Abstract

Elastic dissipation through radiation towards the substrate is a major loss channel in micro- and nanomechanical resonators. Engineering the coupling of these resonators with optical cavities further complicates and constrains the design of low-loss optomechanical devices. In this work we rely on the coherent cancellation of mechanical radiation to demonstrate material and surface absorption limited silicon near-field optomechanical resonators oscillating at tens of MHz. The effectiveness of our dissipation suppression scheme is investigated at room and cryogenic temperatures. While at room temperature we can reach a maximum quality factor of 7.61k (fQ-product of the order of 1011 Hz), at 22 K the quality factor increases to 37k, resulting in a fQ-product of 2 × 1012 Hz.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (3)

Y. Tsaturyan, A. Barg, E. S. Polzik, and A. Schliesser, “Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution,” Nat. Nanotechnol. 12, 776 (2017).
[Crossref] [PubMed]

F. G. S. Santos, Y. A. V. Espinel, G. O. Luiz, R. S. Benevides, G. S. Wiederhecker, and T. P. Mayer Alegre, “Hybrid confinement of optical and mechanical modes in a bullseye optomechanical resonator,” Opt. Express 25, 508 (2017).
[Crossref] [PubMed]

R. Benevides, F. G. S. Santos, G. O. Luiz, G. S. Wiederhecker, and T. P. M. Alegre, “Ultrahigh-Q optomechanical crystal cavities fabricated in a CMOS foundry,” Sci. Rep. 7, 2491 (2017).
[Crossref] [PubMed]

2016 (3)

C. Reinhardt, T. Müller, A. Bourassa, and J. C. Sankey, “Ultralow-Noise SiN Trampoline Resonators for Sensing and Optomechanics,” Phys. Rev. X 6, 021001 (2016).

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] [PubMed]

Y. Tao, R. Hauert, and C. L. Degen, “Exclusively Gas-Phase Passivation of Native Oxide-Free Silicon(100) and Silicon(111) Surfaces,” ACS Appl. Mater. Interfaces 8(20), 13157–13165 (2016).
[Crossref] [PubMed]

2015 (3)

Y. Tao, P. Navaretti, R. Hauert, U. Grob, M. Poggio, and C L Degen, “Permanent reduction of dissipation in nanomechanical Si resonators by chemical surface protection,” Nanotechnology 26, 465501 (2015).
[Crossref] [PubMed]

M. Zhang, S. Shah, J. Cardenas, and M. Lipson, “Synchronization and Phase Noise Reduction in Micromechanical Oscillator Arrays Coupled through Light,” Phys. Rev. Lett. 115, 163902 (2015).
[Crossref] [PubMed]

R. Zhang, C. Ti, M. I. Davanço, Y. Ren, V. Aksyuk, Y. Liu, and K. Srinivasan, “Integrated tuning fork nanocavity optomechanical transducers with high fMQM product and stress-engineered frequency tuning,” Appl. Phys. Lett. 107, 131110 (2015).
[Crossref]

2014 (8)

S. A. Zotov, B. R. Simon, I. P. Prikhodko, A. A. Trusov, and A. M. Shkel, “Quality Factor Maximization Through Dynamic Balancing of Tuning Fork Resonator,” IEEE Sens. J. 14, 2706–2714 (2014).
[Crossref]

M. Zhang, G. Luiz, S. Shah, G. Wiederhecker, and M. Lipson, “Eliminating anchor loss in optomechanical resonators using elastic wave interference,” Appl. Phys. Lett. 105, 051904 (2014).
[Crossref]

C. Doolin, P. H. Kim, B. D. Hauer, A. J. R. MacDonald, and J. P. Davis, “Multidimensional optomechanical cantilevers for high-frequency force sensing,” New J. Phys. 16, 035001 (2014).
[Crossref]

A. Xuereb, C. Genes, G. Pupillo, M. Paternostro, and A. Dantan, “Reconfigurable Long-Range Phonon Dynamics in Optomechanical Arrays,” Phys. Rev. Lett. 112, 133604 (2014).
[Crossref] [PubMed]

L. Ying, Y.-C. Lai, and C. Grebogi, “Quantum manifestation of a synchronization transition in optomechanical systems,” Phys. Rev. A 90, 053810 (2014).
[Crossref]

F. Guzmán Cervantes, L. Kumanchik, J. Pratt, and J. M. Taylor, “High sensitivity optomechanical reference accelerometer over 10 kHz,” Appl. Phys. Lett. 104, 221111 (2014).
[Crossref]

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

2013 (5)

S. Ghaffari, S. A. Chandorkar, S. Wang, E. J. Ng, C. H. Ahn, V. Hong, Y. Yang, and T. W. Kenny, “Quantum Limit of Quality Factor in Silicon Micro and Nano Mechanical Resonators,” Sci. Rep. 3, 3244 (2013).
[Crossref] [PubMed]

C. Huang, J. Fan, R. Zhang, and L. Zhu, “Optomechanical transductions in single and coupled wheel resonators,” Opt. Express 21, 6371 (2013).
[Crossref] [PubMed]

M. Ludwig and F. Marquardt, “Quantum Many-Body Dynamics in Optomechanical Arrays,” Phys. Rev. Lett. 111, 073603 (2013).
[Crossref] [PubMed]

F. Liu, S. Alaie, Z. C. Leseman, and M. Hossein-Zadeh, “Sub-pg mass sensing and measurement with an optomechanical oscillator,” Opt. Express 21, 19555–67 (2013).
[Crossref] [PubMed]

P. H. Kim, C. Doolin, B. D. Hauer, A. J. R. MacDonald, M. R. Freeman, P. E. Barclay, and J. P. Davis, “Nanoscale torsional optomechanics,” Appl. Phys. Lett. 102, 053102 (2013).
[Crossref]

2012 (5)

X. Sun, J. Zheng, M. Poot, C. W. Wong, and H. X. Tang, “Femtogram Doubly Clamped Nanomechanical Resonators Embedded in a High- Q Two-Dimensional Photonic Crystal Nanocavity,” Nano Lett. 12, 2299–2305 (2012).
[Crossref] [PubMed]

C. A. Holmes, C. P. Meaney, and G. J. Milburn, “Synchronization of many nanomechanical resonators coupled via a common cavity field,” Phys. Rev. E 85, 066203 (2012).
[Crossref]

A. Xuereb, C. Genes, and A. Dantan, “Strong Coupling and Long-Range Collective Interactions in Optomechanical Arrays,” Phys. Rev. Lett. 109, 223601 (2012).
[Crossref]

