Abstract

Design of a doubly-clamped beam structure capable of localizing mechanical and optical energy at the nanoscale is presented. The optical design is based upon photonic crystal concepts in which patterning of a nanoscale-cross-section beam can result in strong optical localization to an effective optical mode volume of 0.2 cubic wavelengths ((λc)3). By placing two identical nanobeams within the near field of each other, strong optomechanical coupling can be realized for differential motion between the beams. Current designs for thin film silicon nitride beams at a wavelength of λ = 1.5 μ m indicate that such structures can simultaneously realize an optical Q -factor of 7 × 106, motional mass mu ~ 40 picograms, mechanical mode frequency ΩM/2π ~ 170 MHz, and an optomechanical coupling factor (g OM = dωc/dx = ωc/Lom) with effective length L OM ~ λ = 1.5 μm.

© 2009 Optical Society of America

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    [PubMed]
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2008 (10)

T. J. Kippenberg and K. J. Vahala, “Cavity Optomechanics: Back-Action at the Mesoscale,” Science 321, 1172–1176 (2008).
[PubMed]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to micromechanical membrane,” Nature 452, 72–75 (2008).
[PubMed]

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

A. R. M. Zain, N. P. Johnson, M. Solel, and R. M. D. L. Rue, “Ultra high quality factor one-dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI),” Opt. Express 16, 12,084–12,089 (2008).

M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q Nanocavity with 1D Photonic Gap,” Opt. Express 16, 11,905–11,102 (2008).

M. W. McCutcheon and M. Loncar, “Design of a silicon nitride photonic crystal nanocavity with a Quality factor of one million for coupling to a diamond nanocrystal,” Opt. Express 16, 19,136–19,145 (2008).

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

R. H. O. III and I. El-Kady, “Microfabricated phononic crystal devices and applications,” Meas. Sci. Technol.  20, 012002 (2008).

S. Schietinger, T. Schroder, and O. Benson, “One-by-One Coupling of Single Defect Centers in Nanodiamonds to High-Q Modes of an Optical Microresonator,” Nano. Lett.  8, 3911–3915 (2008).
[PubMed]

P. E. Barclay, O. Painter, C. Santori, K.-M. Fu, and R. G. Beausoleil, “Coherent interference effects in a nano-assembled optical cavity-QED system,” ArXiv:0812.4505 (2008).

2007 (4)

M. Hossein-Zadeh and K. J. Vahala, “Observation of optical spring effect in a microtoroidal optomechanical resonator,” Opt. Lett.  32, 1611–1613 (2007).
[PubMed]

M. V. G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum Register Based on Individual Electronic and Nuclear Spin Qubits in Diamond,” Science 316(5829), 1312–1316 (2007).

T. J. Kippenberg and K. Vahala, “Cavity Optomechanics,” Opt. Express 15, 17,172–17,205 (2007).

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett.  99, 160801 (2007).
[PubMed]

2006 (9)

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–73 (2006).
[PubMed]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. As-pelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[PubMed]

A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, “Radiation Pressure Cooling of a Micromechanical Oscillator Using Dynamical Backaction,” Phys. Rev. Lett.  97, 243905 (2006).

P. Velha, J. C. Rodier, P. Lalanne, J. D. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett.  89, 171121 (2006).

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical Wavelength and Energy Conversion in High-Q Double-Layer Cavities of Photonic Crystal Slabs,” Phys. Rev. Lett.  97, 023903 (2006).
[PubMed]

L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent Dynamics of Coupled Electron and Nuclear Spin Qubits in Diamond,” Science 314(5797), 281–285 (2006).

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

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).

C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. D. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent Population Trapping of Single Spins in Diamond under Optical Excitation,” Phys. Rev. Lett.  97, 247401 (2006).

2005 (5)

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microcavities excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005).
[PubMed]

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

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett.  30, 3042–3044 (2005).
[PubMed]

C. Sauvan, P. Lalanne, and J. P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B  71, 165118 (2005).

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

2004 (2)

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, “Observation and characterization of an optical spring,” Phys. Rev. A  69, 051801(R) (2004).

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of Coherent Oscillation of a Single Nuclear Spin and Realization of a Two-Qubit Conditional Quantum Gate,” Phys. Rev. Lett.  93, 130501 (2004).
[PubMed]

2003 (1)

O. Painter, K. Srinivasan, and P. E. Barclay, “A Wannier-like equation for photon states of locally perturbed photonic crystals,” Phys. Rev. B  68, 035214 (2003).

2002 (1)

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

2001 (2)

A. Beveratos, R. Brouri, T. Gacoin, J.-P. Poizat, and P. Grangier, “Nonclassical radiation from diamond nanocrys-tals,” Phys. Rev. A  64, 061802 (2001).

