Abstract

Nonlinear optomechanical coupling is the basis for many potential future experiments in quantum optomechanics (e.g., quantum nondemolition measurements, preparation of nonclassical states), which to date have been difficult to realize due to small nonlinearity in typical optomechanical devices. Here we introduce an optomechanical system combining strong nonlinear optomechanical coupling, low mass, and large optical mode spacing. This nanoscale “paddle nanocavity” supports mechanical resonances with hundreds of femtograms of mass that couple nonlinearly to optical modes with a quadratic optomechanical coupling coefficient g(2)>2π×400MHz/nm2, and a single-photon to two-phonon optomechanical coupling rate of Δω0>2π×16Hz. This coupling relies on strong phonon–photon interactions in a structure whose optical mode spectrum is highly nondegenerate. Nonlinear optomechanical readout of thermally driven motion in these devices should be observable for T>50mK, and measurement of phonon shot noise is achievable. This shows that strong nonlinear effects can be realized without relying on coupling between nearly degenerate optical modes, thus avoiding the parasitic linear coupling present in two-mode systems.

© 2015 Optical Society of America

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2014 (4)

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, and P. E. Barclay, Phys. Rev. X 4, 021052 (2014).
[Crossref]

J.-Q. Liao and F. Nori, Sci. Rep. 4, 6302 (2014).
[Crossref]

C. Doolin, B. Hauer, P. Kim, A. MacDonald, H. Ramp, and J. Davis, Phys. Rev. A 89, 053838 (2014).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

2013 (3)

M. Karuza, M. Galassi, C. Biancofiore, C. Molinelli, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, J. Opt. 15, 025704 (2013).
[Crossref]

A. C. Hryciw and P. E. Barclay, Opt. Lett. 38, 1612 (2013).
[Crossref]

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, Nature 500, 185 (2013).
[Crossref]

2012 (6)

X. Sun, J. Zhang, M. Poot, C. W. Wong, and H. X. Tang, Nano Lett. 12, 2299 (2012).
[Crossref]

M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquardt, Phys. Rev. Lett. 109, 063601 (2012).
[Crossref]

Y. Liu, H. Miao, V. Aksyuk, and K. Srinivasan, Opt. Express 20, 18268 (2012).
[Crossref]

N. Flowers-Jacobs, S. Hoch, J. Sankey, A. Kashkanova, A. Jayich, C. Deutsch, J. Reichel, and J. Harris, Appl. Phys. Lett. 101, 221109 (2012).
[Crossref]

E. Gavartin, P. Verlot, and T. J. Kippenberg, Nat. Nanotechnol. 7, 509 (2012).
[Crossref]

A. G. Krause, M. Winger, T. D. Blasius, W. Lin, and O. Painter, Nat. Photonics 6, 768 (2012).
[Crossref]

2011 (3)

A. W. Rodriguez, A. P. McCauley, P.-C. Hui, D. Woolf, E. Iwase, F. Capasso, M. Loncar, and S. G. Johnson, Opt. Express 19, 2225 (2011).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, Nature 478, 89 (2011).
[Crossref]

C. Biancofiore, M. Karuza, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, Phys. Rev. A 84, 033814 (2011).
[Crossref]

2010 (5)

A. Nunnenkamp, K. Børkje, J. G. E. Harris, and S. M. Girvin, Phys. Rev. A 82, 021806 (2010).
[Crossref]

J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, Nat. Phys. 6, 707 (2010).
[Crossref]

G. Heinrich, J. Harris, and F. Marquardt, Phys. Rev. A 81, 011801 (2010).
[Crossref]

A. A. Clerk, F. Marquardt, and J. G. E. Harris, Phys. Rev. Lett. 104, 213603 (2010).
[Crossref]

Q. Quan, P. B. Deotare, and M. Loncar, Appl. Phys. Lett. 96, 203102 (2010).
[Crossref]

2009 (3)

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, Opt. Express 17, 20078 (2009).
[Crossref]

M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, Nature 462, 78 (2009).
[Crossref]

H. Miao, S. Danilishin, T. Corbitt, and Y. Chen, Phys. Rev. Lett. 103, 100402 (2009).
[Crossref]

2008 (3)

M. Bhattacharya, H. Uys, and P. Meystre, Phys. Rev. A 77, 033819 (2008).
[Crossref]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, Nature 452, 72 (2008).
[Crossref]

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, New J. Phys. 10, 095008 (2008).
[Crossref]

2002 (1)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
[Crossref]

Aksyuk, V.

