Abstract

In recent years, some of the most interesting discoveries in science and engineering emerged from interdisciplinary areas that defy the traditional classification. One recent and extensively studied example is the advent of optomechanics that explores the radiation pressure-induced nonlinearity in a solid micro-resonator. Instead of using a solid resonator, we studied a liquid droplet resonator in which optical pressure could actively interact with the fluid interface. The droplet resonator supported high-quality whispering gallery modes along its equatorial plane, which produced a radiation pressure that counterbalances the interfacial tension, resulting in a droplet with damped harmonic oscillation. A major goal of this study was to demonstrate that such a novel and all-liquid platform could lead to a single-photon-level nonlinearity at room temperature. If successful, such a highly nonlinear system may lead to new research paradigms in photonics, fluid mechanics, as well as quantum information science.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (3)

A. Giorgini, S. Avino, P. Malara, P. D. Natale, M. Yannai, T. Carmon, and G. Gagliardi, “Stimulated Brillouin Cavity Optomechanics in Liquid Droplets,” Phys. Rev. Lett. 120(7), 073902 (2018).
[Crossref]

D. Bar-david, S. Maayani, L. Martin, and T. Carmon, “Cavity optofluidics: a µdroplet’s whispering-gallery mode makes a µvortex,” Opt. Express 26(15), 19115–19122 (2018).
[Crossref]

S. Sun, H. Kim, Z. Luo, G. Solomon, and E. Waks, “A single-photon switch and transistor enabled by a solid-state quantum memory,” Science 361(6397), 57–60 (2018).
[Crossref]

2017 (3)

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
[Crossref]

H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys. 13(1), 94–103 (2017).
[Crossref]

K. Qian, J. Tang, H. Guo, W. Liu, J. Liu, C. Xue, Y. Zheng, and C. Zhang, “Under-coupling Whispering Gallery Mode Resonator Applied to Resonant Micro-Optic Gyroscope,” Sensors 17(12), 100 (2017).
[Crossref]

2016 (7)

P. Zhang, S. Jung, A. Lee, and Y. Xu, “Comparative analysis of nonlinear optofluidic processes in microdroplets,” Phys. Rev. E 93(6), 063119 (2016).
[Crossref]

S. T. Attar, V. Shuvayev, L. Deych, L. L. Martin, and T. Carmon, “Level-crossing and modal structure in microdroplet resonators,” Opt. Express 24(12), 13134–13141 (2016).
[Crossref]

S. Maayani, L. L. Martin, and T. Carmon, “Water-walled microfluidics for high-optical finesse cavities,” Nat. Commun. 7(1), 10435 (2016).
[Crossref]

S. Kaminski, L. L. Martin, S. Maayani, and T. Carmon, “Ripplon laser through stimulated emission mediated by water waves,” Nat. Photonics 10(12), 758–761 (2016).
[Crossref]

S. Maayani, L. L. Martin, S. Kaminski, and T. Carmon, “Cavity optocapillaries,” Optica 3(5), 552–555 (2016).
[Crossref]

R. Dahan, L. L. Martin, and T. Carmon, “Droplet optomechanics,” Optica 3(2), 175–178 (2016).
[Crossref]

G. I. Harris, D. L. McAuslan, E. Sheridan, Y. Sachkou, C. Baker, and W. P. Bowen, “Laser cooling and control of excitations in superfluid helium,” Nat. Phys. 12(8), 788–793 (2016).
[Crossref]

2015 (4)

E. Gil-Santos, C. Baker, D. T. Nguyen, W. Hease, C. Gomez, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High-frequency nano-optomechanical disk resonators in liquids,” Nat. Nanotechnol. 10(9), 810–816 (2015).
[Crossref]

K. Y. Fong, M. Poot, and H. X. Tang, “Nano-Optomechanical Resonators in Microfluidics,” Nano Lett. 15(9), 6116–6120 (2015).
[Crossref]

P. Zhang, S. Jung, A. Lee, and Y. Xu, “Radiation-pressure-induced nonlinearity in microdroplets,” Phys. Rev. E 92(6), 063033 (2015).
[Crossref]

S. Kaminski, L. L. Martin, and T. Carmon, “Tweezers controlled resonator,” Opt. Express 23(22), 28914–28919 (2015).
[Crossref]

2014 (4)