S. Kühn, C. Hettich, C. Schmitt, J-PH. Poizat, and V. Sandoghdar, “Diamond colour centres as a nanoscopic light source for scanning near field microscopy,” J. Microsc.  202, 2–6 (2001).
[PubMed]

1999 (1)

M. Pinard, Y. Hadjar, and A. Heidmann, “Effective mass in quantum effects of radiation pressure,” Eur. Phys. J. D  7, 107–116 (1999).

1997 (3)

A. Gruber, A. Dräbenstedt, C. Tietz, L. Fleury, J. Wratchtrup, and C. v. Borczyskowski, “Scanning confocal optical microscopy and magnetic resonance on single defect centers,” Science 276, 2012–2014 (1997).

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-Bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).

T. D. Stowe, K. Yasumura, T. W. Kenny, D. Botkin, K. Wago, and D. Rugar, “Attonewton force detection using ultrathin silicon cantilevers,” Appl. Phys. Lett.  71, 288–290 (1997).

1985 (1)

P. Meystre, E. M. Wright, J. D. McCullen, and E. Vignes, “Theory of radiation-pressure-driven interferometers,” J. Opt. Soc. Am. B  2, 1830–1840 (1985).

Arcizet, O.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–73 (2006).
[PubMed]

As-pelmeyer, M.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. As-pelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[PubMed]

Barclay, P. E.

P. E. Barclay, O. Painter, C. Santori, K.-M. Fu, and R. G. Beausoleil, “Coherent interference effects in a nano-assembled optical cavity-QED system,” ArXiv:0812.4505 (2008).

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

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microcavities excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005).
[PubMed]

O. Painter, K. Srinivasan, and P. E. Barclay, “A Wannier-like equation for photon states of locally perturbed photonic crystals,” Phys. Rev. B  68, 035214 (2003).

Bäuerle, D.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. As-pelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[PubMed]

Beausoleil, R. G.

P. E. Barclay, O. Painter, C. Santori, K.-M. Fu, and R. G. Beausoleil, “Coherent interference effects in a nano-assembled optical cavity-QED system,” ArXiv:0812.4505 (2008).

C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. D. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent Population Trapping of Single Spins in Diamond under Optical Excitation,” Phys. Rev. Lett.  97, 247401 (2006).

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).

Benson, O.

S. Schietinger, T. Schroder, and O. Benson, “One-by-One Coupling of Single Defect Centers in Nanodiamonds to High-Q Modes of an Optical Microresonator,” Nano. Lett.  8, 3911–3915 (2008).
[PubMed]

Beveratos, A.

A. Beveratos, R. Brouri, T. Gacoin, J.-P. Poizat, and P. Grangier, “Nonclassical radiation from diamond nanocrys-tals,” Phys. Rev. A  64, 061802 (2001).

Blaser, F.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. As-pelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[PubMed]

Bodiya, T.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett.  99, 160801 (2007).
[PubMed]

Böhm, H. R.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. As-pelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[PubMed]

Borczyskowski, C. v.

A. Gruber, A. Dräbenstedt, C. Tietz, L. Fleury, J. Wratchtrup, and C. v. Borczyskowski, “Scanning confocal optical microscopy and magnetic resonance on single defect centers,” Science 276, 2012–2014 (1997).

Botkin, D.

T. D. Stowe, K. Yasumura, T. W. Kenny, D. Botkin, K. Wago, and D. Rugar, “Attonewton force detection using ultrathin silicon cantilevers,” Appl. Phys. Lett.  71, 288–290 (1997).

Briant, T.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–73 (2006).
[PubMed]

Brouri, R.

A. Beveratos, R. Brouri, T. Gacoin, J.-P. Poizat, and P. Grangier, “Nonclassical radiation from diamond nanocrys-tals,” Phys. Rev. A  64, 061802 (2001).

Capasso, F.

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett.  30, 3042–3044 (2005).
[PubMed]

Carmon, T.

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

Charvolin, T.

P. Velha, J. C. Rodier, P. Lalanne, J. D. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett.  89, 171121 (2006).

Chen, L.

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

Childress, L.

M. V. G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum Register Based on Individual Electronic and Nuclear Spin Qubits in Diamond,” Science 316(5829), 1312–1316 (2007).

L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent Dynamics of Coupled Electron and Nuclear Spin Qubits in Diamond,” Science 314(5797), 281–285 (2006).