Alegre, T. P. M.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, Nature 478, 89 (2011).
[Crossref]

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, Nature 500, 185 (2013).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, Nature 478, 89 (2011).
[Crossref]

Barclay, P. E.

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, and P. E. Barclay, Phys. Rev. X 4, 021052 (2014).
[Crossref]

A. C. Hryciw and P. E. Barclay, Opt. Lett. 38, 1612 (2013).
[Crossref]

Bhattacharya, M.

M. Bhattacharya, H. Uys, and P. Meystre, Phys. Rev. A 77, 033819 (2008).
[Crossref]

Biancofiore, C.

M. Karuza, M. Galassi, C. Biancofiore, C. Molinelli, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, J. Opt. 15, 025704 (2013).
[Crossref]

C. Biancofiore, M. Karuza, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, Phys. Rev. A 84, 033814 (2011).
[Crossref]

Blasius, T. D.

A. G. Krause, M. Winger, T. D. Blasius, W. Lin, and O. Painter, Nat. Photonics 6, 768 (2012).
[Crossref]

Boisen, A.

G. A. Brawley, M. R. Vanner, P. E. Larsen, S. Schmid, A. Boisen, and W. P. Bowen, “Non-linear optomechanical measurement of mechanical motion,” arXiv:1404.5746 (2014).

Børkje, K.

A. Nunnenkamp, K. Børkje, J. G. E. Harris, and S. M. Girvin, Phys. Rev. A 82, 021806 (2010).
[Crossref]

Bowen, W. P.

G. A. Brawley, M. R. Vanner, P. E. Larsen, S. Schmid, A. Boisen, and W. P. Bowen, “Non-linear optomechanical measurement of mechanical motion,” arXiv:1404.5746 (2014).

Brawley, G. A.

G. A. Brawley, M. R. Vanner, P. E. Larsen, S. Schmid, A. Boisen, and W. P. Bowen, “Non-linear optomechanical measurement of mechanical motion,” arXiv:1404.5746 (2014).

Camacho, R.

M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, Nature 462, 78 (2009).
[Crossref]

Capasso, F.

Chan, J.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, Nature 500, 185 (2013).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, Nature 478, 89 (2011).
[Crossref]

M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, Nature 462, 78 (2009).
[Crossref]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, Opt. Express 17, 20078 (2009).
[Crossref]

Chen, Y.

H. Miao, S. Danilishin, T. Corbitt, and Y. Chen, Phys. Rev. Lett. 103, 100402 (2009).
[Crossref]

Clerk, A.

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, New J. Phys. 10, 095008 (2008).
[Crossref]

Clerk, A. A.

A. A. Clerk, F. Marquardt, and J. G. E. Harris, Phys. Rev. Lett. 104, 213603 (2010).
[Crossref]

Corbitt, T.

H. Miao, S. Danilishin, T. Corbitt, and Y. Chen, Phys. Rev. Lett. 103, 100402 (2009).
[Crossref]

Danilishin, S.

H. Miao, S. Danilishin, T. Corbitt, and Y. Chen, Phys. Rev. Lett. 103, 100402 (2009).
[Crossref]

Davis, J.

C. Doolin, B. Hauer, P. Kim, A. MacDonald, H. Ramp, and J. Davis, Phys. Rev. A 89, 053838 (2014).
[Crossref]

B. Hauer, J. Maciejko, and J. Davis, “Nonlinear power spectral densities for the harmonic oscillator,” arXiv:1502.02372 (2015).

Davis, J. P.

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, and P. E. Barclay, Phys. Rev. X 4, 021052 (2014).
[Crossref]

Deotare, P. B.

Q. Quan, P. B. Deotare, and M. Loncar, Appl. Phys. Lett. 96, 203102 (2010).
[Crossref]

Deutsch, C.

N. Flowers-Jacobs, S. Hoch, J. Sankey, A. Kashkanova, A. Jayich, C. Deutsch, J. Reichel, and J. Harris, Appl. Phys. Lett. 101, 221109 (2012).
[Crossref]

Di Giuseppe, G.

M. Karuza, M. Galassi, C. Biancofiore, C. Molinelli, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, J. Opt. 15, 025704 (2013).
[Crossref]

C. Biancofiore, M. Karuza, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, Phys. Rev. A 84, 033814 (2011).
[Crossref]

Doolin, C.