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

M. Zhang, G. S. Wiederhecker, S. Manipatruni, A. Barnard, P. McEuen, and M. Lipson, “Synchronization of Micromechanical Oscillators Using Light,” Phys. Rev. Lett. 109, 233906 (2012).
[Crossref]

2011 (5)

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, 89–92 (2011).
[Crossref] [PubMed]

G. D. Cole, I. Wilson-Rae, K. Werbach, M. R. Vanner, and M. Aspelmeyer, “Phonon-tunnelling dissipation in mechanical resonators,” Nat. Commun. 2, 231 (2011).
[Crossref] [PubMed]

F.-C. Hsu, J.-C. Hsu, T.-C. Huang, C.-H. Wang, and P. Chang, “Reducing support loss in micromechanical ring resonators using phononic band-gap structures,” J. Phys. D 44, 375101 (2011).
[Crossref]

K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11, 791–797 (2011).
[Crossref] [PubMed]

I. Wilson-Rae, R. a. Barton, S. S. Verbridge, D. R. Southworth, B. Ilic, H. G. Craighead, and J. M. Parpia, “High-Q Nanomechanics via Destructive Interference of Elastic Waves,” Phys. Rev. Lett. 106, 047205 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (2)

M. Pandey, R. Reichenbach, A. Zehnder, A. Lal, and H. Craighead, “Reducing Anchor Loss in MEMS Resonators Using Mesa Isolation,” J. Microelectromech. Syst. 18, 836–844 (2009).
[Crossref]

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5, 909–914 (2009).
[Crossref]

2008 (1)

A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New J. Phys. 10, 095015 (2008).
[Crossref]

2006 (2)

M. Borselli, T. J. Johnson, and O. Painter, “Measuring the role of surface chemistry in silicon microphotonics,” Appl. Phys. Lett. 88, 131114 (2006).
[Crossref]

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[Crossref]

2005 (2)

T. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. Vahala, “Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity,” Phys. Rev. Lett. 95, 033901 (2005).
[Crossref] [PubMed]

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall Mode Volumes in Dielectric Optical Microcavities,” Phys. Rev. Lett. 95, 143901 (2005).
[Crossref] [PubMed]

2003 (1)

K. L. Aubin, M. Zalalutdinov, R. B. Reichenbach, B. H. Houston, A. T. Zehnder, J. M. Parpia, and H. G. Craighead, “Laser annealing for high-Q MEMS resonators,” Proc. SPIE 5116, 531 (2003.

2002 (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. E 65, 066611 (2002).
[Crossref]

2000 (3)

R. Lifshitz and M. L. Roukes, “Thermoelastic damping in micro- and nanomechanical systems,” Phys. Rev. B 61, 5600–5609 (2000).
[Crossref]

K. Yasumura, T. Stowe, E. Chow, T. Pfafman, T. Kenny, B. Stipe, and D. Rugar, “Quality factors in micron- and submicron-thick cantilevers,” J. Microelectromech. Syst. 9, 117–125 (2000).
[Crossref]

S. Evoy, A. Olkhovets, L. Sekaric, J. M. Parpia, H. G. Craighead, and D. W. Carr, “Temperature-dependent internal friction in silicon nanoelectromechanical systems,” Appl. Phys. Lett. 77, 2397–2399 (2000).
[Crossref]

1998 (1)

M. Asheghi, M. N. Touzelbaev, K. E. Goodson, Y. K. Leung, and S. S. Wong, “Temperature-Dependent Thermal Conductivity of Single-Crystal Silicon Layers in SOI Substrates,” J. Heat Transfer. 120, 30 (1998).
[Crossref]

1997 (1)

1995 (1)

S. D. Lambade, G. G. Sahasrabudhe, and S. Rajagopalan, “Temperature dependence of acoustic attenuation in silicon,” Phys. Rev. B 51, 15861–15866 (1995).
[Crossref]

1986 (1)

P. D. Desai, “Thermodynamic Properties of Iron and Silicon,” J. Phys. Chem. Ref. Data 15, 967 (1986).
[Crossref]

1985 (1)

Y. Ilisavskii and V. Sternin, “Lattice absorption of high-frequency sound in silicon,” Sov. Phys. Solid State 27(2), pp. 236–239 (1985).

1983 (1)

J. Philip and M. A. Breazeale, “Third-order elastic constants and Grüneisen parameters of silicon and germanium between 3 and 300°K,” J. Appl. Phys. 54, 752 (1983).
[Crossref]

1980 (1)

T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
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1977 (1)

K. G. Lyon, G. L. Salinger, C. A. Swenson, and G. K. White, “Linear thermal expansion measurements on silicon from 6 to 340 K,” J. Appl. Phys. 48, 865 (1977).
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1967 (1)

L. P. Khiznichenko, P. F. Kromer, D. K. Kaipnazarov, E. Otenyazov, D. Yustpova, and L. G. Zotova, “The Properties of the Low-Temperature Internal Friction Peak in Silicon,” Phys. Status Solidi B 21, 805–810 (1967).
[Crossref]

1961 (1)

T. O. Woodruff and H. Ehrenreich, “Absorption of Sound in Insulators,” Phys. Rev. 123, 1553–1559 (1961).
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1939 (1)

A. Akhiezer, “On the Absorption of Sound in Solids,” J. Phys. (Moscow) 1, 277 (1939).

1937 (1)

C. Zener, “Internal Friction in Solids. I. Theory of Internal Friction in Reeds,” Phys. Rev. 52, 230–235 (1937).
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Ahn, C. H.

S. Ghaffari, S. A. Chandorkar, S. Wang, E. J. Ng, C. H. Ahn, V. Hong, Y. Yang, and T. W. Kenny, “Quantum Limit of Quality Factor in Silicon Micro and Nano Mechanical Resonators,” Sci. Rep. 3, 3244 (2013).
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Akhiezer, A.

A. Akhiezer, “On the Absorption of Sound in Solids,” J. Phys. (Moscow) 1, 277 (1939).

Aksyuk, V.

R. Zhang, C. Ti, M. I. Davanço, Y. Ren, V. Aksyuk, Y. Liu, and K. Srinivasan, “Integrated tuning fork nanocavity optomechanical transducers with high fMQM product and stress-engineered frequency tuning,” Appl. Phys. Lett. 107, 131110 (2015).
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K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11, 791–797 (2011).
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Alaie, S.

Alegre, T.