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F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of Coherent Oscillation of a Single Nuclear Spin and Realization of a Two-Qubit Conditional Quantum Gate,” Phys. Rev. Lett.  93, 130501 (2004).
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M. V. G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum Register Based on Individual Electronic and Nuclear Spin Qubits in Diamond,” Science 316(5829), 1312–1316 (2007).

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C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. D. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent Population Trapping of Single Spins in Diamond under Optical Excitation,” Phys. Rev. Lett.  97, 247401 (2006).

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J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-Bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).

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

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A. Gruber, A. Dräbenstedt, C. Tietz, L. Fleury, J. Wratchtrup, and C. v. Borczyskowski, “Scanning confocal optical microscopy and magnetic resonance on single defect centers,” Science 276, 2012–2014 (1997).

Foresi, J. S.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-Bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).

Fu, K.-M.

P. E. Barclay, O. Painter, C. Santori, K.-M. Fu, and R. G. Beausoleil, “Coherent interference effects in a nano-assembled optical cavity-QED system,” ArXiv:0812.4505 (2008).

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F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of Coherent Oscillation of a Single Nuclear Spin and Realization of a Two-Qubit Conditional Quantum Gate,” Phys. Rev. Lett.  93, 130501 (2004).
[PubMed]

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[PubMed]

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J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to micromechanical membrane,” Nature 452, 72–75 (2008).
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C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. D. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent Population Trapping of Single Spins in Diamond under Optical Excitation,” Phys. Rev. Lett.  97, 247401 (2006).

Gruber, A.

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of Coherent Oscillation of a Single Nuclear Spin and Realization of a Two-Qubit Conditional Quantum Gate,” Phys. Rev. Lett.  93, 130501 (2004).
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A. Gruber, A. Dräbenstedt, C. Tietz, L. Fleury, J. Wratchtrup, and C. v. Borczyskowski, “Scanning confocal optical microscopy and magnetic resonance on single defect centers,” Science 276, 2012–2014 (1997).

Gurudev Dutt, M. V.

L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent Dynamics of Coupled Electron and Nuclear Spin Qubits in Diamond,” Science 314(5797), 281–285 (2006).

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P. Velha, J. C. Rodier, P. Lalanne, J. D. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett.  89, 171121 (2006).

Harris, J. G. E.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to micromechanical membrane,” Nature 452, 72–75 (2008).
[PubMed]

Heidmann, A.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–73 (2006).
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M. Pinard, Y. Hadjar, and A. Heidmann, “Effective mass in quantum effects of radiation pressure,” Eur. Phys. J. D  7, 107–116 (1999).

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C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. D. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent Population Trapping of Single Spins in Diamond under Optical Excitation,” Phys. Rev. Lett.  97, 247401 (2006).

Hemmer, P. R.

M. V. G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum Register Based on Individual Electronic and Nuclear Spin Qubits in Diamond,” Science 316(5829), 1312–1316 (2007).

L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent Dynamics of Coupled Electron and Nuclear Spin Qubits in Diamond,” Science 314(5797), 281–285 (2006).

Hertzberg, J. B.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. As-pelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[PubMed]

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S. Kühn, C. Hettich, C. Schmitt, J-PH. Poizat, and V. Sandoghdar, “Diamond colour centres as a nanoscopic light source for scanning near field microscopy,” J. Microsc.  202, 2–6 (2001).
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C. Sauvan, P. Lalanne, and J. P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B  71, 165118 (2005).

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M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett.  30, 3042–3044 (2005).
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S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory and Maxwell’s equations with shifting material boundaries,” Phys. Rev. E  65, 066611 (2002).

III, R. H. O.

R. H. O. III and I. El-Kady, “Microfabricated phononic crystal devices and applications,” Meas. Sci. Technol.  20, 012002 (2008).

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J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-Bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).

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J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to micromechanical membrane,” Nature 452, 72–75 (2008).
[PubMed]

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M. V. G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum Register Based on Individual Electronic and Nuclear Spin Qubits in Diamond,” Science 316(5829), 1312–1316 (2007).

L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent Dynamics of Coupled Electron and Nuclear Spin Qubits in Diamond,” Science 314(5797), 281–285 (2006).

C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. D. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent Population Trapping of Single Spins in Diamond under Optical Excitation,” Phys. Rev. Lett.  97, 247401 (2006).

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of Coherent Oscillation of a Single Nuclear Spin and Realization of a Two-Qubit Conditional Quantum Gate,” Phys. Rev. Lett.  93, 130501 (2004).
[PubMed]

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M. V. G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum Register Based on Individual Electronic and Nuclear Spin Qubits in Diamond,” Science 316(5829), 1312–1316 (2007).