C. Doolin, B. Hauer, P. Kim, A. MacDonald, H. Ramp, and J. Davis, Phys. Rev. A 89, 053838 (2014).
[Crossref]

Eichenfield, M.

M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, Nature 462, 78 (2009).
[Crossref]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, Opt. Express 17, 20078 (2009).
[Crossref]

Fink, Y.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
[Crossref]

Flowers-Jacobs, N.

N. Flowers-Jacobs, S. Hoch, J. Sankey, A. Kashkanova, A. Jayich, C. Deutsch, J. Reichel, and J. Harris, Appl. Phys. Lett. 101, 221109 (2012).
[Crossref]

Freeman, M. R.

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, and P. E. Barclay, Phys. Rev. X 4, 021052 (2014).
[Crossref]

Galassi, M.

M. Karuza, M. Galassi, C. Biancofiore, C. Molinelli, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, J. Opt. 15, 025704 (2013).
[Crossref]

C. Biancofiore, M. Karuza, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, Phys. Rev. A 84, 033814 (2011).
[Crossref]

Gavartin, E.

E. Gavartin, P. Verlot, and T. J. Kippenberg, Nat. Nanotechnol. 7, 509 (2012).
[Crossref]

Girvin, S.

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, New J. Phys. 10, 095008 (2008).
[Crossref]

Girvin, S. M.

A. Nunnenkamp, K. Børkje, J. G. E. Harris, and S. M. Girvin, Phys. Rev. A 82, 021806 (2010).
[Crossref]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, Nature 452, 72 (2008).
[Crossref]

Groblacher, S.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, Nature 478, 89 (2011).
[Crossref]

Gröblacher, S.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, Nature 500, 185 (2013).
[Crossref]

Harris, J.

N. Flowers-Jacobs, S. Hoch, J. Sankey, A. Kashkanova, A. Jayich, C. Deutsch, J. Reichel, and J. Harris, Appl. Phys. Lett. 101, 221109 (2012).
[Crossref]

G. Heinrich, J. Harris, and F. Marquardt, Phys. Rev. A 81, 011801 (2010).
[Crossref]

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, New J. Phys. 10, 095008 (2008).
[Crossref]

D. Lee, M. Underwood, D. Mason, A. Shkarin, S. Hoch, and J. Harris, “Multimode optomechanical dynamics in a cavity with avoided crossings,” arXiv:1401.2968 (2014).

Harris, J. G. E.

A. Nunnenkamp, K. Børkje, J. G. E. Harris, and S. M. Girvin, Phys. Rev. A 82, 021806 (2010).
[Crossref]

J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, Nat. Phys. 6, 707 (2010).
[Crossref]

A. A. Clerk, F. Marquardt, and J. G. E. Harris, Phys. Rev. Lett. 104, 213603 (2010).
[Crossref]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, Nature 452, 72 (2008).
[Crossref]

Hauer, B.

C. Doolin, B. Hauer, P. Kim, A. MacDonald, H. Ramp, and J. Davis, Phys. Rev. A 89, 053838 (2014).
[Crossref]

B. Hauer, J. Maciejko, and J. Davis, “Nonlinear power spectral densities for the harmonic oscillator,” arXiv:1502.02372 (2015).

Healey, C.

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, and P. E. Barclay, Phys. Rev. X 4, 021052 (2014).
[Crossref]

Heinrich, G.

G. Heinrich, J. Harris, and F. Marquardt, Phys. Rev. A 81, 011801 (2010).
[Crossref]

Hill, J. T.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, Nature 500, 185 (2013).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, Nature 478, 89 (2011).
[Crossref]

J. T. Hill, “Nonlinear optics and wavelength translation via cavity-optomechanics,” Ph.D. thesis (California Institute of Technology, 2013).

Hoch, S.

N. Flowers-Jacobs, S. Hoch, J. Sankey, A. Kashkanova, A. Jayich, C. Deutsch, J. Reichel, and J. Harris, Appl. Phys. Lett. 101, 221109 (2012).
[Crossref]

D. Lee, M. Underwood, D. Mason, A. Shkarin, S. Hoch, and J. Harris, “Multimode optomechanical dynamics in a cavity with avoided crossings,” arXiv:1401.2968 (2014).

Hryciw, A. C.

