossref]

S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, and P. Rabl, “Continuous mode cooling and phonon routers for phononic quantum networks,” New J. Phys. 14(11), 115004 (2012).
[Crossref]

M. Schmidt, M. Ludwig, and F. Marquardt, “Optomechanical circuits for nanomechanical continuous variable quantum state processing,” New J. Phys. 14(12), 125005 (2012).
[Crossref]

2011 (7)

O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large Quantum Superpositions and Interference of Massive Nanometer-Sized Objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
[Crossref] [PubMed]

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 478(7367), 89–92 (2011).
[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(7356), 359–363 (2011).
[Crossref] [PubMed]

D. E. McClelland, N. Mavalvala, Y. Chen, and R. Schnabel, “Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors,” Laser Photonics Rev. 5(5), 677–696 (2011).

Z. Yan and L. Y. Jiang, “The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects,” Nanotechnology 22(24), 245703 (2011).
[Crossref] [PubMed]

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(2), 023003 (2011).
[Crossref]

M. Winger, T. D. Blasius, T. P. Mayer 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(25), 24905–24921 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (2)

Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458(7241), 1001–1004 (2009).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

2008 (1)

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[Crossref] [PubMed]

2006 (2)

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89(4), 041118 (2006).
[Crossref]

F. W. Strong, J. L. Skinner, P. M. Dentinger, and N. C. Tien, “Electrical breakdown across micron scale gaps in MEMS structures,” Proc. SPIE 6111, 611103 (2006).
[Crossref]

2005 (1)

K. L. Ekinci and M. L. Roukes, “Electromechanical transducers at the nanoscale: actuation and sensing of motion in nanoelectromechanical systems (NEMS),” Small 1(8-9), 786–797 (2005).
[Crossref] [PubMed]

2002 (2)

P. G. Slade and E. D. Taylor, “Electrical breakdown in atmospheric air between closely spaced (0.2 µm–40 µm) electrical contacts,” IEEE Trans. Compon. Packag. Tech. 25(3), 390 (2002).
[Crossref]

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. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

2001 (1)

2000 (1)

J.-M. Torres, M. P. Y. Desmulliez, and R. S. Dhariwal, “Electric field breakdown at micrometre separations in air and nitrogen at atmospheric pressure,” IEEE Proc. Sci. Meas. Technol. 147(5), 261–265 (2000).

1999 (2)

J.-M. Torres and R. S. Dhariwal, “Electric field breakdown at micrometre separations,” Nanotechnology 10(1), 102–107 (1999).
[Crossref]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999).
[Crossref] [PubMed]

1967 (1)

H. C. Nathanson, W. E. Newell, R. A. Wickstrom, and J. R. Davis, “The resonant gate transistor,” IEEE Trans. Electron Dev. 14(3), 117–133 (1967).
[Crossref]

Alegre, T. P. 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 478(7367), 89–92 (2011).
[Crossref] [PubMed]

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(7356), 359–363 (2011).
[Crossref] [PubMed]

Anant, V.

R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gröblacher, “Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530(7590), 313–316 (2016).
[Crossref] [PubMed]

Aspelmeyer, M.

R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gröblacher, “Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530(7590), 313–316 (2016).
[Crossref] [PubMed]

M. Aspelmeyer, T. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
[Crossref] [PubMed]

I. Pikovski, M. R. Vanner, M. Aspelmeyer, M. S. Kim, and Č. Brukner, “Probing Planck-scale physics with quantum optics,” Nat. Phys. 8(5), 393–397 (2012).
[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 478(7367), 89–92 (2011).
[Crossref] [PubMed]

O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large Quantum Superpositions and Interference of Massive Nanometer-Sized Objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
[Crossref] [PubMed]

Badolato, A.

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89(4), 041118 (2006).
[Crossref]

Baehr-Jones, T.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[Crossref] [PubMed]

Blaser, F.

O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large Quantum Superpositions and Interference of Massive Nanometer-Sized Objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
[Crossref] [PubMed]

Blasius, T. D.

Brandt, M.

J.-M. Pirkkalainen, E. Damskägg, M. Brandt, F. Massel, and M. A. Sillanpää, “Squeezing of quantum noise of motion in a micromechanical resonator,” Phys. Rev. Lett. 115(24), 243601 (2015).
[Crossref] [PubMed]

Brendel, C.