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M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett.  30, 3042–3044 (2005).
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S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory and Maxwell’s equations with shifting material boundaries,” Phys. Rev. E  65, 066611 (2002).

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-Bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).

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A. R. M. Zain, N. P. Johnson, M. Solel, and R. M. D. L. Rue, “Ultra high quality factor one-dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI),” Opt. Express 16, 12,084–12,089 (2008).

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M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett.  30, 3042–3044 (2005).
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S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory and Maxwell’s equations with shifting material boundaries,” Phys. Rev. E  65, 066611 (2002).

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J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-Bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).

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T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity,” Phys. Rev. Lett.  95, 033901 (2005).
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S. Kühn, C. Hettich, C. Schmitt, J-PH. Poizat, and V. Sandoghdar, “Diamond colour centres as a nanoscopic light source for scanning near field microscopy,” J. Microsc.  202, 2–6 (2001).
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M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q Nanocavity with 1D Photonic Gap,” Opt. Express 16, 11,905–11,102 (2008).

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical Wavelength and Energy Conversion in High-Q Double-Layer Cavities of Photonic Crystal Slabs,” Phys. Rev. Lett.  97, 023903 (2006).
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P. Velha, J. C. Rodier, P. Lalanne, J. D. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett.  89, 171121 (2006).

C. Sauvan, P. Lalanne, and J. P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B  71, 165118 (2005).

Langer, G.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. As-pelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
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P. E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, “Integration of fiber-coupled high-Q SiNx microdisks with atom chips,” Appl. Phys. Lett.  89, 131108 (2006).

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M. W. McCutcheon and M. Loncar, “Design of a silicon nitride photonic crystal nanocavity with a Quality factor of one million for coupling to a diamond nanocrystal,” Opt. Express 16, 19,136–19,145 (2008).

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett.  30, 3042–3044 (2005).
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M. V. G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum Register Based on Individual Electronic and Nuclear Spin Qubits in Diamond,” Science 316(5829), 1312–1316 (2007).

L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent Dynamics of Coupled Electron and Nuclear Spin Qubits in Diamond,” Science 314(5797), 281–285 (2006).

Mabuchi, H.

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

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J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall Mode Volumes in Dielectric Optical Micro-cavities,” Phys. Rev. Lett.  95, 143901 (2005).
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J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to micromechanical membrane,” Nature 452, 72–75 (2008).
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T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett.  99, 160801 (2007).
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M. V. G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum Register Based on Individual Electronic and Nuclear Spin Qubits in Diamond,” Science 316(5829), 1312–1316 (2007).

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B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, “Observation and characterization of an optical spring,” Phys. Rev. A  69, 051801(R) (2004).

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M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical Wavelength and Energy Conversion in High-Q Double-Layer Cavities of Photonic Crystal Slabs,” Phys. Rev. Lett.  97, 023903 (2006).
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C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. D. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent Population Trapping of Single Spins in Diamond under Optical Excitation,” Phys. Rev. Lett.  97, 247401 (2006).

Nooshi, N.

A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, “Radiation Pressure Cooling of a Micromechanical Oscillator Using Dynamical Backaction,” Phys. Rev. Lett.  97, 243905 (2006).

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M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q Nanocavity with 1D Photonic Gap,” Opt. Express 16, 11,905–11,102 (2008).

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical Wavelength and Energy Conversion in High-Q Double-Layer Cavities of Photonic Crystal Slabs,” Phys. Rev. Lett.  97, 023903 (2006).
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C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. D. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent Population Trapping of Single Spins in Diamond under Optical Excitation,” Phys. Rev. Lett.  97, 247401 (2006).

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T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett.  99, 160801 (2007).
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P. E. Barclay, O. Painter, C. Santori, K.-M. Fu, and R. G. Beausoleil, “Coherent interference effects in a nano-assembled optical cavity-QED system,” ArXiv:0812.4505 (2008).

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

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microcavities excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005).
[PubMed]

O. Painter, K. Srinivasan, and P. E. Barclay, “A Wannier-like equation for photon states of locally perturbed photonic crystals,” Phys. Rev. B  68, 035214 (2003).

Parpia, J. M.

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

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).

Paternostro, M.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. As-pelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[PubMed]

Peyrade, D.

P. Velha, J. C. Rodier, P. Lalanne, J. D. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett.  89, 171121 (2006).

Picard, E.

P. Velha, J. C. Rodier, P. Lalanne, J. D. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett.  89, 171121 (2006).

Pinard, M.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–73 (2006).
[PubMed]

M. Pinard, Y. Hadjar, and A. Heidmann, “Effective mass in quantum effects of radiation pressure,” Eur. Phys. J. D  7, 107–116 (1999).

