Abstract

Single-crystal diamond cavity optomechanical devices are a promising example of a hybrid quantum system: by coupling mechanical resonances to both light and electron spins, they can enable new ways for photons to control solid-state qubits. However, realizing cavity optomechanical devices from high-quality diamond chips has been an outstanding challenge. Here, we demonstrate single-crystal diamond cavity optomechanical devices that can enable photon–phonon spin coupling. Cavity optomechanical coupling to 2 GHz frequency (fm) mechanical resonances is observed. In room-temperature ambient conditions, these resonances have a record combination of low dissipation (mechanical quality factor, Qm>9000) and high frequency, with Qm·fm1.9×1013, which is sufficient for room-temperature single-phonon coherence. The system exhibits high optical quality factor (Qo>104) resonances at infrared and visible wavelengths, is nearly sideband resolved, and exhibits optomechanical cooperativity C3. The devices’ potential for optomechanical control of diamond electron spins is demonstrated through radiation pressure excitation of mechanical self-oscillations whose 31 pm amplitude is predicted to provide 0.6 MHz coupling rates to diamond nitrogen vacancy center ground-state transitions (6 Hz/phonon) and 105 stronger coupling rates to excited-state transitions.

© 2016 Optical Society of America

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2016 (3)

S. Meesala, Y.-I. Sohn, H. A. Atikian, S. Kim, M. J. Burek, J. T. Choy, and M. Lončar, “Enhanced strain coupling of nitrogen-vacancy spins to nanoscale diamond cantilevers,” Phys. Rev. Appl. 5, 034010 (2016).
[Crossref]

D. A. Golter, T. Oo, M. Amezcua, K. A. Stewart, and H. Wang, “Optomechanical quantum control of a nitrogen-vacancy center in diamond,” Phys. Rev. Lett. 116, 143602 (2016).
[Crossref]

R. A. Norte, J. P. Moura, and S. Gröblacher, “Mechanical resonators for quantum optomechanics experiments at room temperature,” Phys. Rev. Lett. 116, 147202 (2016).
[Crossref]

2015 (8)

D. T. Nguyen, W. Hease, C. Baker, E. Gil-Santos, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “Improved optomechanical disk resonator sitting on a pedestal mechanical shield,” New J. Phys. 17, 023016 (2015).
[Crossref]

E. R. MacQuarrie, T. A. Gosavi, A. M. Moehle, N. R. Jungwirth, S. A. Bhave, and G. D. Fuchs, “Coherent control of a nitrogen-vacancy center spin ensemble with a diamond mechanical resonator,” Optica 2, 233–238 (2015).
[Crossref]

A. Barfuss, J. Teissier, E. Neu, A. Nunnenkamp, and P. Maletinsky, “Strong mechanical driving of a single electron spin,” Nat. Phys. 11, 820–824 (2015).
[Crossref]

M. J. A. Schuetz, E. M. Kessler, G. Giedke, L. M. K. Vandersypen, M. D. Lukin, and J. I. Cirac, “Universal quantum transducers based on surface acoustic waves,” Phys. Rev. X 5, 031031 (2015).

E. Gil-Santos, C. Baker, D. Nguyen, W. Hease, A. Lematre, S. Ducci, G. Leo, and I. Favero, “High frequency nano-optomechanical disk resonators in liquids,” Nat. Nanotechnol. 10, 810–816 (2015).

X. Lu, J. Y. Lee, and Q. Lin, “High-frequency and high-quality silicon carbide optomechanical microresonators,” Sci. Rep. 5, 17005 (2015).
[Crossref]

B. Khanaliloo, H. Jayakumar, A. C. Hryciw, D. P. Lake, H. Kaviani, and P. E. Barclay, “Single-crystal diamond nanobeam waveguide optomechanics,” Physical Rev. X 5, 041051 (2015).