R. Lauter, C. Brendel, S. J. M. Habraken, and F. Marquardt, “Pattern phase diagram for two-dimensional arrays of coupled limit-cycle oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 92(1), 012902 (2015).
[Crossref] [PubMed]

V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” Phys. Rev. X 5(3), 031011 (2015).
[Crossref]

Brukner, C.

I. Pikovski, M. R. Vanner, M. Aspelmeyer, M. S. Kim, and Č. Brukner, “Probing Planck-scale physics with quantum optics,” Nat. Phys. 8(5), 393–397 (2012).
[Crossref]

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Chan, J.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
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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 478(7367), 89–92 (2011).
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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(2), 023003 (2011).
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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(8), 081115 (2012).
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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 478(7367), 89–92 (2011).
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M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
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O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large Quantum Superpositions and Interference of Massive Nanometer-Sized Objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
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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 478(7367), 89–92 (2011).
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R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gröblacher, “Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530(7590), 313–316 (2016).
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A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6(11), 768–772 (2012).
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T. Weiss, A. Kronwald, and F. Marquardt, “Noise-induced transitions in optomechanical synchronization,” New J. Phys. 18(1), 013043 (2016).
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R. Lauter, C. Brendel, S. J. M. Habraken, and F. Marquardt, “Pattern phase diagram for two-dimensional arrays of coupled limit-cycle oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 92(1), 012902 (2015).
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Lehnert, K. W.

T. A. Palomaki, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Entangling mechanical motion with microwave fields,” Science 342(6159), 710–713 (2013).
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E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab, “Quantum squeezing of motion in a mechanical resonator,” Science 349(6251), 952–955 (2015).
[Crossref] [PubMed]

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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 475(7356), 359–363 (2011).
[Crossref] [PubMed]

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M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
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T. Weiss, A. Kronwald, and F. Marquardt, “Noise-induced transitions in optomechanical synchronization,” New J. Phys. 18(1), 013043 (2016).
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V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” Phys. Rev. X 5(3), 031011 (2015).
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M. Schmidt, S. Kessler, V. Peano, O. Painter, and F. Marquardt, “Optomechanical creation of magnetic fields for photons on a lattice,” Optica 2(7), 635–641 (2015).
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T. K. Paraïso, M. Kalaee, L. Zang, H. Pfeifer, F. Marquardt, and O. Painter, “Position-squared coupling in a tunable photonic crystal optomechanical cavity,” Phys. Rev. X 5(4), 041024 (2015).
[Crossref]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref]

M. Ludwig and F. Marquardt, “Quantum many-body dynamics in optomechanical arrays,” Phys. Rev. Lett. 111(7), 073603 (2013).
[Crossref] [PubMed]

M. Schmidt, M. Ludwig, and F. Marquardt, “Optomechanical circuits for nanomechanical continuous variable quantum state processing,” New J. Phys. 14(12), 125005 (2012).
[Crossref]

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J.-M. Pirkkalainen, E. Damskägg, M. Brandt, F. Massel, and M. A. Sillanpää, “Squeezing of quantum noise of motion in a micromechanical resonator,” Phys. Rev. Lett. 115(24), 243601 (2015).
[Crossref] [PubMed]

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D. E. McClelland, N. Mavalvala, Y. Chen, and R. Schnabel, “Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors,” Laser Photonics Rev. 5(5), 677–696 (2011).

Mayer Alegre, T. P.

McClelland, D. E.

D. E. McClelland, N. Mavalvala, Y. Chen, and R. Schnabel, “Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors,” Laser Photonics Rev. 5(5), 677–696 (2011).

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(8), 081115 (2012).
[Crossref]

M. Winger, T. D. Blasius, T. P. Mayer 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(25), 24905–24921 (2011).
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R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gröblacher, “Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530(7590), 313–316 (2016).
[Crossref] [PubMed]

Painter, O.