Alegre, T. P. M.

R. Benevides, F. G. S. Santos, G. O. Luiz, G. S. Wiederhecker, and T. P. M. Alegre, “Ultrahigh-Q optomechanical crystal cavities fabricated in a CMOS foundry,” Sci. Rep. 7, 2491 (2017).
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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, 89–92 (2011).
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Anetsberger, G.

M. L. Gorodetsky, A. Schliesser, G. Anetsberger, S. Deleglise, and T. J. Kippenberg, “Determination of the vacuum optomechanical coupling rate using frequency noise calibration,” Opt. Express 18, 23236 (2010).
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G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5, 909–914 (2009).
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A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New J. Phys. 10, 095015 (2008).
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Arcizet, O.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5, 909–914 (2009).
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A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New J. Phys. 10, 095015 (2008).
[Crossref]

Asheghi, M.

M. Asheghi, M. N. Touzelbaev, K. E. Goodson, Y. K. Leung, and S. S. Wong, “Temperature-Dependent Thermal Conductivity of Single-Crystal Silicon Layers in SOI Substrates,” J. Heat Transfer. 120, 30 (1998).
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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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G. D. Cole, I. Wilson-Rae, K. Werbach, M. R. Vanner, and M. Aspelmeyer, “Phonon-tunnelling dissipation in mechanical resonators,” Nat. Commun. 2, 231 (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, 89–92 (2011).
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Aubin, K. L.

K. L. Aubin, M. Zalalutdinov, R. B. Reichenbach, B. H. Houston, A. T. Zehnder, J. M. Parpia, and H. G. Craighead, “Laser annealing for high-Q MEMS resonators,” Proc. SPIE 5116, 531 (2003.

Barclay, P. E.

P. H. Kim, C. Doolin, B. D. Hauer, A. J. R. MacDonald, M. R. Freeman, P. E. Barclay, and J. P. Davis, “Nanoscale torsional optomechanics,” Appl. Phys. Lett. 102, 053102 (2013).
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Barg, A.

Y. Tsaturyan, A. Barg, E. S. Polzik, and A. Schliesser, “Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution,” Nat. Nanotechnol. 12, 776 (2017).
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Barnard, A.

M. Zhang, G. S. Wiederhecker, S. Manipatruni, A. Barnard, P. McEuen, and M. Lipson, “Synchronization of Micromechanical Oscillators Using Light,” Phys. Rev. Lett. 109, 233906 (2012).
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Barton, R. a.

I. Wilson-Rae, R. a. Barton, S. S. Verbridge, D. R. Southworth, B. Ilic, H. G. Craighead, and J. M. Parpia, “High-Q Nanomechanics via Destructive Interference of Elastic Waves,” Phys. Rev. Lett. 106, 047205 (2011).
[Crossref] [PubMed]

Bellan, L. M.

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[Crossref]

Benevides, R.

R. Benevides, F. G. S. Santos, G. O. Luiz, G. S. Wiederhecker, and T. P. M. Alegre, “Ultrahigh-Q optomechanical crystal cavities fabricated in a CMOS foundry,” Sci. Rep. 7, 2491 (2017).
[Crossref] [PubMed]

Benevides, R. S.

Borselli, M.

M. Borselli, T. J. Johnson, and O. Painter, “Measuring the role of surface chemistry in silicon microphotonics,” Appl. Phys. Lett. 88, 131114 (2006).
[Crossref]

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 (2014).
[Crossref]

Bourassa, A.

C. Reinhardt, T. Müller, A. Bourassa, and J. C. Sankey, “Ultralow-Noise SiN Trampoline Resonators for Sensing and Optomechanics,” Phys. Rev. X 6, 021001 (2016).

Breazeale, M. A.

J. Philip and M. A. Breazeale, “Third-order elastic constants and Grüneisen parameters of silicon and germanium between 3 and 300°K,” J. Appl. Phys. 54, 752 (1983).
[Crossref]

Cardenas, J.

M. Zhang, S. Shah, J. Cardenas, and M. Lipson, “Synchronization and Phase Noise Reduction in Micromechanical Oscillator Arrays Coupled through Light,” Phys. Rev. Lett. 115, 163902 (2015).
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Carmon, T.

T. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. Vahala, “Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity,” Phys. Rev. Lett. 95, 033901 (2005).
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Carr, D. W.

S. Evoy, A. Olkhovets, L. Sekaric, J. M. Parpia, H. G. Craighead, and D. W. Carr, “Temperature-dependent internal friction in silicon nanoelectromechanical systems,” Appl. Phys. Lett. 77, 2397–2399 (2000).
[Crossref]

Chan, J.

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

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

Chandorkar, S. A.

S. Ghaffari, S. A. Chandorkar, S. Wang, E. J. Ng, C. H. Ahn, V. Hong, Y. Yang, and T. W. Kenny, “Quantum Limit of Quality Factor in Silicon Micro and Nano Mechanical Resonators,” Sci. Rep. 3, 3244 (2013).
[Crossref] [PubMed]

Chang, P.

F.-C. Hsu, J.-C. Hsu, T.-C. Huang, C.-H. Wang, and P. Chang, “Reducing support loss in micromechanical ring resonators using phononic band-gap structures,” J. Phys. D 44, 375101 (2011).
[Crossref]

Chen, L.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall Mode Volumes in Dielectric Optical Microcavities,” Phys. Rev. Lett. 95, 143901 (2005).
[Crossref] [PubMed]

Chow, E.

K. Yasumura, T. Stowe, E. Chow, T. Pfafman, T. Kenny, B. Stipe, and D. Rugar, “Quality factors in micron- and submicron-thick cantilevers,” J. Microelectromech. Syst. 9, 117–125 (2000).
[Crossref]

Chu, S. T.

Cleland, A. N.

A. N. Cleland, Foundations of Nanomechanics, (SpringerBerlin Heidelberg, 2003).
[Crossref]

Cole, G. D.

G. D. Cole, I. Wilson-Rae, K. Werbach, M. R. Vanner, and M. Aspelmeyer, “Phonon-tunnelling dissipation in mechanical resonators,” Nat. Commun. 2, 231 (2011).
[Crossref] [PubMed]

Couillaud, B.

T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[Crossref]

Craighead, H.

M. Pandey, R. Reichenbach, A. Zehnder, A. Lal, and H. Craighead, “Reducing Anchor Loss in MEMS Resonators Using Mesa Isolation,” J. Microelectromech. Syst. 18, 836–844 (2009).
[Crossref]

Craighead, H. G.