B. Khanaliloo, M. Mitchell, A. C. Hryciw, and P. E. Barclay, “High-Q/V monolithic diamond microdisks fabricated with quasi-isotropic etching,” Nano Lett. 15, 5131–5136 (2015).
[Crossref]

2014 (7)

M. J. Burek, Y. Chu, M. S. Z. Liddy, P. Patel, J. Rochman, S. Meesala, W. Hong, Q. Quan, M. D. Lukin, and M. Lončar, “High quality-factor optical nanocavities in bulk single-crystal diamond,” Nat. Commun. 5, 5718 (2014).
[Crossref]

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

J. Teissier, A. Barfuss, P. Appel, E. Neu, and P. Maletinsky, “Strain coupling of a nitrogen-vacancy center spin to a diamond mechanical oscillator,” Phys. Rev. Lett. 113, 020503 (2014).
[Crossref]

P. Ovartchaiyapong, K. W. Lee, B. A. Myers, and A. C. B. Jayich, “Dynamic strain-mediated coupling of a single diamond spin to a mechanical resonator,” Nat. Commun. 5, 4429 (2014).
[Crossref]

B. J. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lončar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
[Crossref]

M. Mitchell, A. C. Hryciw, and P. E. Barclay, “Cavity optomechanics in gallium phosphide microdisks,” Appl. Phys. Lett. 104, 141104 (2014).
[Crossref]

C. Baker, W. Hease, D.-T. Nguyen, A. Andronico, S. Ducci, G. Leo, and I. Favero, “Photoelastic coupling in gallium arsenide optomechanical disk resonators,” Opt. Express 22, 14072–14086 (2014).
[Crossref]

2013 (8)

N. Bar-Gill, L. Pham, A. Jarmola, D. Budker, and R. Walsworth, “Solid-state electronic spin coherence time approaching one second,” Nat. Commun. 4, 1743 (2013).
[Crossref]

E. R. MacQuarrie, T. A. Gosavi, N. R. Jungwirth, S. A. Bhave, and G. D. Fuchs, “Mechanical spin control of nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 111, 227602 (2013).
[Crossref]

K. V. Kepesidis, S. D. Bennett, S. Portolan, M. D. Lukin, and P. Rabl, “Phonon cooling and lasing with nitrogen-vacancy centers in diamond,” Physical Rev. B 88, 064105 (2013).
[Crossref]

Y. Liu, M. Davanço, V. Aksyuk, and K. Srinivasan, “Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators,” Phys. Rev. Lett. 110, 223603 (2013).
[Crossref]

D. T. Nguyen, C. Baker, W. Hease, S. Sejil, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “Ultrahigh Q-frequency product for optomechanical disk resonators with a mechanical shield,” Appl. Phys. Lett. 103, 241112 (2013).
[Crossref]

T. Ramos, V. Sudhir, K. Stannigel, P. Zoller, and T. J. Kippenberg, “Nonlinear quantum optomechanics via individual intrinsic two-level defects,” Phys. Rev. Lett. 110, 193602 (2013).
[Crossref]

P. Rath, S. Khasminskaya, C. Nebel, C. Wild, and W. H. Pernice, “Diamond-integrated optomechanical circuits,” Nat. Commun. 4, 1690 (2013).
[Crossref]

Y. Tao, J. M. Boss, B. A. Moores, and C. L. Degen, “Single-crystal diamond nanomechanical resonators with quality factors exceeding one million,” Nat. Commun. 5, 3638 (2013).

2012 (11)

P. Ovartchaiyapong, L. M. A. Pascal, B. A. Myers, P. Lauria, and A. C. B. Jayich, “High quality factor single-crystal diamond mechanical resonators,” Appl. Phys. Lett. 101, 163505 (2012).
[Crossref]

M. J. Burek, N. P. de Leon, B. J. Shields, B. J. Hausmann, Y. Chu, Q. Quan, A. S. Zibrov, H. Park, M. D. Lukin, and M. Lončar, “Free-standing mechanical and photonic nanostructures in single-crystal diamond,” Nano Lett. 12, 6084–6089 (2012).
[Crossref]

X. Sun, X. Zhang, and H. X. Tang, “High-q silicon optomechanical microdisk resonators at gigahertz frequencies,” Appl. Phys. Lett. 100, 173116 (2012).
[Crossref]

P. Maletinsky, S. Hong, M. S. Grinolds, B. Hausmann, M. D. Lukin, R. L. Walsworth, M. Lončar, and A. Yacoby, “A robust scanning diamond sensor for nanoscale imaging with single nitrogen-vacancy centres,” Nat. Nanotechnol. 7, 320–324 (2012).
[Crossref]