Y. Xu, P. Zhang, S. Jung, and A. Lee, “Analysis of radiation pressure induced nonlinear optofluidics,” Opt. Express 22(23), 28875–28889 (2014).
[Crossref]

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

I. Teraoka, “Analyssi of thermal stabilization of whispering gallery mode resonance,” Opt. Commun. 310, 212–216 (2014).
[Crossref]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref]

2013 (3)

2012 (3)

A. Jonas, Y. Karadog, M. Mestre, and A. Kiraz, “Probing of ultrahigh optical Q-factors of individual liquid microdroplets on superhydrophobic surfaces using tapered optical fiber waveguides,” J. Opt. Soc. Am. B 29(12), 3240–3247 (2012).
[Crossref]

D. Brooks, T. Botter, S. Schereppler, T. P. Purdy, N. Brahms, and D. M. S.-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488(7412), 476–480 (2012).
[Crossref]

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 605–609 (2012).
[Crossref]

2011 (2)

S. Tallur, S. Sridaran, and S. A. Bhave, “A monolithic radiation-pressure driven, low phase noise silicon nitride opto-mechanical oscillator,” Opt. Express 19(24), 24522–24529 (2011).
[Crossref]

R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83(6), 063835 (2011).
[Crossref]

2010 (3)

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-Q crystalline microresonators,” Phys. Rev. A 82(3), 031804 (2010).
[Crossref]

A. Cho, “Putting Light’s Light Touch to Work As Optics Meets Mechanics,” Science 328(5980), 812–813 (2010).
[Crossref]

D. L. Creedon, M. E. Tobar, J.-M. L. Floch, Y. Reshtnyk, and T. Duty, “Single-crystal sapphire resonator at millikelvin temperatures: Observation of thermal bistability in high-Q factor whispering gallery modes,” Phys. Rev. B 82(10), 104305 (2010).
[Crossref]

2009 (1)

G. Anetsberger, O. Arcizet, Q. P. Untterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

2008 (1)

T. J. Kippenberg and K. J. Vahala, “Cavity Optomechanics: Back-Action at the Mesoscale,” Science 321(5893), 1172–1176 (2008).
[Crossref]

2006 (1)

2004 (1)

2003 (1)

2001 (2)

A. Casner and J.-P. Delville, “Giant Deformations of a Liquid-Liquid Interface Induced by the Optical Radiation Pressure,” Phys. Rev. Lett. 87(5), 054503 (2001).
[Crossref]

A. Casner and J.-P. Delville, “Adaptive lensing driven by the radiation pressure of a continuous-wave laser wave upon a near-critical liquid-liquid interface,” Opt. Lett. 26(18), 1418–1420 (2001).
[Crossref]

2000 (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[Crossref]

1999 (2)

1997 (1)

1995 (1)

1990 (1)

H. M. Lai, P. T. Leung, and K. Young, “Limitations on the photon storage lifetime in electromagnetic resonances of highly transparent microdroplets,”,” Phys. Rev. A 41(9), 5199–5204 (1990).
[Crossref]

1989 (2)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Inchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137(7-8), 393–397 (1989).
[Crossref]

H. M. Lai, P. T. Leung, K. L. Poon, and K. Young, “Electrostrictive distortion of a micrometer-sized droplet by a laser pulse,” J. Opt. Soc. Am. B 6(12), 2430–2437 (1989).
[Crossref]

1988 (3)

I. I. Komissarovak, G. V. Ostrovskaya, and E. N. Shedova, “Light pressure induced deformations of a free liquid surface,” Opt. Commun. 66(1), 15–20 (1988).
[Crossref]

J.-Z. Zhang and R. K. Chang, “Shape distortion of a single water droplet by laser-induced electrostriction,” Opt. Lett. 13(10), 916–918 (1988).
[Crossref]

D. Mcmorrow, W. Lotshaw, and G. K.-Wallace, “Femtosecond Optical Kerr Studies on the Origin of the Nonlinear Responses in Simple Liquids,” IEEE J. Quantum Electron. 24(2), 443–454 (1988).
[Crossref]

1973 (1)

A. Ashkin and J. M. Dziedzic, “Radiation pressure on a free liquid surface,” Phys. Rev. Lett. 30(4), 139–142 (1973).
[Crossref]

Anetsberger, G.

G. Anetsberger, O. Arcizet, Q. P. Untterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

Arcizet, O.