I. Wilson-Rae, R. a. Barton, S. S. Verbridge, D. R. Southworth, B. Ilic, H. G. Craighead, and J. M. Parpia, “High-Q Nanomechanics via Destructive Interference of Elastic Waves,” Phys. Rev. Lett. 106, 047205 (2011).
[Crossref] [PubMed]

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[Crossref]

K. L. Aubin, M. Zalalutdinov, R. B. Reichenbach, B. H. Houston, A. T. Zehnder, J. M. Parpia, and H. G. Craighead, “Laser annealing for high-Q MEMS resonators,” Proc. SPIE 5116, 531 (2003.

S. Evoy, A. Olkhovets, L. Sekaric, J. M. Parpia, H. G. Craighead, and D. W. Carr, “Temperature-dependent internal friction in silicon nanoelectromechanical systems,” Appl. Phys. Lett. 77, 2397–2399 (2000).
[Crossref]

Dantan, A.

A. Xuereb, C. Genes, G. Pupillo, M. Paternostro, and A. Dantan, “Reconfigurable Long-Range Phonon Dynamics in Optomechanical Arrays,” Phys. Rev. Lett. 112, 133604 (2014).
[Crossref] [PubMed]

A. Xuereb, C. Genes, and A. Dantan, “Strong Coupling and Long-Range Collective Interactions in Optomechanical Arrays,” Phys. Rev. Lett. 109, 223601 (2012).
[Crossref]

Davanço, M.

K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11, 791–797 (2011).
[Crossref] [PubMed]

Davanço, M. I.

R. Zhang, C. Ti, M. I. Davanço, Y. Ren, V. Aksyuk, Y. Liu, and K. Srinivasan, “Integrated tuning fork nanocavity optomechanical transducers with high fMQM product and stress-engineered frequency tuning,” Appl. Phys. Lett. 107, 131110 (2015).
[Crossref]

Davis, J. P.

C. Doolin, P. H. Kim, B. D. Hauer, A. J. R. MacDonald, and J. P. Davis, “Multidimensional optomechanical cantilevers for high-frequency force sensing,” New J. Phys. 16, 035001 (2014).
[Crossref]

P. H. Kim, C. Doolin, B. D. Hauer, A. J. R. MacDonald, M. R. Freeman, P. E. Barclay, and J. P. Davis, “Nanoscale torsional optomechanics,” Appl. Phys. Lett. 102, 053102 (2013).
[Crossref]

Degen, C L

Y. Tao, P. Navaretti, R. Hauert, U. Grob, M. Poggio, and C L Degen, “Permanent reduction of dissipation in nanomechanical Si resonators by chemical surface protection,” Nanotechnology 26, 465501 (2015).
[Crossref] [PubMed]

Degen, C. L.

Y. Tao, R. Hauert, and C. L. Degen, “Exclusively Gas-Phase Passivation of Native Oxide-Free Silicon(100) and Silicon(111) Surfaces,” ACS Appl. Mater. Interfaces 8(20), 13157–13165 (2016).
[Crossref] [PubMed]

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 (2014).
[Crossref]

Deleglise, S.

Desai, P. D.

P. D. Desai, “Thermodynamic Properties of Iron and Silicon,” J. Phys. Chem. Ref. Data 15, 967 (1986).
[Crossref]

Doolin, C.

C. Doolin, P. H. Kim, B. D. Hauer, A. J. R. MacDonald, and J. P. Davis, “Multidimensional optomechanical cantilevers for high-frequency force sensing,” New J. Phys. 16, 035001 (2014).
[Crossref]

P. H. Kim, C. Doolin, B. D. Hauer, A. J. R. MacDonald, M. R. Freeman, P. E. Barclay, and J. P. Davis, “Nanoscale torsional optomechanics,” Appl. Phys. Lett. 102, 053102 (2013).
[Crossref]

Ehrenreich, H.

T. O. Woodruff and H. Ehrenreich, “Absorption of Sound in Insulators,” Phys. Rev. 123, 1553–1559 (1961).
[Crossref]

Espinel, Y. A. V.

Evoy, S.

S. Evoy, A. Olkhovets, L. Sekaric, J. M. Parpia, H. G. Craighead, and D. W. Carr, “Temperature-dependent internal friction in silicon nanoelectromechanical systems,” Appl. Phys. Lett. 77, 2397–2399 (2000).
[Crossref]

Fan, J.

Fink, Y.

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 65, 066611 (2002).
[Crossref]

Freeman, M. R.

P. H. Kim, C. Doolin, B. D. Hauer, A. J. R. MacDonald, M. R. Freeman, P. E. Barclay, and J. P. Davis, “Nanoscale torsional optomechanics,” Appl. Phys. Lett. 102, 053102 (2013).
[Crossref]

Genes, C.

A. Xuereb, C. Genes, G. Pupillo, M. Paternostro, and A. Dantan, “Reconfigurable Long-Range Phonon Dynamics in Optomechanical Arrays,” Phys. Rev. Lett. 112, 133604 (2014).
[Crossref] [PubMed]

A. Xuereb, C. Genes, and A. Dantan, “Strong Coupling and Long-Range Collective Interactions in Optomechanical Arrays,” Phys. Rev. Lett. 109, 223601 (2012).
[Crossref]

Ghaffari, S.

S. Ghaffari, S. A. Chandorkar, S. Wang, E. J. Ng, C. H. Ahn, V. Hong, Y. Yang, and T. W. Kenny, “Quantum Limit of Quality Factor in Silicon Micro and Nano Mechanical Resonators,” Sci. Rep. 3, 3244 (2013).
[Crossref] [PubMed]

Goodson, K. E.

M. Asheghi, M. N. Touzelbaev, K. E. Goodson, Y. K. Leung, and S. S. Wong, “Temperature-Dependent Thermal Conductivity of Single-Crystal Silicon Layers in SOI Substrates,” J. Heat Transfer. 120, 30 (1998).
[Crossref]

Gorodetsky, M. L.

Grebogi, C.

L. Ying, Y.-C. Lai, and C. Grebogi, “Quantum manifestation of a synchronization transition in optomechanical systems,” Phys. Rev. A 90, 053810 (2014).
[Crossref]

Grob, U.

Y. Tao, P. Navaretti, R. Hauert, U. Grob, M. Poggio, and C L Degen, “Permanent reduction of dissipation in nanomechanical Si resonators by chemical surface protection,” Nanotechnology 26, 465501 (2015).
[Crossref] [PubMed]

Gröblacher, S.