W. C. Jiang, X. Lu, J. Zhang, and Q. Lin, “High-frequency silicon optomechanical oscillator with an ultralow threshold,” Opt. Express 20, 15991–15996 (2012).
[Crossref]

J. Hodges, L. Li, M. Lu, E. H. Chen, M. Trusheim, S. Allegri, X. Yao, O. Gaathon, H. Bakhru, and D. Englund, “Long-lived NV- spin coherence in high-purity diamond membranes,” New J. Phys. 14, 093004 (2012).
[Crossref]

C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012).
[Crossref]

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref]

K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
[Crossref]

W. Li, N. Mingo, L. Lindsay, D. A. Broido, D. A. Stewart, and N. A. Katcho, “Thermal conductivity of diamond nanowires from first principles,” Physical Rev. B 85, 195436 (2012).
[Crossref]

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

2011 (5)

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a color center in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
[Crossref]

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

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

I. Aharonovich, A. D. Greentree, and S. Prawer, “Diamond photonics,” Nat. Photonics 5, 397–405 (2011).
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O. Arcizet, V. Jacques, A. Siria, P. Poncharal, P. Vincent, and S. Seidelin, “A single nitrogen-vacancy defect coupled to a nanomechanical oscillator,” Nat. Phys. 7, 879–883 (2011).
[Crossref]

2010 (3)

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
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P. Rabl, S. Kolkowitz, F. Koppens, J. Harris, P. Zoller, and M. Lukin, “A quantum spin transducer based on nanoelectromechanical resonator arrays,” Nat. Phys. 6, 602–608 (2010).
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K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105, 220501 (2010).
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2009 (3)

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. Hemmer, F. Jelezko, and F. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009).
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M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
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A. Batalov, V. Jacques, F. Kaiser, P. Siyushev, P. Neumann, L. J. Rogers, R. L. McMurtrie, N. B. Manson, F. Jelezko, and J. Wrachtrup, “Low temperature studies of the excited-state structure of negatively charged nitrogen-vacancy color centers in diamond,” Phys. Rev. Lett. 102, 195506 (2009).
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2007 (2)

2006 (1)

L. S. Hounsome, R. Jones, M. J. Shaw, and P. R. Briddon, “Photoelastic constants in diamond and silicon,” Phys. Status Solidi A 203, 3088–3093 (2006).
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2005 (1)

J. R. Clark, W.-T. Hsu, M. A. Abdelmoneum, and C. T.-C. Nguyen, “High-Q UHF micromechanical radial-contour mode disk resonators,” J. Microelectromech. Syst. 14, 1298–1310 (2005).

2004 (3)

M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85, 3693–3695 (2004).
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K. Ekinci, Y. Yang, and M. Roukes, “Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems,” J. Appl. Phys. 95, 2682–2689 (2004).
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I. Wilson-Rae, P. Zoller, and A. Imamoğlu, “Laser cooling of a nanomechanical resonator mode to its quantum ground state,” Phys. Rev. Lett. 92, 075507 (2004).
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2003 (1)

D. Li, Y. Wu, P. Kim, L. Shi, P. Yang, and A. Majumdar, “Thermal conductivity of individual silicon nanowires,” Appl. Phys. Lett. 83, 2934–2936 (2003).
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1976 (1)

G. Davies and M. F. Hamer, “Optical studies of the 1.945  eV vibronic band in diamond,” Proc. R. Soc. London A 348, 285–298 (1976).
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Abdelmoneum, M. A.

J. R. Clark, W.-T. Hsu, M. A. Abdelmoneum, and C. T.-C. Nguyen, “High-Q UHF micromechanical radial-contour mode disk resonators,” J. Microelectromech. Syst. 14, 1298–1310 (2005).

Achard, J.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. Hemmer, F. Jelezko, and F. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009).
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Aharonovich, I.

I. Aharonovich, A. D. Greentree, and S. Prawer, “Diamond photonics,” Nat. Photonics 5, 397–405 (2011).
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Aksyuk, V.

Y. Liu, M. Davanço, V. Aksyuk, and K. Srinivasan, “Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators,” Phys. Rev. Lett. 110, 223603 (2013).
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Alegre, T. M.