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, and P. E. Barclay, Phys. Rev. X 4, 021052 (2014).
[Crossref]

A. C. Hryciw and P. E. Barclay, Opt. Lett. 38, 1612 (2013).
[Crossref]

Hui, P.-C.

Ibanescu, M.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
[Crossref]

Iwase, E.

Jayakumar, H.

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, and P. E. Barclay, Phys. Rev. X 4, 021052 (2014).
[Crossref]

Jayich, A.

N. Flowers-Jacobs, S. Hoch, J. Sankey, A. Kashkanova, A. Jayich, C. Deutsch, J. Reichel, and J. Harris, Appl. Phys. Lett. 101, 221109 (2012).
[Crossref]

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, New J. Phys. 10, 095008 (2008).
[Crossref]

Jayich, A. M.

J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, Nat. Phys. 6, 707 (2010).
[Crossref]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, Nature 452, 72 (2008).
[Crossref]

Joannopoulos, J. D.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
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Johnson, S. G.

A. W. Rodriguez, A. P. McCauley, P.-C. Hui, D. Woolf, E. Iwase, F. Capasso, M. Loncar, and S. G. Johnson, Opt. Express 19, 2225 (2011).
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S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
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Karuza, M.

M. Karuza, M. Galassi, C. Biancofiore, C. Molinelli, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, J. Opt. 15, 025704 (2013).
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C. Biancofiore, M. Karuza, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, Phys. Rev. A 84, 033814 (2011).
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N. Flowers-Jacobs, S. Hoch, J. Sankey, A. Kashkanova, A. Jayich, C. Deutsch, J. Reichel, and J. Harris, Appl. Phys. Lett. 101, 221109 (2012).
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C. Doolin, B. Hauer, P. Kim, A. MacDonald, H. Ramp, and J. Davis, Phys. Rev. A 89, 053838 (2014).
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M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
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E. Gavartin, P. Verlot, and T. J. Kippenberg, Nat. Nanotechnol. 7, 509 (2012).
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J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, Nature 478, 89 (2011).
[Crossref]

Krause, A. G.

A. G. Krause, M. Winger, T. D. Blasius, W. Lin, and O. Painter, Nat. Photonics 6, 768 (2012).
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Lake, D. P.

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, and P. E. Barclay, Phys. Rev. X 4, 021052 (2014).
[Crossref]

Larsen, P. E.

G. A. Brawley, M. R. Vanner, P. E. Larsen, S. Schmid, A. Boisen, and W. P. Bowen, “Non-linear optomechanical measurement of mechanical motion,” arXiv:1404.5746 (2014).

Lee, D.

D. Lee, M. Underwood, D. Mason, A. Shkarin, S. Hoch, and J. Harris, “Multimode optomechanical dynamics in a cavity with avoided crossings,” arXiv:1401.2968 (2014).

Liao, J.-Q.

J.-Q. Liao and F. Nori, Sci. Rep. 4, 6302 (2014).
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Lin, W.

A. G. Krause, M. Winger, T. D. Blasius, W. Lin, and O. Painter, Nat. Photonics 6, 768 (2012).
[Crossref]

Liu, Y.

Loncar, M.

Ludwig, M.

M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquardt, Phys. Rev. Lett. 109, 063601 (2012).
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MacDonald, A.

C. Doolin, B. Hauer, P. Kim, A. MacDonald, H. Ramp, and J. Davis, Phys. Rev. A 89, 053838 (2014).
[Crossref]

Maciejko, J.

B. Hauer, J. Maciejko, and J. Davis, “Nonlinear power spectral densities for the harmonic oscillator,” arXiv:1502.02372 (2015).

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M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
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M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquardt, Phys. Rev. Lett. 109, 063601 (2012).
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A. A. Clerk, F. Marquardt, and J. G. E. Harris, Phys. Rev. Lett. 104, 213603 (2010).
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G. Heinrich, J. Harris, and F. Marquardt, Phys. Rev. A 81, 011801 (2010).
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A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, New J. Phys. 10, 095008 (2008).
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J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, Nature 452, 72 (2008).
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Mason, D.

D. Lee, M. Underwood, D. Mason, A. Shkarin, S. Hoch, and J. Harris, “Multimode optomechanical dynamics in a cavity with avoided crossings,” arXiv:1401.2968 (2014).

McCauley, A. P.

Meystre, P.