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] [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, 89–92 (2011).
[Crossref] [PubMed]

Guzmán Cervantes, F.

F. Guzmán Cervantes, L. Kumanchik, J. Pratt, and J. M. Taylor, “High sensitivity optomechanical reference accelerometer over 10 kHz,” Appl. Phys. Lett. 104, 221111 (2014).
[Crossref]

Hansch, T.

T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[Crossref]

Hauer, B. D.

C. Doolin, P. H. Kim, B. D. Hauer, A. J. R. MacDonald, and J. P. Davis, “Multidimensional optomechanical cantilevers for high-frequency force sensing,” New J. Phys. 16, 035001 (2014).
[Crossref]

P. H. Kim, C. Doolin, B. D. Hauer, A. J. R. MacDonald, M. R. Freeman, P. E. Barclay, and J. P. Davis, “Nanoscale torsional optomechanics,” Appl. Phys. Lett. 102, 053102 (2013).
[Crossref]

Hauert, R.

Y. Tao, R. Hauert, and C. L. Degen, “Exclusively Gas-Phase Passivation of Native Oxide-Free Silicon(100) and Silicon(111) Surfaces,” ACS Appl. Mater. Interfaces 8(20), 13157–13165 (2016).
[Crossref] [PubMed]

Y. Tao, P. Navaretti, R. Hauert, U. Grob, M. Poggio, and C L Degen, “Permanent reduction of dissipation in nanomechanical Si resonators by chemical surface protection,” Nanotechnology 26, 465501 (2015).
[Crossref] [PubMed]

Hill, J. T.

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

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

Holmes, C. A.

C. A. Holmes, C. P. Meaney, and G. J. Milburn, “Synchronization of many nanomechanical resonators coupled via a common cavity field,” Phys. Rev. E 85, 066203 (2012).
[Crossref]

Hong, V.

S. Ghaffari, S. A. Chandorkar, S. Wang, E. J. Ng, C. H. Ahn, V. Hong, Y. Yang, and T. W. Kenny, “Quantum Limit of Quality Factor in Silicon Micro and Nano Mechanical Resonators,” Sci. Rep. 3, 3244 (2013).
[Crossref] [PubMed]

Hossein-Zadeh, M.

Houston, B. H.

K. L. Aubin, M. Zalalutdinov, R. B. Reichenbach, B. H. Houston, A. T. Zehnder, J. M. Parpia, and H. G. Craighead, “Laser annealing for high-Q MEMS resonators,” Proc. SPIE 5116, 531 (2003.

Hsu, F.-C.

F.-C. Hsu, J.-C. Hsu, T.-C. Huang, C.-H. Wang, and P. Chang, “Reducing support loss in micromechanical ring resonators using phononic band-gap structures,” J. Phys. D 44, 375101 (2011).
[Crossref]

Hsu, J.-C.

F.-C. Hsu, J.-C. Hsu, T.-C. Huang, C.-H. Wang, and P. Chang, “Reducing support loss in micromechanical ring resonators using phononic band-gap structures,” J. Phys. D 44, 375101 (2011).
[Crossref]

Huang, C.

Huang, T.-C.

F.-C. Hsu, J.-C. Hsu, T.-C. Huang, C.-H. Wang, and P. Chang, “Reducing support loss in micromechanical ring resonators using phononic band-gap structures,” J. Phys. D 44, 375101 (2011).
[Crossref]

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. E 65, 066611 (2002).
[Crossref]

Ilic, B.

I. Wilson-Rae, R. a. Barton, S. S. Verbridge, D. R. Southworth, B. Ilic, H. G. Craighead, and J. M. Parpia, “High-Q Nanomechanics via Destructive Interference of Elastic Waves,” Phys. Rev. Lett. 106, 047205 (2011).
[Crossref] [PubMed]

Ilisavskii, Y.

Y. Ilisavskii and V. Sternin, “Lattice absorption of high-frequency sound in silicon,” Sov. Phys. Solid State 27(2), pp. 236–239 (1985).

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. E 65, 066611 (2002).
[Crossref]

Johnson, S. G.

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

Johnson, T. J.

M. Borselli, T. J. Johnson, and O. Painter, “Measuring the role of surface chemistry in silicon microphotonics,” Appl. Phys. Lett. 88, 131114 (2006).
[Crossref]

Kaipnazarov, D. K.

L. P. Khiznichenko, P. F. Kromer, D. K. Kaipnazarov, E. Otenyazov, D. Yustpova, and L. G. Zotova, “The Properties of the Low-Temperature Internal Friction Peak in Silicon,” Phys. Status Solidi B 21, 805–810 (1967).
[Crossref]

Kenny, T.

K. Yasumura, T. Stowe, E. Chow, T. Pfafman, T. Kenny, B. Stipe, and D. Rugar, “Quality factors in micron- and submicron-thick cantilevers,” J. Microelectromech. Syst. 9, 117–125 (2000).
[Crossref]

Kenny, T. W.

S. Ghaffari, S. A. Chandorkar, S. Wang, E. J. Ng, C. H. Ahn, V. Hong, Y. Yang, and T. W. Kenny, “Quantum Limit of Quality Factor in Silicon Micro and Nano Mechanical Resonators,” Sci. Rep. 3, 3244 (2013).
[Crossref] [PubMed]

Khiznichenko, L. P.

L. P. Khiznichenko, P. F. Kromer, D. K. Kaipnazarov, E. Otenyazov, D. Yustpova, and L. G. Zotova, “The Properties of the Low-Temperature Internal Friction Peak in Silicon,” Phys. Status Solidi B 21, 805–810 (1967).
[Crossref]

Kim, B.

W.-C. Li, Y. Lin, B. Kim, Z. Ren, and C. T.-C. Nguyen, “Quality factor enhancement in micromechanical resonators at cryogenic temperatures,” in Proceedings of IEEE TRANSDUCERS 2009 - 2009 International Solid-State Sensors, Actuators and Microsystems Conference (IEEE, 2009), pp. 1445–1448.

Kim, P. H.