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

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

J. Hodges, L. Li, M. Lu, E. H. Chen, M. Trusheim, S. Allegri, X. Yao, O. Gaathon, H. Bakhru, and D. Englund, “Long-lived NV- spin coherence in high-purity diamond membranes,” New J. Phys. 14, 093004 (2012).
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D. A. Golter, T. Oo, M. Amezcua, K. A. Stewart, and H. Wang, “Optomechanical quantum control of a nitrogen-vacancy center in diamond,” Phys. Rev. Lett. 116, 143602 (2016).
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Andronico, A.

Appel, P.

J. Teissier, A. Barfuss, P. Appel, E. Neu, and P. Maletinsky, “Strain coupling of a nitrogen-vacancy center spin to a diamond mechanical oscillator,” Phys. Rev. Lett. 113, 020503 (2014).
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Arcizet, O.

O. Arcizet, V. Jacques, A. Siria, P. Poncharal, P. Vincent, and S. Seidelin, “A single nitrogen-vacancy defect coupled to a nanomechanical oscillator,” Nat. Phys. 7, 879–883 (2011).
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S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
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Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
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J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
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Atikian, H. A.

S. Meesala, Y.-I. Sohn, H. A. Atikian, S. Kim, M. J. Burek, J. T. Choy, and M. Lončar, “Enhanced strain coupling of nitrogen-vacancy spins to nanoscale diamond cantilevers,” Phys. Rev. Appl. 5, 034010 (2016).
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M. J. Burek, J. D. Cohen, S. M. Meenehan, T. Ruelle, S. Meesala, J. Rochman, H. A. Atikian, M. Markham, D. J. Twitchen, M. D. Lukin, O. Painter, and M. Lončar, “Diamond optomechanical crystals,” arXiv:1512.04166 (2015).

Baker, C.

D. T. Nguyen, W. Hease, C. Baker, E. Gil-Santos, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “Improved optomechanical disk resonator sitting on a pedestal mechanical shield,” New J. Phys. 17, 023016 (2015).
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E. Gil-Santos, C. Baker, D. Nguyen, W. Hease, A. Lematre, S. Ducci, G. Leo, and I. Favero, “High frequency nano-optomechanical disk resonators in liquids,” Nat. Nanotechnol. 10, 810–816 (2015).

C. Baker, W. Hease, D.-T. Nguyen, A. Andronico, S. Ducci, G. Leo, and I. Favero, “Photoelastic coupling in gallium arsenide optomechanical disk resonators,” Opt. Express 22, 14072–14086 (2014).
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D. T. Nguyen, C. Baker, W. Hease, S. Sejil, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “Ultrahigh Q-frequency product for optomechanical disk resonators with a mechanical shield,” Appl. Phys. Lett. 103, 241112 (2013).
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Bakhru, H.

J. Hodges, L. Li, M. Lu, E. H. Chen, M. Trusheim, S. Allegri, X. Yao, O. Gaathon, H. Bakhru, and D. Englund, “Long-lived NV- spin coherence in high-purity diamond membranes,” New J. Phys. 14, 093004 (2012).
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Balasubramanian, G.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. Hemmer, F. Jelezko, and F. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009).
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Barclay, P. E.

B. Khanaliloo, H. Jayakumar, A. C. Hryciw, D. P. Lake, H. Kaviani, and P. E. Barclay, “Single-crystal diamond nanobeam waveguide optomechanics,” Physical Rev. X 5, 041051 (2015).

B. Khanaliloo, M. Mitchell, A. C. Hryciw, and P. E. Barclay, “High-Q/V monolithic diamond microdisks fabricated with quasi-isotropic etching,” Nano Lett. 15, 5131–5136 (2015).
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M. Mitchell, A. C. Hryciw, and P. E. Barclay, “Cavity optomechanics in gallium phosphide microdisks,” Appl. Phys. Lett. 104, 141104 (2014).
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A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a color center in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
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M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85, 3693–3695 (2004).
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Barfuss, A.

A. Barfuss, J. Teissier, E. Neu, A. Nunnenkamp, and P. Maletinsky, “Strong mechanical driving of a single electron spin,” Nat. Phys. 11, 820–824 (2015).
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J. Teissier, A. Barfuss, P. Appel, E. Neu, and P. Maletinsky, “Strain coupling of a nitrogen-vacancy center spin to a diamond mechanical oscillator,” Phys. Rev. Lett. 113, 020503 (2014).
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Bar-Gill, N.