T. K. Paraïso, M. Kalaee, L. Zang, H. Pfeifer, F. Marquardt, and O. Painter, “Position-squared coupling in a tunable photonic crystal optomechanical cavity,” Phys. Rev. X 5(4), 041024 (2015).
[Crossref]

M. Schmidt, S. Kessler, V. Peano, O. Painter, and F. Marquardt, “Optomechanical creation of magnetic fields for photons on a lattice,” Optica 2(7), 635–641 (2015).
[Crossref]

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
[Crossref] [PubMed]

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6(11), 768–772 (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(8), 081115 (2012).
[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(2), 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 478(7367), 89–92 (2011).
[Crossref] [PubMed]

M. Winger, T. D. Blasius, T. P. Mayer 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(25), 24905–24921 (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. Express 18(14), 14926–14943 (2010).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Palomaki, T. A.

T. A. Palomaki, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Entangling mechanical motion with microwave fields,” Science 342(6159), 710–713 (2013).
[Crossref] [PubMed]

Paraïso, T. K.

T. K. Paraïso, M. Kalaee, L. Zang, H. Pfeifer, F. Marquardt, and O. Painter, “Position-squared coupling in a tunable photonic crystal optomechanical cavity,” Phys. Rev. X 5(4), 041024 (2015).
[Crossref]

Peano, V.

V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” Phys. Rev. X 5(3), 031011 (2015).
[Crossref]

M. Schmidt, S. Kessler, V. Peano, O. Painter, and F. Marquardt, “Optomechanical creation of magnetic fields for photons on a lattice,” Optica 2(7), 635–641 (2015).
[Crossref]

Pernice, W. H. P.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[Crossref] [PubMed]

Peterson, R. W.

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3(3), 031012 (2013).
[Crossref]

Pfeifer, H.

T. K. Paraïso, M. Kalaee, L. Zang, H. Pfeifer, F. Marquardt, and O. Painter, “Position-squared coupling in a tunable photonic crystal optomechanical cavity,” Phys. Rev. X 5(4), 041024 (2015).
[Crossref]

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O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large Quantum Superpositions and Interference of Massive Nanometer-Sized Objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
[Crossref] [PubMed]

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I. Pikovski, M. R. Vanner, M. Aspelmeyer, M. S. Kim, and Č. Brukner, “Probing Planck-scale physics with quantum optics,” Nat. Phys. 8(5), 393–397 (2012).
[Crossref]

Pirkkalainen, J.-M.

J.-M. Pirkkalainen, E. Damskägg, M. Brandt, F. Massel, and M. A. Sillanpää, “Squeezing of quantum noise of motion in a micromechanical resonator,” Phys. Rev. Lett. 115(24), 243601 (2015).
[Crossref] [PubMed]

Purdy, T. P.

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3(3), 031012 (2013).
[Crossref]

Rabl, P.

S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, and P. Rabl, “Continuous mode cooling and phonon routers for phononic quantum networks,” New J. Phys. 14(11), 115004 (2012).
[Crossref]

Regal, C. A.

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3(3), 031012 (2013).
[Crossref]

Riedinger, R.

R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gröblacher, “Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530(7590), 313–316 (2016).
[Crossref] [PubMed]

Romero-Isart, O.

O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large Quantum Superpositions and Interference of Massive Nanometer-Sized Objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
[Crossref] [PubMed]

Roukes, M. L.

K. L. Ekinci and M. L. Roukes, “Electromechanical transducers at the nanoscale: actuation and sensing of motion in nanoelectromechanical systems (NEMS),” Small 1(8-9), 786–797 (2005).
[Crossref] [PubMed]

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 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(8), 081115 (2012).
[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(2), 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 478(7367), 89–92 (2011).
[Crossref] [PubMed]

M. Winger, T. D. Blasius, T. P. Mayer 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(25), 24905–24921 (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. Express 18(14), 14926–14943 (2010).
[Crossref] [PubMed]

Scherer, A.

Schmidt, M.

M. Schmidt, S. Kessler, V. Peano, O. Painter, and F. Marquardt, “Optomechanical creation of magnetic fields for photons on a lattice,” Optica 2(7), 635–641 (2015).
[Crossref]

V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” Phys. Rev. X 5(3), 031011 (2015).
[Crossref]

M. Schmidt, M. Ludwig, and F. Marquardt, “Optomechanical circuits for nanomechanical continuous variable quantum state processing,” New J. Phys. 14(12), 125005 (2012).
[Crossref]

Schnabel, R.

D. E. McClelland, N. Mavalvala, Y. Chen, and R. Schnabel, “Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors,” Laser Photonics Rev. 5(5), 677–696 (2011).

Schwab, K. C.