R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83(6), 063835 (2011).
[Crossref]

G. Anetsberger, O. Arcizet, Q. P. Untterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

Ashkin, A.

A. Ashkin and J. M. Dziedzic, “Radiation pressure on a free liquid surface,” Phys. Rev. Lett. 30(4), 139–142 (1973).
[Crossref]

Aspelmeyer, M.

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

Attar, S. T.

Avino, S.

A. Giorgini, S. Avino, P. Malara, P. D. Natale, M. Yannai, T. Carmon, and G. Gagliardi, “Stimulated Brillouin Cavity Optomechanics in Liquid Droplets,” Phys. Rev. Lett. 120(7), 073902 (2018).
[Crossref]

Badolato, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 605–609 (2012).
[Crossref]

Bahl, G.

G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat. Commun. 4(1), 1994 (2013).
[Crossref]

Baker, C.

G. I. Harris, D. L. McAuslan, E. Sheridan, Y. Sachkou, C. Baker, and W. P. Bowen, “Laser cooling and control of excitations in superfluid helium,” Nat. Phys. 12(8), 788–793 (2016).
[Crossref]

E. Gil-Santos, C. Baker, D. T. Nguyen, W. Hease, C. Gomez, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High-frequency nano-optomechanical disk resonators in liquids,” Nat. Nanotechnol. 10(9), 810–816 (2015).
[Crossref]

Bar-david, D.

Bhave, S. A.

Botter, T.

D. Brooks, T. Botter, S. Schereppler, T. P. Purdy, N. Brahms, and D. M. S.-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488(7412), 476–480 (2012).
[Crossref]

Bowen, W. P.

G. I. Harris, D. L. McAuslan, E. Sheridan, Y. Sachkou, C. Baker, and W. P. Bowen, “Laser cooling and control of excitations in superfluid helium,” Nat. Phys. 12(8), 788–793 (2016).
[Crossref]

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, and V. S. Inchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137(7-8), 393–397 (1989).
[Crossref]

Brahms, N.

D. Brooks, T. Botter, S. Schereppler, T. P. Purdy, N. Brahms, and D. M. S.-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488(7412), 476–480 (2012).
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G. I. Harris, D. L. McAuslan, E. Sheridan, Y. Sachkou, C. Baker, and W. P. Bowen, “Laser cooling and control of excitations in superfluid helium,” Nat. Phys. 12(8), 788–793 (2016).
[Crossref]

Mcmorrow, D.

D. Mcmorrow, W. Lotshaw, and G. K.-Wallace, “Femtosecond Optical Kerr Studies on the Origin of the Nonlinear Responses in Simple Liquids,” IEEE J. Quantum Electron. 24(2), 443–454 (1988).
[Crossref]

Mestre, M.

Natale, P. D.

A. Giorgini, S. Avino, P. Malara, P. D. Natale, M. Yannai, T. Carmon, and G. Gagliardi, “Stimulated Brillouin Cavity Optomechanics in Liquid Droplets,” Phys. Rev. Lett. 120(7), 073902 (2018).
[Crossref]

Nguyen, D. T.

E. Gil-Santos, C. Baker, D. T. Nguyen, W. Hease, C. Gomez, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High-frequency nano-optomechanical disk resonators in liquids,” Nat. Nanotechnol. 10(9), 810–816 (2015).
[Crossref]

Ostrovskaya, G. V.

I. I. Komissarovak, G. V. Ostrovskaya, and E. N. Shedova, “Light pressure induced deformations of a free liquid surface,” Opt. Commun. 66(1), 15–20 (1988).
[Crossref]

Pavesi, L.

Pfeiffer, M. H. P.

H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys. 13(1), 94–103 (2017).
[Crossref]

Pfeifle, J.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref]

Pichler, H.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
[Crossref]

Poon, K. L.

Poot, M.

K. Y. Fong, M. Poot, and H. X. Tang, “Nano-Optomechanical Resonators in Microfluidics,” Nano Lett. 15(9), 6116–6120 (2015).
[Crossref]

Prtljaga, N.

Pu, X.

Pucker, G.

Purdy, T. P.

D. Brooks, T. Botter, S. Schereppler, T. P. Purdy, N. Brahms, and D. M. S.-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488(7412), 476–480 (2012).
[Crossref]

Qian, K.