N. Bar-Gill, L. Pham, A. Jarmola, D. Budker, and R. Walsworth, “Solid-state electronic spin coherence time approaching one second,” Nat. Commun. 4, 1743 (2013).
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Batalov, A.

A. Batalov, V. Jacques, F. Kaiser, P. Siyushev, P. Neumann, L. J. Rogers, R. L. McMurtrie, N. B. Manson, F. Jelezko, and J. Wrachtrup, “Low temperature studies of the excited-state structure of negatively charged nitrogen-vacancy color centers in diamond,” Phys. Rev. Lett. 102, 195506 (2009).
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Beausoleil, R. G.

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a color center in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
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Beck, J.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. Hemmer, F. Jelezko, and F. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009).
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Bennett, S. D.

K. V. Kepesidis, S. D. Bennett, S. Portolan, M. D. Lukin, and P. Rabl, “Phonon cooling and lasing with nitrogen-vacancy centers in diamond,” Physical Rev. B 88, 064105 (2013).
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K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
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E. R. MacQuarrie, T. A. Gosavi, A. M. Moehle, N. R. Jungwirth, S. A. Bhave, and G. D. Fuchs, “Coherent control of a nitrogen-vacancy center spin ensemble with a diamond mechanical resonator,” Optica 2, 233–238 (2015).
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E. R. MacQuarrie, T. A. Gosavi, N. R. Jungwirth, S. A. Bhave, and G. D. Fuchs, “Mechanical spin control of nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 111, 227602 (2013).
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Borselli, M.

C. P. Michael, M. Borselli, T. J. Johnson, C. Chrystala, and O. Painter, “An optical fiber-taper probe for wafer-scale microphotonic device characterization,” Opt. Express 15, 4745–4752 (2007).
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M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85, 3693–3695 (2004).
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Boss, J. M.

Y. Tao, J. M. Boss, B. A. Moores, and C. L. Degen, “Single-crystal diamond nanomechanical resonators with quality factors exceeding one million,” Nat. Commun. 5, 3638 (2013).

Briddon, P. R.

L. S. Hounsome, R. Jones, M. J. Shaw, and P. R. Briddon, “Photoelastic constants in diamond and silicon,” Phys. Status Solidi A 203, 3088–3093 (2006).
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Broido, D. A.

W. Li, N. Mingo, L. Lindsay, D. A. Broido, D. A. Stewart, and N. A. Katcho, “Thermal conductivity of diamond nanowires from first principles,” Physical Rev. B 85, 195436 (2012).
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Budker, D.

N. Bar-Gill, L. Pham, A. Jarmola, D. Budker, and R. Walsworth, “Solid-state electronic spin coherence time approaching one second,” Nat. Commun. 4, 1743 (2013).
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Bulu, I.

B. J. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lončar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
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Burek, M. J.

S. Meesala, Y.-I. Sohn, H. A. Atikian, S. Kim, M. J. Burek, J. T. Choy, and M. Lončar, “Enhanced strain coupling of nitrogen-vacancy spins to nanoscale diamond cantilevers,” Phys. Rev. Appl. 5, 034010 (2016).
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M. J. Burek, Y. Chu, M. S. Z. Liddy, P. Patel, J. Rochman, S. Meesala, W. Hong, Q. Quan, M. D. Lukin, and M. Lončar, “High quality-factor optical nanocavities in bulk single-crystal diamond,” Nat. Commun. 5, 5718 (2014).
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M. J. Burek, N. P. de Leon, B. J. Shields, B. J. Hausmann, Y. Chu, Q. Quan, A. S. Zibrov, H. Park, M. D. Lukin, and M. Lončar, “Free-standing mechanical and photonic nanostructures in single-crystal diamond,” Nano Lett. 12, 6084–6089 (2012).
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M. J. Burek, J. D. Cohen, S. M. Meenehan, T. Ruelle, S. Meesala, J. Rochman, H. A. Atikian, M. Markham, D. J. Twitchen, M. D. Lukin, O. Painter, and M. Lončar, “Diamond optomechanical crystals,” arXiv:1512.04166 (2015).

Camacho, R.

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

J. Chan, A. Safavi-Naeini, J. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
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J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
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A. H. Safavi-Naeini, T. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
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J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
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M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
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Chang, D.