E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab, “Quantum squeezing of motion in a mechanical resonator,” Science 349(6251), 952–955 (2015).
[Crossref] [PubMed]

Shang, J.

R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gröblacher, “Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530(7590), 313–316 (2016).
[Crossref] [PubMed]

Sillanpää, M. A.

J.-M. Pirkkalainen, E. Damskägg, M. Brandt, F. Massel, and M. A. Sillanpää, “Squeezing of quantum noise of motion in a micromechanical resonator,” Phys. Rev. Lett. 115(24), 243601 (2015).
[Crossref] [PubMed]

Simmonds, R. W.

T. A. Palomaki, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Entangling mechanical motion with microwave fields,” Science 342(6159), 710–713 (2013).
[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(7356), 359–363 (2011).
[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(7356), 359–363 (2011).
[Crossref] [PubMed]

Skinner, J. L.

F. W. Strong, J. L. Skinner, P. M. Dentinger, and N. C. Tien, “Electrical breakdown across micron scale gaps in MEMS structures,” Proc. SPIE 6111, 611103 (2006).
[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. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

Slade, P. G.

P. G. Slade and E. D. Taylor, “Electrical breakdown in atmospheric air between closely spaced (0.2 µm–40 µm) electrical contacts,” IEEE Trans. Compon. Packag. Tech. 25(3), 390 (2002).
[Crossref]

Slater, J. A.

R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gröblacher, “Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530(7590), 313–316 (2016).
[Crossref] [PubMed]

Stannigel, K.

S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, and P. Rabl, “Continuous mode cooling and phonon routers for phononic quantum networks,” New J. Phys. 14(11), 115004 (2012).
[Crossref]

Stobbe, S.

Strong, F. W.

F. W. Strong, J. L. Skinner, P. M. Dentinger, and N. C. Tien, “Electrical breakdown across micron scale gaps in MEMS structures,” Proc. SPIE 6111, 611103 (2006).
[Crossref]

Suh, J.

E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab, “Quantum squeezing of motion in a mechanical resonator,” Science 349(6251), 952–955 (2015).
[Crossref] [PubMed]

Tang, H. X.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[Crossref] [PubMed]

Taylor, E. D.

P. G. Slade and E. D. Taylor, “Electrical breakdown in atmospheric air between closely spaced (0.2 µm–40 µm) electrical contacts,” IEEE Trans. Compon. Packag. Tech. 25(3), 390 (2002).
[Crossref]

Teufel, J. D.

T. A. Palomaki, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Entangling mechanical motion with microwave fields,” Science 342(6159), 710–713 (2013).
[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(7356), 359–363 (2011).
[Crossref] [PubMed]

Tien, N. C.

F. W. Strong, J. L. Skinner, P. M. Dentinger, and N. C. Tien, “Electrical breakdown across micron scale gaps in MEMS structures,” Proc. SPIE 6111, 611103 (2006).
[Crossref]

Torres, J.-M.

J.-M. Torres, M. P. Y. Desmulliez, and R. S. Dhariwal, “Electric field breakdown at micrometre separations in air and nitrogen at atmospheric pressure,” IEEE Proc. Sci. Meas. Technol. 147(5), 261–265 (2000).

J.-M. Torres and R. S. Dhariwal, “Electric field breakdown at micrometre separations,” Nanotechnology 10(1), 102–107 (1999).
[Crossref]

Unterreithmeier, Q. P.

Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458(7241), 1001–1004 (2009).
[Crossref] [PubMed]

Vahala, K. J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Vanner, M. R.

I. Pikovski, M. R. Vanner, M. Aspelmeyer, M. S. Kim, and Č. Brukner, “Probing Planck-scale physics with quantum optics,” Nat. Phys. 8(5), 393–397 (2012).
[Crossref]

Wang, Y.

Y. Wang, T. Li, and H. Yang, “Nanofabrication, effects and sensors based on micro-electro-mechanical systems technology,” Philos. Trans. A Math. Phys. Eng. Sci. 371(2000), 20120315 (2013).
[Crossref] [PubMed]

Weig, E. M.

Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458(7241), 1001–1004 (2009).
[Crossref] [PubMed]

Weinstein, A. J.

E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab, “Quantum squeezing of motion in a mechanical resonator,” Science 349(6251), 952–955 (2015).
[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. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

Weiss, T.