C. Doolin, P. H. Kim, B. D. Hauer, A. J. R. MacDonald, and J. P. Davis, “Multidimensional optomechanical cantilevers for high-frequency force sensing,” New J. Phys. 16, 035001 (2014).
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T. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. Vahala, “Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity,” Phys. Rev. Lett. 95, 033901 (2005).
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M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
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M. L. Gorodetsky, A. Schliesser, G. Anetsberger, S. Deleglise, and T. J. Kippenberg, “Determination of the vacuum optomechanical coupling rate using frequency noise calibration,” Opt. Express 18, 23236 (2010).
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G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5, 909–914 (2009).
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A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New J. Phys. 10, 095015 (2008).
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G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5, 909–914 (2009).
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W.-C. Li, Y. Lin, B. Kim, Z. Ren, and C. T.-C. Nguyen, “Quality factor enhancement in micromechanical resonators at cryogenic temperatures,” in Proceedings of IEEE TRANSDUCERS 2009 - 2009 International Solid-State Sensors, Actuators and Microsystems Conference (IEEE, 2009), pp. 1445–1448.

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M. Zhang, S. Shah, J. Cardenas, and M. Lipson, “Synchronization and Phase Noise Reduction in Micromechanical Oscillator Arrays Coupled through Light,” Phys. Rev. Lett. 115, 163902 (2015).
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M. Zhang, G. Luiz, S. Shah, G. Wiederhecker, and M. Lipson, “Eliminating anchor loss in optomechanical resonators using elastic wave interference,” Appl. Phys. Lett. 105, 051904 (2014).
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M. Zhang, G. S. Wiederhecker, S. Manipatruni, A. Barnard, P. McEuen, and M. Lipson, “Synchronization of Micromechanical Oscillators Using Light,” Phys. Rev. Lett. 109, 233906 (2012).
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Liu, F.

Liu, Y.

R. Zhang, C. Ti, M. I. Davanço, Y. Ren, V. Aksyuk, Y. Liu, and K. Srinivasan, “Integrated tuning fork nanocavity optomechanical transducers with high fMQM product and stress-engineered frequency tuning,” Appl. Phys. Lett. 107, 131110 (2015).
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M. Zhang, G. Luiz, S. Shah, G. Wiederhecker, and M. Lipson, “Eliminating anchor loss in optomechanical resonators using elastic wave interference,” Appl. Phys. Lett. 105, 051904 (2014).
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F. G. S. Santos, Y. A. V. Espinel, G. O. Luiz, R. S. Benevides, G. S. Wiederhecker, and T. P. Mayer Alegre, “Hybrid confinement of optical and mechanical modes in a bullseye optomechanical resonator,” Opt. Express 25, 508 (2017).
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R. Benevides, F. G. S. Santos, G. O. Luiz, G. S. Wiederhecker, and T. P. M. Alegre, “Ultrahigh-Q optomechanical crystal cavities fabricated in a CMOS foundry,” Sci. Rep. 7, 2491 (2017).
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K. G. Lyon, G. L. Salinger, C. A. Swenson, and G. K. White, “Linear thermal expansion measurements on silicon from 6 to 340 K,” J. Appl. Phys. 48, 865 (1977).
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C. Doolin, P. H. Kim, B. D. Hauer, A. J. R. MacDonald, and J. P. Davis, “Multidimensional optomechanical cantilevers for high-frequency force sensing,” New J. Phys. 16, 035001 (2014).
[Crossref]

P. H. Kim, C. Doolin, B. D. Hauer, A. J. R. MacDonald, M. R. Freeman, P. E. Barclay, and J. P. Davis, “Nanoscale torsional optomechanics,” Appl. Phys. Lett. 102, 053102 (2013).
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M. Zhang, G. S. Wiederhecker, S. Manipatruni, A. Barnard, P. McEuen, and M. Lipson, “Synchronization of Micromechanical Oscillators Using Light,” Phys. Rev. Lett. 109, 233906 (2012).
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J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall Mode Volumes in Dielectric Optical Microcavities,” Phys. Rev. Lett. 95, 143901 (2005).
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M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
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M. Ludwig and F. Marquardt, “Quantum Many-Body Dynamics in Optomechanical Arrays,” Phys. Rev. Lett. 111, 073603 (2013).
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McEuen, P.

M. Zhang, G. S. Wiederhecker, S. Manipatruni, A. Barnard, P. McEuen, and M. Lipson, “Synchronization of Micromechanical Oscillators Using Light,” Phys. Rev. Lett. 109, 233906 (2012).
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K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11, 791–797 (2011).
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C. Reinhardt, T. Müller, A. Bourassa, and J. C. Sankey, “Ultralow-Noise SiN Trampoline Resonators for Sensing and Optomechanics,” Phys. Rev. X 6, 021001 (2016).

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Y. Tao, P. Navaretti, R. Hauert, U. Grob, M. Poggio, and C L Degen, “Permanent reduction of dissipation in nanomechanical Si resonators by chemical surface protection,” Nanotechnology 26, 465501 (2015).
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W.-C. Li, Y. Lin, B. Kim, Z. Ren, and C. T.-C. Nguyen, “Quality factor enhancement in micromechanical resonators at cryogenic temperatures,” in Proceedings of IEEE TRANSDUCERS 2009 - 2009 International Solid-State Sensors, Actuators and Microsystems Conference (IEEE, 2009), pp. 1445–1448.

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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, 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, 89–92 (2011).
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M. Pandey, R. Reichenbach, A. Zehnder, A. Lal, and H. Craighead, “Reducing Anchor Loss in MEMS Resonators Using Mesa Isolation,” J. Microelectromech. Syst. 18, 836–844 (2009).
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I. Wilson-Rae, R. a. Barton, S. S. Verbridge, D. R. Southworth, B. Ilic, H. G. Craighead, and J. M. Parpia, “High-Q Nanomechanics via Destructive Interference of Elastic Waves,” Phys. Rev. Lett. 106, 047205 (2011).
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S. Evoy, A. Olkhovets, L. Sekaric, J. M. Parpia, H. G. Craighead, and D. W. Carr, “Temperature-dependent internal friction in silicon nanoelectromechanical systems,” Appl. Phys. Lett. 77, 2397–2399 (2000).
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Y. Tsaturyan, A. Barg, E. S. Polzik, and A. Schliesser, “Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution,” Nat. Nanotechnol. 12, 776 (2017).
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F. Guzmán Cervantes, L. Kumanchik, J. Pratt, and J. M. Taylor, “High sensitivity optomechanical reference accelerometer over 10 kHz,” Appl. Phys. Lett. 104, 221111 (2014).
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S. A. Zotov, B. R. Simon, I. P. Prikhodko, A. A. Trusov, and A. M. Shkel, “Quality Factor Maximization Through Dynamic Balancing of Tuning Fork Resonator,” IEEE Sens. J. 14, 2706–2714 (2014).
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A. Xuereb, C. Genes, G. Pupillo, M. Paternostro, and A. Dantan, “Reconfigurable Long-Range Phonon Dynamics in Optomechanical Arrays,” Phys. Rev. Lett. 112, 133604 (2014).
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K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11, 791–797 (2011).
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M. Pandey, R. Reichenbach, A. Zehnder, A. Lal, and H. Craighead, “Reducing Anchor Loss in MEMS Resonators Using Mesa Isolation,” J. Microelectromech. Syst. 18, 836–844 (2009).
[Crossref]

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S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
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Reinhardt, C.