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

J. Hodges, L. Li, M. Lu, E. H. Chen, M. Trusheim, S. Allegri, X. Yao, O. Gaathon, H. Bakhru, and D. Englund, “Long-lived NV- spin coherence in high-purity diamond membranes,” New J. Phys. 14, 093004 (2012).
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Choy, J. T.

S. Meesala, Y.-I. Sohn, H. A. Atikian, S. Kim, M. J. Burek, J. T. Choy, and M. Lončar, “Enhanced strain coupling of nitrogen-vacancy spins to nanoscale diamond cantilevers,” Phys. Rev. Appl. 5, 034010 (2016).
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Chrystala, C.

Chu, Y.

M. J. Burek, Y. Chu, M. S. Z. Liddy, P. Patel, J. Rochman, S. Meesala, W. Hong, Q. Quan, M. D. Lukin, and M. Lončar, “High quality-factor optical nanocavities in bulk single-crystal diamond,” Nat. Commun. 5, 5718 (2014).
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M. J. Burek, N. P. de Leon, B. J. Shields, B. J. Hausmann, Y. Chu, Q. Quan, A. S. Zibrov, H. Park, M. D. Lukin, and M. Lončar, “Free-standing mechanical and photonic nanostructures in single-crystal diamond,” Nano Lett. 12, 6084–6089 (2012).
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M. J. A. Schuetz, E. M. Kessler, G. Giedke, L. M. K. Vandersypen, M. D. Lukin, and J. I. Cirac, “Universal quantum transducers based on surface acoustic waves,” Phys. Rev. X 5, 031031 (2015).

Clark, J. R.

J. R. Clark, W.-T. Hsu, M. A. Abdelmoneum, and C. T.-C. Nguyen, “High-Q UHF micromechanical radial-contour mode disk resonators,” J. Microelectromech. Syst. 14, 1298–1310 (2005).

Cohen, J. D.

M. J. Burek, J. D. Cohen, S. M. Meenehan, T. Ruelle, S. Meesala, J. Rochman, H. A. Atikian, M. Markham, D. J. Twitchen, M. D. Lukin, O. Painter, and M. Lončar, “Diamond optomechanical crystals,” arXiv:1512.04166 (2015).

Davanço, M.

Y. Liu, M. Davanço, V. Aksyuk, and K. Srinivasan, “Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators,” Phys. Rev. Lett. 110, 223603 (2013).
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G. Davies and M. F. Hamer, “Optical studies of the 1.945  eV vibronic band in diamond,” Proc. R. Soc. London A 348, 285–298 (1976).
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M. J. Burek, N. P. de Leon, B. J. Shields, B. J. Hausmann, Y. Chu, Q. Quan, A. S. Zibrov, H. Park, M. D. Lukin, and M. Lončar, “Free-standing mechanical and photonic nanostructures in single-crystal diamond,” Nano Lett. 12, 6084–6089 (2012).
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Y. Tao, J. M. Boss, B. A. Moores, and C. L. Degen, “Single-crystal diamond nanomechanical resonators with quality factors exceeding one million,” Nat. Commun. 5, 3638 (2013).

Deléglise, S.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
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B. J. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lončar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
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C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012).
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D. T. Nguyen, W. Hease, C. Baker, E. Gil-Santos, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “Improved optomechanical disk resonator sitting on a pedestal mechanical shield,” New J. Phys. 17, 023016 (2015).
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E. Gil-Santos, C. Baker, D. Nguyen, W. Hease, A. Lematre, S. Ducci, G. Leo, and I. Favero, “High frequency nano-optomechanical disk resonators in liquids,” Nat. Nanotechnol. 10, 810–816 (2015).

C. Baker, W. Hease, D.-T. Nguyen, A. Andronico, S. Ducci, G. Leo, and I. Favero, “Photoelastic coupling in gallium arsenide optomechanical disk resonators,” Opt. Express 22, 14072–14086 (2014).
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D. T. Nguyen, C. Baker, W. Hease, S. Sejil, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “Ultrahigh Q-frequency product for optomechanical disk resonators with a mechanical shield,” Appl. Phys. Lett. 103, 241112 (2013).
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Eichenfield, M.

A. H. Safavi-Naeini, T. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
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M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
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K. Ekinci, Y. Yang, and M. Roukes, “Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems,” J. Appl. Phys. 95, 2682–2689 (2004).
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Englund, D.