T. Weiss, A. Kronwald, and F. Marquardt, “Noise-induced transitions in optomechanical synchronization,” New J. Phys. 18(1), 013043 (2016).
[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(7356), 359–363 (2011).
[Crossref] [PubMed]

Wickstrom, R. A.

H. C. Nathanson, W. E. Newell, R. A. Wickstrom, and J. R. Davis, “The resonant gate transistor,” IEEE Trans. Electron Dev. 14(3), 117–133 (1967).
[Crossref]

Winger, M.

Wollman, E. E.

E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab, “Quantum squeezing of motion in a mechanical resonator,” Science 349(6251), 952–955 (2015).
[Crossref] [PubMed]

Xiong, C.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[Crossref] [PubMed]

Xu, Y.

Yan, Z.

Z. Yan and L. Y. Jiang, “The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects,” Nanotechnology 22(24), 245703 (2011).
[Crossref] [PubMed]

Yang, H.

Y. Wang, T. Li, and H. Yang, “Nanofabrication, effects and sensors based on micro-electro-mechanical systems technology,” Philos. Trans. A Math. Phys. Eng. Sci. 371(2000), 20120315 (2013).
[Crossref] [PubMed]

Yariv, A.

Yu, P.-L.

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3(3), 031012 (2013).
[Crossref]

Zang, L.

T. K. Paraïso, M. Kalaee, L. Zang, H. Pfeifer, F. Marquardt, and O. Painter, “Position-squared coupling in a tunable photonic crystal optomechanical cavity,” Phys. Rev. X 5(4), 041024 (2015).
[Crossref]

Zoller, P.

S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, and P. Rabl, “Continuous mode cooling and phonon routers for phononic quantum networks,” New J. Phys. 14(11), 115004 (2012).
[Crossref]

Appl. Phys. Lett. (2)

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoğlu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89(4), 041118 (2006).
[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(8), 081115 (2012).
[Crossref]

IEEE Proc. Sci. Meas. Technol. (1)

J.-M. Torres, M. P. Y. Desmulliez, and R. S. Dhariwal, “Electric field breakdown at micrometre separations in air and nitrogen at atmospheric pressure,” IEEE Proc. Sci. Meas. Technol. 147(5), 261–265 (2000).

IEEE Trans. Compon. Packag. Tech. (1)

P. G. Slade and E. D. Taylor, “Electrical breakdown in atmospheric air between closely spaced (0.2 µm–40 µm) electrical contacts,” IEEE Trans. Compon. Packag. Tech. 25(3), 390 (2002).
[Crossref]

IEEE Trans. Electron Dev. (1)

H. C. Nathanson, W. E. Newell, R. A. Wickstrom, and J. R. Davis, “The resonant gate transistor,” IEEE Trans. Electron Dev. 14(3), 117–133 (1967).
[Crossref]

Laser Photonics Rev. (1)

D. E. McClelland, N. Mavalvala, Y. Chen, and R. Schnabel, “Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors,” Laser Photonics Rev. 5(5), 677–696 (2011).

Nanotechnology (2)

Z. Yan and L. Y. Jiang, “The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects,” Nanotechnology 22(24), 245703 (2011).
[Crossref] [PubMed]

J.-M. Torres and R. S. Dhariwal, “Electric field breakdown at micrometre separations,” Nanotechnology 10(1), 102–107 (1999).
[Crossref]

Nat. Photonics (1)

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6(11), 768–772 (2012).
[Crossref]

Nat. Phys. (1)

I. Pikovski, M. R. Vanner, M. Aspelmeyer, M. S. Kim, and Č. Brukner, “Probing Planck-scale physics with quantum optics,” Nat. Phys. 8(5), 393–397 (2012).
[Crossref]

Nature (7)

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 478(7367), 89–92 (2011).
[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(7356), 359–363 (2011).
[Crossref] [PubMed]

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gröblacher, “Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530(7590), 313–316 (2016).
[Crossref] [PubMed]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[Crossref] [PubMed]

Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458(7241), 1001–1004 (2009).
[Crossref] [PubMed]

New J. Phys. (4)

T. Weiss, A. Kronwald, and F. Marquardt, “Noise-induced transitions in optomechanical synchronization,” New J. Phys. 18(1), 013043 (2016).
[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(2), 023003 (2011).
[Crossref]