C. Reinhardt, T. Müller, A. Bourassa, and J. C. Sankey, “Ultralow-Noise SiN Trampoline Resonators for Sensing and Optomechanics,” Phys. Rev. X 6, 021001 (2016).

Ren, Y.

R. Zhang, C. Ti, M. I. Davanço, Y. Ren, V. Aksyuk, Y. Liu, and K. Srinivasan, “Integrated tuning fork nanocavity optomechanical transducers with high fMQM product and stress-engineered frequency tuning,” Appl. Phys. Lett. 107, 131110 (2015).
[Crossref]

Ren, Z.

W.-C. Li, Y. Lin, B. Kim, Z. Ren, and C. T.-C. Nguyen, “Quality factor enhancement in micromechanical resonators at cryogenic temperatures,” in Proceedings of IEEE TRANSDUCERS 2009 - 2009 International Solid-State Sensors, Actuators and Microsystems Conference (IEEE, 2009), pp. 1445–1448.

Rivière, R.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5, 909–914 (2009).
[Crossref]

A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New J. Phys. 10, 095015 (2008).
[Crossref]

Robinson, J. T.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall Mode Volumes in Dielectric Optical Microcavities,” Phys. Rev. Lett. 95, 143901 (2005).
[Crossref] [PubMed]

Rokhsari, H.

T. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. Vahala, “Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity,” Phys. Rev. Lett. 95, 033901 (2005).
[Crossref] [PubMed]

Roukes, M. L.

R. Lifshitz and M. L. Roukes, “Thermoelastic damping in micro- and nanomechanical systems,” Phys. Rev. B 61, 5600–5609 (2000).
[Crossref]

Rugar, D.

K. Yasumura, T. Stowe, E. Chow, T. Pfafman, T. Kenny, B. Stipe, and D. Rugar, “Quality factors in micron- and submicron-thick cantilevers,” J. Microelectromech. Syst. 9, 117–125 (2000).
[Crossref]

Safavi-Naeini, A.

Safavi-Naeini, A. H.

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

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

Sahasrabudhe, G. G.

S. D. Lambade, G. G. Sahasrabudhe, and S. Rajagopalan, “Temperature dependence of acoustic attenuation in silicon,” Phys. Rev. B 51, 15861–15866 (1995).
[Crossref]

Salinger, G. L.

K. G. Lyon, G. L. Salinger, C. A. Swenson, and G. K. White, “Linear thermal expansion measurements on silicon from 6 to 340 K,” J. Appl. Phys. 48, 865 (1977).
[Crossref]

Sankey, J. C.

C. Reinhardt, T. Müller, A. Bourassa, and J. C. Sankey, “Ultralow-Noise SiN Trampoline Resonators for Sensing and Optomechanics,” Phys. Rev. X 6, 021001 (2016).

Santos, F. G. S.

F. G. S. Santos, Y. A. V. Espinel, G. O. Luiz, R. S. Benevides, G. S. Wiederhecker, and T. P. Mayer Alegre, “Hybrid confinement of optical and mechanical modes in a bullseye optomechanical resonator,” Opt. Express 25, 508 (2017).
[Crossref] [PubMed]

R. Benevides, F. G. S. Santos, G. O. Luiz, G. S. Wiederhecker, and T. P. M. Alegre, “Ultrahigh-Q optomechanical crystal cavities fabricated in a CMOS foundry,” Sci. Rep. 7, 2491 (2017).
[Crossref] [PubMed]

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T. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. Vahala, “Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity,” Phys. Rev. Lett. 95, 033901 (2005).
[Crossref] [PubMed]

Schliesser, A.

Y. Tsaturyan, A. Barg, E. S. Polzik, and A. Schliesser, “Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution,” Nat. Nanotechnol. 12, 776 (2017).
[Crossref] [PubMed]

M. L. Gorodetsky, A. Schliesser, G. Anetsberger, S. Deleglise, and T. J. Kippenberg, “Determination of the vacuum optomechanical coupling rate using frequency noise calibration,” Opt. Express 18, 23236 (2010).
[Crossref] [PubMed]

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5, 909–914 (2009).
[Crossref]

A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New J. Phys. 10, 095015 (2008).
[Crossref]

Sekaric, L.

S. Evoy, A. Olkhovets, L. Sekaric, J. M. Parpia, H. G. Craighead, and D. W. Carr, “Temperature-dependent internal friction in silicon nanoelectromechanical systems,” Appl. Phys. Lett. 77, 2397–2399 (2000).
[Crossref]

Shah, S.

M. Zhang, S. Shah, J. Cardenas, and M. Lipson, “Synchronization and Phase Noise Reduction in Micromechanical Oscillator Arrays Coupled through Light,” Phys. Rev. Lett. 115, 163902 (2015).
[Crossref] [PubMed]

M. Zhang, G. Luiz, S. Shah, G. Wiederhecker, and M. Lipson, “Eliminating anchor loss in optomechanical resonators using elastic wave interference,” Appl. Phys. Lett. 105, 051904 (2014).
[Crossref]

Shkel, A. M.

S. A. Zotov, B. R. Simon, I. P. Prikhodko, A. A. Trusov, and A. M. Shkel, “Quality Factor Maximization Through Dynamic Balancing of Tuning Fork Resonator,” IEEE Sens. J. 14, 2706–2714 (2014).
[Crossref]

Simon, B. R.

S. A. Zotov, B. R. Simon, I. P. Prikhodko, A. A. Trusov, and A. M. Shkel, “Quality Factor Maximization Through Dynamic Balancing of Tuning Fork Resonator,” IEEE Sens. J. 14, 2706–2714 (2014).
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I. Wilson-Rae, R. a. Barton, S. S. Verbridge, D. R. Southworth, B. Ilic, H. G. Craighead, and J. M. Parpia, “High-Q Nanomechanics via Destructive Interference of Elastic Waves,” Phys. Rev. Lett. 106, 047205 (2011).
[Crossref] [PubMed]

Srinivasan, K.