K. Qian, J. Tang, H. Guo, W. Liu, J. Liu, C. Xue, Y. Zheng, and C. Zhang, “Under-coupling Whispering Gallery Mode Resonator Applied to Resonant Micro-Optic Gyroscope,” Sensors 17(12), 100 (2017).
[Crossref]

R.-Manzano, F.

Rauschenbeutel, A.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
[Crossref]

Reinhard, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 605–609 (2012).
[Crossref]

Reshtnyk, Y.

D. L. Creedon, M. E. Tobar, J.-M. L. Floch, Y. Reshtnyk, and T. Duty, “Single-crystal sapphire resonator at millikelvin temperatures: Observation of thermal bistability in high-Q factor whispering gallery modes,” Phys. Rev. B 82(10), 104305 (2010).
[Crossref]

Riviere, R.

R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83(6), 063835 (2011).
[Crossref]

G. Anetsberger, O. Arcizet, Q. P. Untterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

S.-Kurn, D. M.

D. Brooks, T. Botter, S. Schereppler, T. P. Purdy, N. Brahms, and D. M. S.-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488(7412), 476–480 (2012).
[Crossref]

Sachkou, Y.

G. I. Harris, D. L. McAuslan, E. Sheridan, Y. Sachkou, C. Baker, and W. P. Bowen, “Laser cooling and control of excitations in superfluid helium,” Nat. Phys. 12(8), 788–793 (2016).
[Crossref]

Schereppler, S.

D. Brooks, T. Botter, S. Schereppler, T. P. Purdy, N. Brahms, and D. M. S.-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488(7412), 476–480 (2012).
[Crossref]

Schindler, P.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref]

Schliesser, A.

R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83(6), 063835 (2011).
[Crossref]

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-Q crystalline microresonators,” Phys. Rev. A 82(3), 031804 (2010).
[Crossref]

G. Anetsberger, O. Arcizet, Q. P. Untterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

Schmogrow, R.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref]

Schneeweiss, P.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
[Crossref]

Shedova, E. N.

I. I. Komissarovak, G. V. Ostrovskaya, and E. N. Shedova, “Light pressure induced deformations of a free liquid surface,” Opt. Commun. 66(1), 15–20 (1988).
[Crossref]

Sheridan, E.

G. I. Harris, D. L. McAuslan, E. Sheridan, Y. Sachkou, C. Baker, and W. P. Bowen, “Laser cooling and control of excitations in superfluid helium,” Nat. Phys. 12(8), 788–793 (2016).
[Crossref]

Shuvayev, V.

Solomon, G.

S. Sun, H. Kim, Z. Luo, G. Solomon, and E. Waks, “A single-photon switch and transistor enabled by a solid-state quantum memory,” Science 361(6397), 57–60 (2018).
[Crossref]

Sridaran, S.

Stobbe, S.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
[Crossref]

Sun, S.

S. Sun, H. Kim, Z. Luo, G. Solomon, and E. Waks, “A single-photon switch and transistor enabled by a solid-state quantum memory,” Science 361(6397), 57–60 (2018).
[Crossref]

Tallur, S.

Tang, H. X.

K. Y. Fong, M. Poot, and H. X. Tang, “Nano-Optomechanical Resonators in Microfluidics,” Nano Lett. 15(9), 6116–6120 (2015).
[Crossref]

Tang, J.

K. Qian, J. Tang, H. Guo, W. Liu, J. Liu, C. Xue, Y. Zheng, and C. Zhang, “Under-coupling Whispering Gallery Mode Resonator Applied to Resonant Micro-Optic Gyroscope,” Sensors 17(12), 100 (2017).
[Crossref]

Teraoka, I.

I. Teraoka, “Analyssi of thermal stabilization of whispering gallery mode resonance,” Opt. Commun. 310, 212–216 (2014).
[Crossref]

Tobar, M. E.

D. L. Creedon, M. E. Tobar, J.-M. L. Floch, Y. Reshtnyk, and T. Duty, “Single-crystal sapphire resonator at millikelvin temperatures: Observation of thermal bistability in high-Q factor whispering gallery modes,” Phys. Rev. B 82(10), 104305 (2010).
[Crossref]

Untterreithmeier, Q. P.

G. Anetsberger, O. Arcizet, Q. P. Untterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

Vahala, K. J.

Volz, J.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
[Crossref]

Volz, T.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 605–609 (2012).
[Crossref]

Waks, E.