S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, and P. Rabl, “Continuous mode cooling and phonon routers for phononic quantum networks,” New J. Phys. 14(11), 115004 (2012).
[Crossref]

M. Schmidt, M. Ludwig, and F. Marquardt, “Optomechanical circuits for nanomechanical continuous variable quantum state processing,” New J. Phys. 14(12), 125005 (2012).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Optica (1)

Philos. Trans. A Math. Phys. Eng. Sci. (1)

Y. Wang, T. Li, and H. Yang, “Nanofabrication, effects and sensors based on micro-electro-mechanical systems technology,” Philos. Trans. A Math. Phys. Eng. Sci. 371(2000), 20120315 (2013).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (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. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

R. Lauter, C. Brendel, S. J. M. Habraken, and F. Marquardt, “Pattern phase diagram for two-dimensional arrays of coupled limit-cycle oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 92(1), 012902 (2015).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

J.-M. Pirkkalainen, E. Damskägg, M. Brandt, F. Massel, and M. A. Sillanpää, “Squeezing of quantum noise of motion in a micromechanical resonator,” Phys. Rev. Lett. 115(24), 243601 (2015).
[Crossref] [PubMed]

M. Ludwig and F. Marquardt, “Quantum many-body dynamics in optomechanical arrays,” Phys. Rev. Lett. 111(7), 073603 (2013).
[Crossref] [PubMed]

O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large Quantum Superpositions and Interference of Massive Nanometer-Sized Objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
[Crossref] [PubMed]

Phys. Rev. X (3)

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3(3), 031012 (2013).
[Crossref]

V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” Phys. Rev. X 5(3), 031011 (2015).
[Crossref]

T. K. Paraïso, M. Kalaee, L. Zang, H. Pfeifer, F. Marquardt, and O. Painter, “Position-squared coupling in a tunable photonic crystal optomechanical cavity,” Phys. Rev. X 5(4), 041024 (2015).
[Crossref]

Proc. SPIE (1)

F. W. Strong, J. L. Skinner, P. M. Dentinger, and N. C. Tien, “Electrical breakdown across micron scale gaps in MEMS structures,” Proc. SPIE 6111, 611103 (2006).
[Crossref]

Rev. Mod. Phys. (1)

M. Aspelmeyer, T. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

Science (2)

E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab, “Quantum squeezing of motion in a mechanical resonator,” Science 349(6251), 952–955 (2015).
[Crossref] [PubMed]

T. A. Palomaki, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Entangling mechanical motion with microwave fields,” Science 342(6159), 710–713 (2013).
[Crossref] [PubMed]

Small (1)

K. L. Ekinci and M. L. Roukes, “Electromechanical transducers at the nanoscale: actuation and sensing of motion in nanoelectromechanical systems (NEMS),” Small 1(8-9), 786–797 (2005).
[Crossref] [PubMed]

Other (8)

J. J. Allen, Micro Electro Mechanical System Design (Taylor & Francis Group, 2005), Ch. 8.

J. J. Sniegowski and C. Smith, “An application of mechanical leverage to microactuation,” in Proceedings of Transducers ’95 Eurosensors IX (1995), pp. 364–367.

K. Fang, M. H. Matheny, X. Luan, and O. Painter, “Phonon routing in integrated optomechanical cavity-waveguide systems,” arXiv:1508.05138 (2015).

M. Schmidt, V. Peano, and F. Marquardt, “Optomechanical metamaterials: Dirac polaritons, Gauge fields, and instabilities,” arXiv:1311.7095 (2013).

A. H. Safavi-Naeini and O. Painter, “Optomechanical crystal devices,” in Cavity Optomechanics, M. Aspelmeyer, T. J. Kippenberg and F. Marquardt, eds. (Springer, 2014).

C. O. M. S. O. L. Multiphysics, 5.1, http://www.comsol.com

M. H. Matheny, J. G. Redford and O. Painter, are preparing a manuscript to be called “Enhancing the optomechanical interaction via dimerization in one-dimensional optomechanical crystals.”

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals (Princeton University Press, 2008).