Poizat, J.-P.

A. Beveratos, R. Brouri, T. Gacoin, J.-P. Poizat, and P. Grangier, “Nonclassical radiation from diamond nanocrys-tals,” Phys. Rev. A  64, 061802 (2001).

Poizat, J-PH.

S. Kühn, C. Hettich, C. Schmitt, J-PH. Poizat, and V. Sandoghdar, “Diamond colour centres as a nanoscopic light source for scanning near field microscopy,” J. Microsc.  202, 2–6 (2001).
[PubMed]

Popa, I.

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of Coherent Oscillation of a Single Nuclear Spin and Realization of a Two-Qubit Conditional Quantum Gate,” Phys. Rev. Lett.  93, 130501 (2004).
[PubMed]

Povinelli, M. L.

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett.  30, 3042–3044 (2005).
[PubMed]

Prawer, S.

C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. D. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent Population Trapping of Single Spins in Diamond under Optical Excitation,” Phys. Rev. Lett.  97, 247401 (2006).

Rabeau, J.

C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. D. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent Population Trapping of Single Spins in Diamond under Optical Excitation,” Phys. Rev. Lett.  97, 247401 (2006).

Regal, C. A.

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

Reichenbach, R. B.

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).

Robinson, J. T.

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

Rodier, J. C.

P. Velha, J. C. Rodier, P. Lalanne, J. D. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett.  89, 171121 (2006).

Rokhsari, H.

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

Rue, R. M. D. L.

A. R. M. Zain, N. P. Johnson, M. Solel, and R. M. D. L. Rue, “Ultra high quality factor one-dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI),” Opt. Express 16, 12,084–12,089 (2008).

Rugar, D.

T. D. Stowe, K. Yasumura, T. W. Kenny, D. Botkin, K. Wago, and D. Rugar, “Attonewton force detection using ultrathin silicon cantilevers,” Appl. Phys. Lett.  71, 288–290 (1997).

Sandoghdar, V.

S. Kühn, C. Hettich, C. Schmitt, J-PH. Poizat, and V. Sandoghdar, “Diamond colour centres as a nanoscopic light source for scanning near field microscopy,” J. Microsc.  202, 2–6 (2001).
[PubMed]

Santori, C.

P. E. Barclay, O. Painter, C. Santori, K.-M. Fu, and R. G. Beausoleil, “Coherent interference effects in a nano-assembled optical cavity-QED system,” ArXiv:0812.4505 (2008).

C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. D. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent Population Trapping of Single Spins in Diamond under Optical Excitation,” Phys. Rev. Lett.  97, 247401 (2006).

Sauvan, C.

C. Sauvan, P. Lalanne, and J. P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B  71, 165118 (2005).

Scherer, A.

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

Schietinger, S.

S. Schietinger, T. Schroder, and O. Benson, “One-by-One Coupling of Single Defect Centers in Nanodiamonds to High-Q Modes of an Optical Microresonator,” Nano. Lett.  8, 3911–3915 (2008).
[PubMed]

Schliesser, A.

A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, “Radiation Pressure Cooling of a Micromechanical Oscillator Using Dynamical Backaction,” Phys. Rev. Lett.  97, 243905 (2006).

Schmitt, C.

S. Kühn, C. Hettich, C. Schmitt, J-PH. Poizat, and V. Sandoghdar, “Diamond colour centres as a nanoscopic light source for scanning near field microscopy,” J. Microsc.  202, 2–6 (2001).
[PubMed]

Schroder, T.

S. Schietinger, T. Schroder, and O. Benson, “One-by-One Coupling of Single Defect Centers in Nanodiamonds to High-Q Modes of an Optical Microresonator,” Nano. Lett.  8, 3911–3915 (2008).
[PubMed]

Schwab, K. C.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. As-pelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[PubMed]

Sheard, B. S.

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, “Observation and characterization of an optical spring,” Phys. Rev. A  69, 051801(R) (2004).

Sigg, D.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett.  99, 160801 (2007).
[PubMed]

Skorobogatiy, M. A.

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

Smith, H. I.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-Bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).

Smith, N.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett.  99, 160801 (2007).
[PubMed]

Smythe, E. J.

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett.  30, 3042–3044 (2005).
[PubMed]

Solel, M.

A. R. M. Zain, N. P. Johnson, M. Solel, and R. M. D. L. Rue, “Ultra high quality factor one-dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI),” Opt. Express 16, 12,084–12,089 (2008).

Srinivasan, K.

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

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microcavities excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005).
[PubMed]

O. Painter, K. Srinivasan, and P. E. Barclay, “A Wannier-like equation for photon states of locally perturbed photonic crystals,” Phys. Rev. B  68, 035214 (2003).