S. Sun, H. Kim, Z. Luo, G. Solomon, and E. Waks, “A single-photon switch and transistor enabled by a solid-state quantum memory,” Science 361(6397), 57–60 (2018).
[Crossref]

Wegner, D.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref]

Weig, E. M.

G. Anetsberger, O. Arcizet, Q. P. Untterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[Crossref]

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J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref]

Weis, S.

R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83(6), 063835 (2011).
[Crossref]

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T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 605–609 (2012).
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P. Zhang, S. Jung, A. Lee, and Y. Xu, “Comparative analysis of nonlinear optofluidic processes in microdroplets,” Phys. Rev. E 93(6), 063119 (2016).
[Crossref]

P. Zhang, S. Jung, A. Lee, and Y. Xu, “Radiation-pressure-induced nonlinearity in microdroplets,” Phys. Rev. E 92(6), 063033 (2015).
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Y. Xu, P. Zhang, S. Jung, and A. Lee, “Analysis of radiation pressure induced nonlinear optofluidics,” Opt. Express 22(23), 28875–28889 (2014).
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K. Qian, J. Tang, H. Guo, W. Liu, J. Liu, C. Xue, Y. Zheng, and C. Zhang, “Under-coupling Whispering Gallery Mode Resonator Applied to Resonant Micro-Optic Gyroscope,” Sensors 17(12), 100 (2017).
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Yannai, M.

A. Giorgini, S. Avino, P. Malara, P. D. Natale, M. Yannai, T. Carmon, and G. Gagliardi, “Stimulated Brillouin Cavity Optomechanics in Liquid Droplets,” Phys. Rev. Lett. 120(7), 073902 (2018).
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J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
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Zhang, C.

K. Qian, J. Tang, H. Guo, W. Liu, J. Liu, C. Xue, Y. Zheng, and C. Zhang, “Under-coupling Whispering Gallery Mode Resonator Applied to Resonant Micro-Optic Gyroscope,” Sensors 17(12), 100 (2017).
[Crossref]

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Zhang, P.

P. Zhang, S. Jung, A. Lee, and Y. Xu, “Comparative analysis of nonlinear optofluidic processes in microdroplets,” Phys. Rev. E 93(6), 063119 (2016).
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P. Zhang, S. Jung, A. Lee, and Y. Xu, “Radiation-pressure-induced nonlinearity in microdroplets,” Phys. Rev. E 92(6), 063033 (2015).
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Y. Xu, P. Zhang, S. Jung, and A. Lee, “Analysis of radiation pressure induced nonlinear optofluidics,” Opt. Express 22(23), 28875–28889 (2014).
[Crossref]

Zheng, Y.

K. Qian, J. Tang, H. Guo, W. Liu, J. Liu, C. Xue, Y. Zheng, and C. Zhang, “Under-coupling Whispering Gallery Mode Resonator Applied to Resonant Micro-Optic Gyroscope,” Sensors 17(12), 100 (2017).
[Crossref]

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P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
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J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (7)

Nano Lett. (1)

K. Y. Fong, M. Poot, and H. X. Tang, “Nano-Optomechanical Resonators in Microfluidics,” Nano Lett. 15(9), 6116–6120 (2015).
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Nat. Commun. (2)

S. Maayani, L. L. Martin, and T. Carmon, “Water-walled microfluidics for high-optical finesse cavities,” Nat. Commun. 7(1), 10435 (2016).
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G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat. Commun. 4(1), 1994 (2013).
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Nat. Nanotechnol. (1)

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S. Kaminski, L. L. Martin, S. Maayani, and T. Carmon, “Ripplon laser through stimulated emission mediated by water waves,” Nat. Photonics 10(12), 758–761 (2016).
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J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref]

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 605–609 (2012).
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Nat. Phys. (3)

H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys. 13(1), 94–103 (2017).
[Crossref]

G. I. Harris, D. L. McAuslan, E. Sheridan, Y. Sachkou, C. Baker, and W. P. Bowen, “Laser cooling and control of excitations in superfluid helium,” Nat. Phys. 12(8), 788–793 (2016).
[Crossref]

G. Anetsberger, O. Arcizet, Q. P. Untterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
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Nature (2)

D. Brooks, T. Botter, S. Schereppler, T. P. Purdy, N. Brahms, and D. M. S.-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature 488(7412), 476–480 (2012).
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P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
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Opt. Commun. (2)