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Figures (7)

Fig. 1
Fig. 1 (a) Tuning principle using an on-chip capacitor that exerts a force onto an optomechanical crystal nanobeam. The force is determined by the capacitor geometry and the applied voltage. (b) The maximal force, given by the capacitor’s breakdown voltage, can be increased by stacking capacitors on multiple connected pads.
Fig. 2
Fig. 2 Simulated [40] displacement along the beam axis and stress distribution in the structure for the case of 4 connected capacitors. All boundary surfaces and the unreleased capacitor plate are assumed to be fixed in this configuration. The maximum displacement of the capacitor carrying pads being held by the connected beam is as low as ~5 pm/V2. The largest stress and thereby the exerted force appears on the transition element towards the nanobeam.
Fig. 3
Fig. 3 (a) Unit cells and cross-sectional area for different nanobeam designs. Smaller cross sections support potentially stronger tunabilities. (b) Geometry in the following (b,px,py,a,t) = (50,400,300,600,220) nm and corresponding band diagram of the “connected-pad” design with a full bandgap. Highlighted are modes that are even under σy and σz vector parity operation (mirror symmetry in xy-/xz-plane). The modal plots show the magnitude of displacement at Γ- and X-point. (c) Displacement at a nanobeam featuring a localized acoustic mode in the bandgap of the outer cells from (b). The deformation of the central unit cells to (b,px,py,a,t) = (50,100,100,640,220) nm pulls the mode’s frequency of the first symmetric band of (b) into the gap. Simulations for (b) and (c) were performed with [40].
Fig. 4
Fig. 4 Geometry and band diagrams of two different mirror unit cell designs, displacements of localized modes on acoustic nanobeams and their corresponding tunabilities. (a), definition of the geometry parameters for the new unit cell type used in (c). Design (b) corresponds to the geometry of Fig. 3, (c) employs a dimerization of the unit cell to pull a band of similar mode shape from the Γ-point. The mirror unit cell of (c) uses (bx,by,p1,p2,a,t) = (205,85,135,210,650,220) nm. The central cell uses (bx,by,p1,p2,a,t) = (325,50,100,125,650,220) nm. The nanobeam modes were designed through unit cell deformation and the tunabilities were extracted from simulations of the eigenfrequencies of differently pre-stressed structures.
Fig. 5
Fig. 5 (a) Photonic bandstructure of a bare acoustic cell with (b,px,py,a,t) = (50,280,220,640,220) nm and of the same cell with an added ribbon structure (simulated with [44]). The geometrical parameters used here are (sx,sy,r,d) = (192,296,211,130) nm. The increasing amount of high refractive index material pushes the photonic bands towards lower frequencies. TM-like modes are plotted in light grey, TE-like modes appear in red (antisymmetric to green dashed plane) and dark grey (symmetric). (b) Proposed structure geometry, so that the added ribbons cannot affect acoustic properties or the force applied central beam.
Fig. 6
Fig. 6 Comparison of the photonic bandstructures and modes [44] of the single pad (a) and dimerized (b) defect unit cells with ribbons. The right column shows an overlay of the |E|2 field magnitude at the X-point and the displacement field of the employed acoustic modes at the X- (a) and Γ-point (b) for a waveguide of the respective cells. In (a) the silicon boundaries along the waveguide are alternatingly displaced towards and away from the light field maxima. In contrast to that, the boundaries in (b) are along the whole waveguide either displaced away or towards the next light field maximum for a certain time in the oscillation cycle. The geometry of (a) is the same as in Fig. 5(a), while (b) uses (bx,by,p1,p2,a,t) = (295,50,100,125,620,220) nm and (sx,sy,r,d) = (126, 317,150,50) nm.
Fig. 7
Fig. 7 (a) Photonic bandstructure of dimerized mirror unit cell, (b) frequencies of the photonic X-point modes for the unit cell geometries along the nanobeam and (c) photonic bandstructure of the defect cell. (d) Plot of the Ey component of the localized optical mode created from the first band by the deformation of unit cells.

Tables (1)

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Table 1 Simulated nanobeam parameters.

Equations (4)

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F = - (d) ( C(d) 2 U 2 ) = - (d) ( εhL d ) U 2 2 = εhL 2 d 2 U 2 .
g 0,MB = ω 0 2 δV ( Q n )(Δε E || 2 Δ ε 1 D 2 )dS E D dV x zpf .
g 0,PE = ω 0 2 E | ε α | E E D dV x zpf ,
ε ij α = ε 0 n 4 p ijkl S kl ,

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