J. Hodges, L. Li, M. Lu, E. H. Chen, M. Trusheim, S. Allegri, X. Yao, O. Gaathon, H. Bakhru, and D. Englund, “Long-lived NV- spin coherence in high-purity diamond membranes,” New J. Phys. 14, 093004 (2012).
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A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a color center in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
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Favero, I.

E. Gil-Santos, C. Baker, D. Nguyen, W. Hease, A. Lematre, S. Ducci, G. Leo, and I. Favero, “High frequency nano-optomechanical disk resonators in liquids,” Nat. Nanotechnol. 10, 810–816 (2015).

D. T. Nguyen, W. Hease, C. Baker, E. Gil-Santos, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “Improved optomechanical disk resonator sitting on a pedestal mechanical shield,” New J. Phys. 17, 023016 (2015).
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C. Baker, W. Hease, D.-T. Nguyen, A. Andronico, S. Ducci, G. Leo, and I. Favero, “Photoelastic coupling in gallium arsenide optomechanical disk resonators,” Opt. Express 22, 14072–14086 (2014).
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D. T. Nguyen, C. Baker, W. Hease, S. Sejil, P. Senellart, A. Lemaître, S. Ducci, G. Leo, and I. Favero, “Ultrahigh Q-frequency product for optomechanical disk resonators with a mechanical shield,” Appl. Phys. Lett. 103, 241112 (2013).
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R. Yang, Z. Wang, J. Lee, K. Ladhane, D. J. Young, and P. X. L. Feng, “Temperature dependence of torsional and flexural modes in 6H-SiC microdisk resonators,” in IEEE International Frequency Control Symposium (FCS) (2014), pp. 1–3.

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C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012).
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A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a color center in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
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Supplementary Material (1)

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Figures (3)

Fig. 1.
Fig. 1.

Characterization of diamond microdisk optical and mechanical modes at low optical input power. (a) SEM image of a 5 μm diameter microdisk, with minimum pedestal width of 100 nm. Inset: Simulated displacement distribution of the RBM mechanical resonance of this device. (b) Highest Qo TM-like optical modes of a 5 μm (left) and 5.5 μm (right) diameter microdisk, with intrinsic quality factors for each doublet resonances, as labeled. (c) High-Qo visible mode with intrinsic quality factor, as shown for a 6.2 μm diameter microdisk. (d) SP(f) produced by the thermal motion of the RBM of the microdisks in (b), showing that the larger diameter, larger pedestal waist microdisk has a lower Qm.

Fig. 2.
Fig. 2.

Optomechanical backaction measuerments. (a) SP(f,λs) and corresponding fiber transmission T(λ) for Pi corresponding to maximum N6.5×105 and Pd1.5  mW. The regularly spaced horizontal features are electronic noise from the apparatus. (b) Observed and predicted optomechanical linewidth narrowing of the RBM. The predicted δγm depends on measured N and Δ for each point, as well as fitting parameter g0/2π=26±2  kHz. Error bars indicate 95% confidence interval for γm extracted from SP(f) at each data point. (c) Observed and predicted δωm. Both the predicted shift due to optomechanical backaction for g0 found from the fits in (b) and the predicted shift, including an additional static thermal softening determined by a free-fitting parameter, are shown.

Fig. 3.
Fig. 3.

Observation of microdisk self-oscillation. (a) SP(f;λopt) as a function of dropped power. (b) Normalized cross sections of (a), where S˜P(f) is given by SP(f;λopt) normalized by the transduction gain so that the area under the curve represents the mechanical energy of the RBM. The black data is the thermal displacement spectra. (c, d) Maximum displacement amplitude and stress for 5 μm diameter devices with (c) Qm9000, Qo(t)6×104, and (d) Qm8000, Qo(t)4×104. (e, f) Simulated stress along (e) radial and (f) vertical cuts in the microdisk, as indicated by the red lines in the insets, for the self-oscillating amplitude in (c).

Equations (2)

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δωm(Δ)=g02N(Δωmγo2/4+(Δωm)2+Δ+ωmγo2/4+(Δ+ωm)2)+αPd.
PT=meffωo2gom2γmγo(i)ωmγo(t)(γo(t)/2)2[(2ωm)2+(γo(t)/2)2],

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