Steinmeyer, G.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-Bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).

Stowe, T. D.

T. D. Stowe, K. Yasumura, T. W. Kenny, D. Botkin, K. Wago, and D. Rugar, “Attonewton force detection using ultrathin silicon cantilevers,” Appl. Phys. Lett.  71, 288–290 (1997).

Tamarat, P.

C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. D. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent Population Trapping of Single Spins in Diamond under Optical Excitation,” Phys. Rev. Lett.  97, 247401 (2006).

Taniyama, H.

M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q Nanocavity with 1D Photonic Gap,” Opt. Express 16, 11,905–11,102 (2008).

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical Wavelength and Energy Conversion in High-Q Double-Layer Cavities of Photonic Crystal Slabs,” Phys. Rev. Lett.  97, 023903 (2006).
[PubMed]

Taylor, J. M.

L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent Dynamics of Coupled Electron and Nuclear Spin Qubits in Diamond,” Science 314(5797), 281–285 (2006).

Thoen, E. R.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-Bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).

Thompson, J. D.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to micromechanical membrane,” Nature 452, 72–75 (2008).
[PubMed]

Tietz, C.

A. Gruber, A. Dräbenstedt, C. Tietz, L. Fleury, J. Wratchtrup, and C. v. Borczyskowski, “Scanning confocal optical microscopy and magnetic resonance on single defect centers,” Science 276, 2012–2014 (1997).

Togan, E.

M. V. G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum Register Based on Individual Electronic and Nuclear Spin Qubits in Diamond,” Science 316(5829), 1312–1316 (2007).

Tuefel, J. D.

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

Vahala, K.

T. J. Kippenberg and K. Vahala, “Cavity Optomechanics,” Opt. Express 15, 17,172–17,205 (2007).

Vahala, K. J.

T. J. Kippenberg and K. J. Vahala, “Cavity Optomechanics: Back-Action at the Mesoscale,” Science 321, 1172–1176 (2008).
[PubMed]

M. Hossein-Zadeh and K. J. Vahala, “Observation of optical spring effect in a microtoroidal optomechanical resonator,” Opt. Lett.  32, 1611–1613 (2007).
[PubMed]

A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, “Radiation Pressure Cooling of a Micromechanical Oscillator Using Dynamical Backaction,” Phys. Rev. Lett.  97, 243905 (2006).

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

van der Straten, P.

H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping, Graduate Texts in Contemporary Physics (Springer, New York, NY, 1999).

Velha, P.

P. Velha, J. C. Rodier, P. Lalanne, J. D. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett.  89, 171121 (2006).

Verbridge, S. S.

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

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).

Vignes, E.

P. Meystre, E. M. Wright, J. D. McCullen, and E. Vignes, “Theory of radiation-pressure-driven interferometers,” J. Opt. Soc. Am. B  2, 1830–1840 (1985).

Villeneuve, P. R.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-Bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).

Wago, K.

T. D. Stowe, K. Yasumura, T. W. Kenny, D. Botkin, K. Wago, and D. Rugar, “Attonewton force detection using ultrathin silicon cantilevers,” Appl. Phys. Lett.  71, 288–290 (1997).

Weisberg, O.

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

Whitcomb, S.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett.  99, 160801 (2007).
[PubMed]

Whitcomb, S. E.

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, “Observation and characterization of an optical spring,” Phys. Rev. A  69, 051801(R) (2004).

Wipf, C.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett.  99, 160801 (2007).
[PubMed]

Wrachtrup, J.

L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent Dynamics of Coupled Electron and Nuclear Spin Qubits in Diamond,” Science 314(5797), 281–285 (2006).

C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. D. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent Population Trapping of Single Spins in Diamond under Optical Excitation,” Phys. Rev. Lett.  97, 247401 (2006).

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of Coherent Oscillation of a Single Nuclear Spin and Realization of a Two-Qubit Conditional Quantum Gate,” Phys. Rev. Lett.  93, 130501 (2004).
[PubMed]

Wratchtrup, J.

A. Gruber, A. Dräbenstedt, C. Tietz, L. Fleury, J. Wratchtrup, and C. v. Borczyskowski, “Scanning confocal optical microscopy and magnetic resonance on single defect centers,” Science 276, 2012–2014 (1997).

Wright, E. M.

P. Meystre, E. M. Wright, J. D. McCullen, and E. Vignes, “Theory of radiation-pressure-driven interferometers,” J. Opt. Soc. Am. B  2, 1830–1840 (1985).

Yasumura, K.