M. Bhattacharya, H. Uys, and P. Meystre, Phys. Rev. A 77, 033819 (2008).
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Miao, H.

Y. Liu, H. Miao, V. Aksyuk, and K. Srinivasan, Opt. Express 20, 18268 (2012).
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H. Miao, S. Danilishin, T. Corbitt, and Y. Chen, Phys. Rev. Lett. 103, 100402 (2009).
[Crossref]

Molinelli, C.

M. Karuza, M. Galassi, C. Biancofiore, C. Molinelli, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, J. Opt. 15, 025704 (2013).
[Crossref]

Natali, R.

M. Karuza, M. Galassi, C. Biancofiore, C. Molinelli, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, J. Opt. 15, 025704 (2013).
[Crossref]

C. Biancofiore, M. Karuza, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, Phys. Rev. A 84, 033814 (2011).
[Crossref]

Nori, F.

J.-Q. Liao and F. Nori, Sci. Rep. 4, 6302 (2014).
[Crossref]

Nunnenkamp, A.

A. Nunnenkamp, K. Børkje, J. G. E. Harris, and S. M. Girvin, Phys. Rev. A 82, 021806 (2010).
[Crossref]

Painter, O.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, Nature 500, 185 (2013).
[Crossref]

M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquardt, Phys. Rev. Lett. 109, 063601 (2012).
[Crossref]

A. G. Krause, M. Winger, T. D. Blasius, W. Lin, and O. Painter, Nat. Photonics 6, 768 (2012).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, Nature 478, 89 (2011).
[Crossref]

M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, Nature 462, 78 (2009).
[Crossref]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, Opt. Express 17, 20078 (2009).
[Crossref]

Poot, M.

X. Sun, J. Zhang, M. Poot, C. W. Wong, and H. X. Tang, Nano Lett. 12, 2299 (2012).
[Crossref]

Quan, Q.

Q. Quan, P. B. Deotare, and M. Loncar, Appl. Phys. Lett. 96, 203102 (2010).
[Crossref]

Ramp, H.

C. Doolin, B. Hauer, P. Kim, A. MacDonald, H. Ramp, and J. Davis, Phys. Rev. A 89, 053838 (2014).
[Crossref]

Reichel, J.

N. Flowers-Jacobs, S. Hoch, J. Sankey, A. Kashkanova, A. Jayich, C. Deutsch, J. Reichel, and J. Harris, Appl. Phys. Lett. 101, 221109 (2012).
[Crossref]

Rodriguez, A. W.

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, Nature 500, 185 (2013).
[Crossref]

M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquardt, Phys. Rev. Lett. 109, 063601 (2012).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, Nature 478, 89 (2011).
[Crossref]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, Opt. Express 17, 20078 (2009).
[Crossref]

Sankey, J.

N. Flowers-Jacobs, S. Hoch, J. Sankey, A. Kashkanova, A. Jayich, C. Deutsch, J. Reichel, and J. Harris, Appl. Phys. Lett. 101, 221109 (2012).
[Crossref]

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, New J. Phys. 10, 095008 (2008).
[Crossref]

Sankey, J. C.

J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, Nat. Phys. 6, 707 (2010).
[Crossref]

Schmid, S.

G. A. Brawley, M. R. Vanner, P. E. Larsen, S. Schmid, A. Boisen, and W. P. Bowen, “Non-linear optomechanical measurement of mechanical motion,” arXiv:1404.5746 (2014).

Shkarin, A.

D. Lee, M. Underwood, D. Mason, A. Shkarin, S. Hoch, and J. Harris, “Multimode optomechanical dynamics in a cavity with avoided crossings,” arXiv:1401.2968 (2014).

Skorobogatiy, M. A.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
[Crossref]

Srinivasan, K.

Sun, X.

X. Sun, J. Zhang, M. Poot, C. W. Wong, and H. X. Tang, Nano Lett. 12, 2299 (2012).
[Crossref]

Tang, H. X.

X. Sun, J. Zhang, M. Poot, C. W. Wong, and H. X. Tang, Nano Lett. 12, 2299 (2012).
[Crossref]

Thompson, J.

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, New J. Phys. 10, 095008 (2008).
[Crossref]

Thompson, J. D.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, Nature 452, 72 (2008).
[Crossref]

Tombesi, P.