I. Teraoka, “Analyssi of thermal stabilization of whispering gallery mode resonance,” Opt. Commun. 310, 212–216 (2014).
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Optica (2)

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Phys. Rev. B (1)

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P. Zhang, S. Jung, A. Lee, and Y. Xu, “Comparative analysis of nonlinear optofluidic processes in microdroplets,” Phys. Rev. E 93(6), 063119 (2016).
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Phys. Rev. Lett. (3)

A. Giorgini, S. Avino, P. Malara, P. D. Natale, M. Yannai, T. Carmon, and G. Gagliardi, “Stimulated Brillouin Cavity Optomechanics in Liquid Droplets,” Phys. Rev. Lett. 120(7), 073902 (2018).
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Sensors (1)

K. Qian, J. Tang, H. Guo, W. Liu, J. Liu, C. Xue, Y. Zheng, and C. Zhang, “Under-coupling Whispering Gallery Mode Resonator Applied to Resonant Micro-Optic Gyroscope,” Sensors 17(12), 100 (2017).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1. Experimental configuration and characterization of a droplet WGR. (a) Schematic diagram of the droplet WGM experimental setup (DAQ: data acquisition, PD: photodetector, PC: polarization controller, PZT: piezoelectric transducer). (b) Illustration of a droplet resonator (left) and the WGM pattern in r-θ plane (right). (c) WGM transmission spectrum of a droplet resonator. (d) Examples of high-Q droplet resonances (blue: $Q = 2.1 \times {10^6}$, red: $Q = 1.7 \times {10^7}$) ($\Delta {P_{in}} = 8\; \mu \textrm{W}$). (e) Typical nonlinearities in WGM resonances observed during up-scan (blue) and down-scan (red) ($\Delta {P_{in}} = 200\; \mu \textrm{W}$).
Fig. 2.
Fig. 2. Theoretical analysis of droplet deformation. (a) Polar dependence of droplet deformation (blue solid curve: exact solution, red dashed curve: lowest spherical harmonic expansion (L = 2)). (b) Radiation pressure induced droplet deformation ($\Delta R/{R_0}$) for our droplet samples with different radii (red) at PWGM = 1 W. Two other results are estimated using the same liquid properties but ultralow interfacial tensions.
Fig. 3.
Fig. 3. Experimental result of radiation pressure-induced nonlinearity during up-scan. (a-d) Radiation pressure-induced resonance shift at different input power and laser scan speeds: Vscan = (a) 1.17 nm/s, (b) 2.33 nm/s, (c) 3.50 nm/s, (d) 7.00 nm/s (grey dots: experimental result, black errorbars: statistical distribution of grey dots, blue dashed curve: HO model, red dashed line: linear estimation). In (d), simulation results for $\Delta {P_{in}}$ up to 300 μW is added as an inset. (e, f) WGM transmission spectra at different up-scan speeds: Vscan = (e) 1.17 nm/s, (f) 7.00 nm/s. (grey solid curve: experimental observation, blue dashed curve: HO model)
Fig. 4.
Fig. 4. Spectral pattern of WGM transmission during downscan. (a) FWHM of squeezed resonance during down-scan at scan speeds: Vscan = red: 1.17 nm/s, green: 2.33 nm/s, blue: 3.50 nm/s, magenta: 7.00 nm/s. (markers: experimental result, dashed lines: HO model) (b) WGM transmission spectra during down-scan. (blue: experimental result, red: HO model, magenta: cold resonance).
Fig. 5.
Fig. 5. Theoretical analysis of the feasibility of single-photon nonlinearity. (a) The saturation power Psat for droplets with different radii and surface tensions. (b) The change of droplet radius due to the presence of a single-photon versus droplet radius at different interfacial tensions. (c) Optical bistability for a droplet with low interfacial tension.

Tables (1)

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Table 1. Optofluidic parameters of core and cladding of liquid WGR configurationa

Equations (3)

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Δ R ¨ + 2 μ L Δ R ˙ + ω L 2 Δ R = ω L 2 R 0 P W G M P s a t ,
P W G M = τ r 2 κ 2 | τ r τ c exp ( i ϕ ( t ) ) | 2 P i n ,
P t r a n s = | τ r τ c exp ( i ϕ ( t ) ) | 2 | τ r τ c exp ( i ϕ ( t ) ) | 2 P i n ,

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