T. D. Stowe, K. Yasumura, T. W. Kenny, D. Botkin, K. Wago, and D. Rugar, “Attonewton force detection using ultrathin silicon cantilevers,” Appl. Phys. Lett.  71, 288–290 (1997).

Zain, A. R. M.

A. R. M. Zain, N. P. Johnson, M. Solel, and R. M. D. L. Rue, “Ultra high quality factor one-dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI),” Opt. Express 16, 12,084–12,089 (2008).

Zeilinger, A.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. As-pelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[PubMed]

Zibrov, A. S.

M. V. G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum Register Based on Individual Electronic and Nuclear Spin Qubits in Diamond,” Science 316(5829), 1312–1316 (2007).

L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent Dynamics of Coupled Electron and Nuclear Spin Qubits in Diamond,” Science 314(5797), 281–285 (2006).

Zwickl, B. M.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to micromechanical membrane,” Nature 452, 72–75 (2008).
[PubMed]

Appl. Phys. Lett (4)

T. D. Stowe, K. Yasumura, T. W. Kenny, D. Botkin, K. Wago, and D. Rugar, “Attonewton force detection using ultrathin silicon cantilevers,” Appl. Phys. Lett.  71, 288–290 (1997).

P. Velha, J. C. Rodier, P. Lalanne, J. D. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett.  89, 171121 (2006).

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

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

Eur. Phys. J (1)

M. Pinard, Y. Hadjar, and A. Heidmann, “Effective mass in quantum effects of radiation pressure,” Eur. Phys. J. D  7, 107–116 (1999).

J. Appl. Phys (1)

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).

J. Microsc (1)

S. Kühn, C. Hettich, C. Schmitt, J-PH. Poizat, and V. Sandoghdar, “Diamond colour centres as a nanoscopic light source for scanning near field microscopy,” J. Microsc.  202, 2–6 (2001).
[PubMed]

J. Opt. Soc. Am (1)

P. Meystre, E. M. Wright, J. D. McCullen, and E. Vignes, “Theory of radiation-pressure-driven interferometers,” J. Opt. Soc. Am. B  2, 1830–1840 (1985).

Meas. Sci. Technol (1)

R. H. O. III and I. El-Kady, “Microfabricated phononic crystal devices and applications,” Meas. Sci. Technol.  20, 012002 (2008).

Nano. Lett (1)

S. Schietinger, T. Schroder, and O. Benson, “One-by-One Coupling of Single Defect Centers in Nanodiamonds to High-Q Modes of an Optical Microresonator,” Nano. Lett.  8, 3911–3915 (2008).
[PubMed]

Nature (4)

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-Bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–73 (2006).
[PubMed]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. As-pelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[PubMed]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to micromechanical membrane,” Nature 452, 72–75 (2008).
[PubMed]

Nature Phys (1)

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

Opt. Express (5)

M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q Nanocavity with 1D Photonic Gap,” Opt. Express 16, 11,905–11,102 (2008).

M. W. McCutcheon and M. Loncar, “Design of a silicon nitride photonic crystal nanocavity with a Quality factor of one million for coupling to a diamond nanocrystal,” Opt. Express 16, 19,136–19,145 (2008).

T. J. Kippenberg and K. Vahala, “Cavity Optomechanics,” Opt. Express 15, 17,172–17,205 (2007).

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microcavities excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005).
[PubMed]

A. R. M. Zain, N. P. Johnson, M. Solel, and R. M. D. L. Rue, “Ultra high quality factor one-dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI),” Opt. Express 16, 12,084–12,089 (2008).

Opt. Lett (2)

M. Hossein-Zadeh and K. J. Vahala, “Observation of optical spring effect in a microtoroidal optomechanical resonator,” Opt. Lett.  32, 1611–1613 (2007).
[PubMed]

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COMSOL is a multiphysics software package for performing finite-element-method (FEM) simulations. See COMSOL AB, http://www.comsol.com/. We use the COMSOL multiphysics software package to perform both optical and mechanical numerical simulations of the zipper cavity.

Lumerical FDTD Solutions is a finite-difference time-domain software package for performing electromagnetic simulations. See Lumerical Solutions, Inc., http://www.lumerical.com/.

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Figures (10)

Fig. 1.
Fig. 1.