R. Zhang, C. Ti, M. I. Davanço, Y. Ren, V. Aksyuk, Y. Liu, and K. Srinivasan, “Integrated tuning fork nanocavity optomechanical transducers with high fMQM product and stress-engineered frequency tuning,” Appl. Phys. Lett. 107, 131110 (2015).
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[Crossref]

W.-C. Li, Y. Lin, B. Kim, Z. Ren, and C. T.-C. Nguyen, “Quality factor enhancement in micromechanical resonators at cryogenic temperatures,” in Proceedings of IEEE TRANSDUCERS 2009 - 2009 International Solid-State Sensors, Actuators and Microsystems Conference (IEEE, 2009), pp. 1445–1448.

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Figures (11)

Fig. 1
Fig. 1 (a) Scanning electron microscopy of the device. (b) Finite element method (FEM) simulation of the normalized energy distribution of the mechanical modes of interest for the device with δ = −15 nm in (c, d); displacement is exaggerated and colors indicate normalized energy distribution. c, d) Mechanical frequency and Q-factor dependence on paddles balance (δ) from FEM simulations. (e) Perturbation theory estimate for the optomechanical coupling for different radial order optical TE modes with λ = 1520 nm (see appendix B for more information); insets: |Er| distribution profiles of the first (bottom) and 8th (top) radial order TE modes; darker colors correspond to higher intensities. In (b–d) only radiation to the substrate is considered.
Fig. 2
Fig. 2 (a) Schematics of the experimental setup. (b) Optical spectrum of a typical device-marked in green is the resonance used to probe the mechanical modes. (c) Measured resonance (green) and fitted counter-propagating coupled modes function (red) - λ0 = 1516.68 nm and loaded quality factor Qopt = 40k. In (a): PM = phase-modulator; PC - polarization control; BS = beam splitter; PBS = polarizing beam splitter; ESA = electric spectrum analyzer; OSC - oscilloscope. In (c): fitting (red) of the peak marked in (b) (green).
Fig. 3
Fig. 3 (a, b) S (a) and AS (b) modes calibrated power spectrum density at room (orange) and cryogenic (green) temperatures; data in colors and fitted Lorentzians in black; fm ≈ 56 MHz. (c–f) Asymmetry dependence of frequency difference between S (blue) and AS (red) modes at room temperature (c), g0 measured at room temperature (d), Q-factor at room (e) and cryogenic (f) temperatures; marks are data while lines are fitted curves of the coupled oscillators model. (g) Temperature dependence of quality factor in log × log scale; blue and red lines are the estimated S and AS modes TED limited Q’s; the gray area is bounded by the upper and lower AKE limits. In (a), (b), (g)): data of device with δ = −50 nm.
Fig. 4
Fig. 4 Q-factor of S (blue) and AS (red) modes for different situations. (a) After a few months stored in a box with N2 rich atmosphere; (b) After cleaning with piranha and HF dip; (c) After in-situ laser annealing — device with δ = −75 nm. We keep the first cool down measure in every figure for comparison (lighter colors). Gray area marks the Akhiezer limits and the blue and red lines the TED limits.
Fig. 5
Fig. 5 (a) Dispersion of experimental (colored circles) FEM calculated (solid lines) TE-like optical modes. (b) Experimental optical spectra for the TE-like polarization. Circles on (a) and (b) are related by color. The green star marks the optical mode used to probe the mechanical resonator. In (a) the FEM calculated modes increase radial order from bottom to top (1st to 7th).
Fig. 6
Fig. 6 (a) Effetive mode volume (Veff) and ρ, calculated at 200 nm away from the disk’s border, for different radial order modes, normalized by the value for the first order mode. (b) FEM calculated evanescent field profile, for three different radial order modes, outside of a 5 µm radius and 220 nm thick Silicon disk optical cavity. The field in (b) is normalized by the maximum field value for each mode, which occurs inside of the cavity; the dashed vertical line indicates the position of the paddle closest to the disk.
Fig. 7
Fig. 7 Mass-spring lumped coupled oscillators model schematics.
Fig. 8
Fig. 8 (a) Frequency of symmetric (S — blue) and anti-symmetric (AS — blue) modes obtained from the analytical model, varying the mass of oscillator 2. (b) Same as (a) with frequency shifted with respect to the S mode resonance. (c) Damping of S and AS modes obtained from the analytical model.
Fig. 9
Fig. 9 (a) Comparison of numeric and analytical models to TED on a doubly clamped beam; inset: side-view of numerical thermal distribution. (b) Numerical solution of temperature dependent TED limited Q for the S and AS modes of the paddles.
Fig. 10
Fig. 10 Silicon properties versus temperature. (a) Heat capacity [45]; (b) Grüneisen parameter [47]; (c) Coeffcient of thermal expansion [59]; (d) Average Debye sound speed [46]; (e) Mean thermal phonon life-time [46]; (f) Thermal conductivity [58].
Fig. 11
Fig. 11 Calibrated versus measured sample temperature. Marks are data related to those presented in Fig. 3(g) and the red line is a reference with slope 1.

Tables (1)

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Table 1 Fitting parameters of a three coupled lumped mass-spring oscillators model

Equations (7)

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g 0 x x p f = ω 0 2 S | U n | ( Δ ϵ | E t | 2 + Δ ϵ 1 | D n | 2 ) d A V ϵ 0 n 2 | E | 2 d V
V e f f = V ϵ 0 n 2 | E | 2 d V ϵ 0 n m a x 2 | E | m a x 2
g 0 x z p f = ω 0 ρ 2 ϵ 0 n m a x 2 V e f f
ρ = S | U n | ( Δ ϵ | E ˜ t | 2 + Δ ϵ 1 | D ˜ n | 2 ) d A
d x 1 d t = ι ˙ Ω 1 x 1 + ι ˙ κ 13 2 x 3 + ι ˙ κ 12 2 x 2 d x 2 d t = ι ˙ Ω 2 x 2 + ι ˙ κ 23 2 x 3 + ι ˙ κ 21 2 x 2 d x 3 d t = ι ˙ Ω 3 x 3 + ι ˙ κ 31 2 x 1 + ι ˙ κ 32 2 x 2
Ω 1 , 2 = α 1 2 Y t 3 w 12 m L 3 ,
Γ AKE = γ 2 c p T 3 ρ v D 2 4 π 2 f m 2 τ

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