M. Karuza, M. Galassi, C. Biancofiore, C. Molinelli, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, J. Opt. 15, 025704 (2013).
[Crossref]

C. Biancofiore, M. Karuza, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, Phys. Rev. A 84, 033814 (2011).
[Crossref]

Underwood, M.

D. Lee, M. Underwood, D. Mason, A. Shkarin, S. Hoch, and J. Harris, “Multimode optomechanical dynamics in a cavity with avoided crossings,” arXiv:1401.2968 (2014).

Uys, H.

M. Bhattacharya, H. Uys, and P. Meystre, Phys. Rev. A 77, 033819 (2008).
[Crossref]

Vahala, K.

M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, Nature 462, 78 (2009).
[Crossref]

Vahala, K. J.

Vanner, M. R.

G. A. Brawley, M. R. Vanner, P. E. Larsen, S. Schmid, A. Boisen, and W. P. Bowen, “Non-linear optomechanical measurement of mechanical motion,” arXiv:1404.5746 (2014).

Verlot, P.

E. Gavartin, P. Verlot, and T. J. Kippenberg, Nat. Nanotechnol. 7, 509 (2012).
[Crossref]

Vitali, D.

M. Karuza, M. Galassi, C. Biancofiore, C. Molinelli, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, J. Opt. 15, 025704 (2013).
[Crossref]

C. Biancofiore, M. Karuza, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, Phys. Rev. A 84, 033814 (2011).
[Crossref]

Weisberg, O.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
[Crossref]

Winger, M.

A. G. Krause, M. Winger, T. D. Blasius, W. Lin, and O. Painter, Nat. Photonics 6, 768 (2012).
[Crossref]

Wong, C. W.

X. Sun, J. Zhang, M. Poot, C. W. Wong, and H. X. Tang, Nano Lett. 12, 2299 (2012).
[Crossref]

Woolf, D.

Wu, M.

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, and P. E. Barclay, Phys. Rev. X 4, 021052 (2014).
[Crossref]

Yang, C.

J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, Nat. Phys. 6, 707 (2010).
[Crossref]

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, New J. Phys. 10, 095008 (2008).
[Crossref]

Zhang, J.

X. Sun, J. Zhang, M. Poot, C. W. Wong, and H. X. Tang, Nano Lett. 12, 2299 (2012).
[Crossref]

Zwickl, B.

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, New J. Phys. 10, 095008 (2008).
[Crossref]

Zwickl, B. M.

J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, Nat. Phys. 6, 707 (2010).
[Crossref]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, Nature 452, 72 (2008).
[Crossref]

Appl. Phys. Lett. (2)

N. Flowers-Jacobs, S. Hoch, J. Sankey, A. Kashkanova, A. Jayich, C. Deutsch, J. Reichel, and J. Harris, Appl. Phys. Lett. 101, 221109 (2012).
[Crossref]

Q. Quan, P. B. Deotare, and M. Loncar, Appl. Phys. Lett. 96, 203102 (2010).
[Crossref]

J. Opt. (1)

M. Karuza, M. Galassi, C. Biancofiore, C. Molinelli, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, J. Opt. 15, 025704 (2013).
[Crossref]

Nano Lett. (1)

X. Sun, J. Zhang, M. Poot, C. W. Wong, and H. X. Tang, Nano Lett. 12, 2299 (2012).
[Crossref]

Nat. Nanotechnol. (1)

E. Gavartin, P. Verlot, and T. J. Kippenberg, Nat. Nanotechnol. 7, 509 (2012).
[Crossref]

Nat. Photonics (1)

A. G. Krause, M. Winger, T. D. Blasius, W. Lin, and O. Painter, Nat. Photonics 6, 768 (2012).
[Crossref]

Nat. Phys. (1)

J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, Nat. Phys. 6, 707 (2010).
[Crossref]

Nature (4)

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, Nature 478, 89 (2011).
[Crossref]

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, Nature 500, 185 (2013).
[Crossref]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, Nature 452, 72 (2008).
[Crossref]

M. Eichenfield, J. Chan, R. Camacho, K. Vahala, and O. Painter, Nature 462, 78 (2009).
[Crossref]

New J. Phys. (1)

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, New J. Phys. 10, 095008 (2008).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (5)