Bandstructure properties of the photonic crystal nanowire. (a) Axial bandstructure of the single beam photonic crystal structure, with nominal width and thickness. k is the wavevector of light in the direction of the 1D photonic lattice, a is the lattice period, and a0 is the “normalized” optical frequency for free-space wavelength λ0. The light cone, denoted by the grey area and deliniated by the black light line, represents regions of frequency-wave-vector space in the bandstructure diagram in which light can radiate into the two transverse directions orthogonal to the axis of the photonic lattice. The two inset images show the electric field energy density of the valence (i) and conduction (ii) band-edge modes (the white outline is a contour plot of the refractive index of the nanowire). (b) Schematic of the double beam zipper cavity indicating the slot gap (s), the lattice constant (a), the beam width (w), and the axial and transverse hole lengths, hx and hy , respectively. (c) Lattice constant (normalized to the lattice period in the mirror section of the cavity, am ) versus hole number (nh ) within the photonic lattice of the cavity. (c,d) Resulting frequency of the valence band-edge mode versus hole number. In (d) the normalized frequency in terms of the local lattice constant, (a0) nh , is displayed. In (e) the local band-edge frequency is referenced to the valence band-edge in the mirror section of the cavity. The solid blue (dashed red) curve is the valence (conduction) band-edge.

Fig. 2.
Fig. 2.

Optical design principle of the zipper cavity. (a) Axial bandstructure of the double beam quasi-1D photonic crystal structure, with nominal width, thickness, and slot gap. The blue curves are the bonded bands and the red curves are the anti-bonded bands. Valence and conduction band-edge modes of the bonded (b,c) and anti-bonded (d,e) bands, respectively. (f) Illustration of the defect cavity formation at the Brillouin-zone boundary. The splitting between the two manifolds is indicated by ∆λ+,-.

Fig. 3.
Fig. 3.

Transverse electric field (E y ) mode profile of the fundamental bonded mode (TE+,0): (a) top-view, (b) cross-section. Transverse electric field (E y ) mode profile of the fundamental anti-bonded mode (TE-,0): (c) top-view, (d) cross-section. The field colormap corresponds to +1 (red), 0 (white), and -1 (blue). Electric field energy density of the (e) fundamental (TE+,0), (f) second-order (TE+,1), and (g) third-order (TE+,2) bonded optical modes. The intensity colormap ranges from +1 (red) to 0 (blue).

Fig. 4.
Fig. 4.

Optical Q-factor (axial, transverse, and total) versus number of hole periods in the cavity, Nh . In these simulations the defect region is maintained the same, with only the number of periods in the mirror section varied. The nominal structure corresponds to the maximum hole number in this plot, Nh = 47.

Fig. 5.
Fig. 5.

(a) Normalized frequency and (b) Optical Q-factor (axial, transverse, and total) versus normalized axial hole length, x . The nominal structure is indicated by the dashed green line.

Fig. 6.
Fig. 6.

(a) Normalized frequency and (b) Optical Q-factor (axial, transverse, and total) versus normalized transverse hole length, y . The nominal structure is indicated by the dashed green line.

Fig. 7.
Fig. 7.

Effective mode volume of the TE0,+ mode versus normalized slot gap, . The nominal structure is indicated by the dashed green line.

Fig. 8.
Fig. 8.

(a) Normalized frequency, (b) Q-factor and (c) Effective mode volume versus normalized beam width. The nominal structure is indicated by the dashed green line.

Fig. 9.
Fig. 9.

Mechanical eigenmode displacement plots: (a) 1st-order in-plane common mode, (b) 1st-order in-plane differential mode, (c) 1st-order out-of-plane common mode, and (d) 1st-order out-of-plane differential mode. The color represents total displacement amplitude, as does the deformation of the structure. The arrows indicate the local direction of displacement.

Fig. 10.
Fig. 10.

(a) Bonded and anti-bonded mode tuning curves versus normalized nanobeam gap. (b) Corresponding normalized effective optomehcanical coupling length, OML OM/am . The nominal structure is indicated by the dashed green line.

Tables (1)

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Table 1. Summary of mechanical mode properties. Optomechanical coupling factor is for the TE0,+ mode.

Equations (6)

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V eff ( r 0 ) ε ( r ) E ( r ) 2 d 3 r ε ( r 0 ) E ( r 0 ) 2 ,
Ω q / 2 π = q 2 π 2 I 2 Y I y ρ A 1 + σA 1 2 q 2 Y I y π 2 ,
u n ( r , t ) = u n i f n ( x ; i ) i 1 1 0 1 f n ( x ; i ) 2 d x ,
g OM , h qd g OM , 0 f ̅ h qd ( x ; i ) E ˜ TE + , 0 ( x ) 2 d x E ˜ TE + , 0 ( x ) 2 d x ,
( Ω M ) 2 = Ω M 2 + ( 2 a 0 2 g OM 2 Δ 2 ω c m u ) Δ o ,
γ M = γ M ( 4 a 0 2 g OM 2 Γ Δ 4 ω c m u ) Δ o ,

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