C. Doolin, B. Hauer, P. Kim, A. MacDonald, H. Ramp, and J. Davis, Phys. Rev. A 89, 053838 (2014).
[Crossref]

G. Heinrich, J. Harris, and F. Marquardt, Phys. Rev. A 81, 011801 (2010).
[Crossref]

M. Bhattacharya, H. Uys, and P. Meystre, Phys. Rev. A 77, 033819 (2008).
[Crossref]

A. Nunnenkamp, K. Børkje, J. G. E. Harris, and S. M. Girvin, Phys. Rev. A 82, 021806 (2010).
[Crossref]

C. Biancofiore, M. Karuza, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, Phys. Rev. A 84, 033814 (2011).
[Crossref]

Phys. Rev. E (1)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
[Crossref]

Phys. Rev. Lett. (3)

H. Miao, S. Danilishin, T. Corbitt, and Y. Chen, Phys. Rev. Lett. 103, 100402 (2009).
[Crossref]

A. A. Clerk, F. Marquardt, and J. G. E. Harris, Phys. Rev. Lett. 104, 213603 (2010).
[Crossref]

M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquardt, Phys. Rev. Lett. 109, 063601 (2012).
[Crossref]

Phys. Rev. X (1)

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, and P. E. Barclay, Phys. Rev. X 4, 021052 (2014).
[Crossref]

Rev. Mod. Phys. (1)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

Sci. Rep. (1)

J.-Q. Liao and F. Nori, Sci. Rep. 4, 6302 (2014).
[Crossref]

Other (4)

G. A. Brawley, M. R. Vanner, P. E. Larsen, S. Schmid, A. Boisen, and W. P. Bowen, “Non-linear optomechanical measurement of mechanical motion,” arXiv:1404.5746 (2014).

D. Lee, M. Underwood, D. Mason, A. Shkarin, S. Hoch, and J. Harris, “Multimode optomechanical dynamics in a cavity with avoided crossings,” arXiv:1401.2968 (2014).

J. T. Hill, “Nonlinear optics and wavelength translation via cavity-optomechanics,” Ph.D. thesis (California Institute of Technology, 2013).

B. Hauer, J. Maciejko, and J. Davis, “Nonlinear power spectral densities for the harmonic oscillator,” arXiv:1502.02372 (2015).

Supplementary Material (1)

» Media 1: PDF (926 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

Schematic of the photonic crystal paddle nanocavity (top-view). The paddle is separated from photonic crystal nanobeam mirrors by gaps d = 50 nm , and has length L = 958 nm . The elliptical hole horizontal and vertical semiaxes ( R x , R y ) are tapered as shown.

Fig. 2.
Fig. 2.

(a) Properties of the localized optical modes of the paddle nanocavity (labeled M1–M7): electric field distribution ( E y component), spatial symmetry in x y plane, optical frequency, and contribution g ω 1 ω n ( 2 ) to the quadratic optomechanical coupling g ( 2 ) describing interaction between mode M1 and the S mechanical resonance shown in (b). (b) Displacement profiles and properties of the paddle nanocavity mechanical resonances. m and f m are indicated for three support geometries, p 1 p 3 , whose cross sections are given in (c).

Fig. 3.
Fig. 3.

(a)  S P ( 2 ) ( ω ) generated by thermal motion of the S mode of a paddle nanocavity for p 1 and p 2 support geometry, assuming room temperature operation, Δ = κ / 2 , P i = 100 μW , and Q m = 10 3 . (b)  S P ( 2 ) ( 2 ω m ) as a function of detuning Δ , for varying quadratic coupling strengths g ( 2 ) .

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

g ( 2 ) = ω 2 | E ω | δ ϵ δ x | E ω | 2 | E ω | ϵ | E ω | 2 + ω ω g ω , ω ( 2 ) .
g ω , ω ( 2 ) = ( ω 3 ω 2 ω 2 ) | E ω | δ ϵ δ x | E ω | 2 E ω | ϵ | E ω E ω | ϵ | E ω .
G 1 = d T d x = g ( 1 ) d T d Δ ,
G 2 = d 2 T d x 2 = g ( 2 ) d T d Δ + ( g ( 1 ) ) 2 d 2 T d Δ 2 .
S x 2 ( ω ) = 2 x z p f 4 ( 2 Γ ( n ¯ + 1 ) 2 Γ 2 + ( ω 2 ω m ) 2 + 2 Γ n ¯ 2 Γ 2 + ( ω + 2 ω m ) 2 + 8 Γ n ¯ ( n ¯ + 1 ) + 1 Γ 2 + ω 2 ) ,

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