Abstract

We study optomechanically induced transparency in a spinning microresonator. We find that in the presence of rotation-induced Sagnac frequency shift, both the transmission rate and the group delay of the signal are strongly affected, leading to a Fano-like spectrum of transparency. In particular, tuning the rotary speed leads to the emergence of nonreciprocal optical sidebands. This indicates a promising new way to control hybrid light–sound devices with spinning resonators.

© 2017 Chinese Laser Press

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  4. F. Lecocq, J. B. Clark, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Mechanically mediated microwave frequency conversion in the quantum regime,” Phys. Rev. Lett. 116, 043601 (2016).
    [Crossref]
  5. X.-W. Xu, Y. Li, A.-X. Chen, and Y.-X. Liu, “Nonreciprocal conversion between microwave and optical photons in electro-optomechanical systems,” Phys. Rev. A 93, 023827 (2016).
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  6. T.-Y. Chen, W.-Z. Zhang, R.-Z. Fang, C.-Z. Hang, and L. Zhou, “Multi-path photon-phonon converter in optomechanical system at single-quantum level,” Opt. Express 25, 10779–10790 (2017).
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    [Crossref]
  27. W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
    [Crossref]
  28. C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Photonic technologies for angular velocity sensing,” Adv. Opt. Photon. 2, 370–404 (2010).
    [Crossref]
  29. L. Ge, R. Sarma, and H. Cao, “Rotation-induced mode coupling in open wavelength-scale microcavities,” Phys. Rev. A 90, 013809 (2014).
    [Crossref]
  30. R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
    [Crossref]
  31. M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
    [Crossref]
  32. G. Li, T. Zentgraf, and S. Zhang, “Rotational Doppler effect in nonlinear optics,” Nat. Phys. 12, 736–740 (2016).
    [Crossref]
  33. S. Franke-Arnold, G. Gibson, R. W. Boyd, and M. J. Padgett, “Rotary photon drag enhanced by a slow-light medium,” Science 333, 65–67 (2011).
    [Crossref]
  34. R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, “Sound isolation and giant linear nonreciprocity in a compact acoustic circulator,” Science 343, 516–519 (2014).
    [Crossref]
  35. Z. Shen, Y.-L. Zhang, Y. Chen, C.-L. Zou, Y.-F. Xiao, X.-B. Zou, F.-W. Sun, G.-C. Guo, and C.-H. Dong, “Experimental realization of optomechanically induced non-reciprocity,” Nat. Photonics 10, 657–661 (2016).
    [Crossref]
  36. F. Ruesink, M.-A. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nat. Commun. 7, 13662 (2016).
    [Crossref]
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    [Crossref]
  38. Q.-T. Cao, H. Wang, C.-H. Dong, H. Jing, R.-S. Liu, X. Chen, L. Ge, Q. Gong, and Y.-F. Xiao, “Experimental demonstration of spontaneous chirality in a nonlinear microresonator,” Phys. Rev. Lett. 118, 033901 (2017).
    [Crossref]
  39. M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeutel, “Quantum optical circulator controlled by a single chirally coupled atom,” Science 354, 1577–1580 (2016).
    [Crossref]
  40. S. Davuluri and Y. V. Rostovtsev, “Quantum optical mouse to detect Coriolis force,” Europhys. Lett. 103, 24001 (2013).
    [Crossref]
  41. S. Davuluri and S. Zhu, “Controlling optomechanically induced transparency through rotation,” Europhys. Lett. 112, 64002 (2015).
    [Crossref]
  42. H. Xu, D. Mason, L. Jiang, and J. G. E. Harris, “Topological energy transfer in an optomechanical system with exceptional points,” Nature 537, 80–83 (2016).
    [Crossref]
  43. H. Jing, Ş. K. Özdemir, H. Lü, and F. Nori, “High-order exceptional points in optomechanics,” Sci. Rep. 7, 3386 (2017).
    [Crossref]
  44. G. B. Malykin, “The Sagnac effect: correct and incorrect explanations,” Phys. Usp. 43, 1229–1252 (2000).
    [Crossref]
  45. 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, 94–102 (2017).
    [Crossref]
  46. S. Maayani and T. Carmon (personal communication).
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    [Crossref]
  48. W. M. Zhang and G. Meng, “Stability, bifurcation and chaos analyses of a high-speed micro-rotor system with rub-impact,” Sens. Actuators A 127, 163–178 (2006).
    [Crossref]
  49. R. Kurose and S. Komori, “Drag and lift forces on a rotating sphere in a linear shear flow,” J. Fluid Mech. 384, 183–206 (1999).
    [Crossref]
  50. D. Sofikitis, L. Bougas, G. E. Katsoprinakis, A. K. Spiliotis, B. Loppinet, and T. P. Rakitzis, “Evanescent-wave and ambient chiral sensing by signal-reversing cavity ringdown polarimetry,” Nature 514, 76–79 (2014).
    [Crossref]

2017 (6)

T.-Y. Chen, W.-Z. Zhang, R.-Z. Fang, C.-Z. Hang, and L. Zhou, “Multi-path photon-phonon converter in optomechanical system at single-quantum level,” Opt. Express 25, 10779–10790 (2017).
[Crossref]

G. Wang, M. Zhao, Y. Qin, Z. Yin, X. Jiang, and M. Xiao, “Demonstration of an ultra-low-threshold phonon laser with coupled microtoroid resonators in vacuum,” Photon. Res. 5, 73–76 (2017).
[Crossref]

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nat. Phys. 13, 465–471 (2017).
[Crossref]

Q.-T. Cao, H. Wang, C.-H. Dong, H. Jing, R.-S. Liu, X. Chen, L. Ge, Q. Gong, and Y.-F. Xiao, “Experimental demonstration of spontaneous chirality in a nonlinear microresonator,” Phys. Rev. Lett. 118, 033901 (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, 94–102 (2017).
[Crossref]

H. Jing, Ş. K. Özdemir, H. Lü, and F. Nori, “High-order exceptional points in optomechanics,” Sci. Rep. 7, 3386 (2017).
[Crossref]

2016 (11)

M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeutel, “Quantum optical circulator controlled by a single chirally coupled atom,” Science 354, 1577–1580 (2016).
[Crossref]

Z. Shen, Y.-L. Zhang, Y. Chen, C.-L. Zou, Y.-F. Xiao, X.-B. Zou, F.-W. Sun, G.-C. Guo, and C.-H. Dong, “Experimental realization of optomechanically induced non-reciprocity,” Nat. Photonics 10, 657–661 (2016).
[Crossref]

F. Ruesink, M.-A. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nat. Commun. 7, 13662 (2016).
[Crossref]

H. Xu, D. Mason, L. Jiang, and J. G. E. Harris, “Topological energy transfer in an optomechanical system with exceptional points,” Nature 537, 80–83 (2016).
[Crossref]

I. M. Mirza, “Strong coupling optical spectra in dipole–dipole interacting optomechanical Tavis–Cummings models,” Opt. Lett. 41, 2422–2425 (2016).
[Crossref]

F. Lecocq, J. B. Clark, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Mechanically mediated microwave frequency conversion in the quantum regime,” Phys. Rev. Lett. 116, 043601 (2016).
[Crossref]

X.-W. Xu, Y. Li, A.-X. Chen, and Y.-X. Liu, “Nonreciprocal conversion between microwave and optical photons in electro-optomechanical systems,” Phys. Rev. A 93, 023827 (2016).
[Crossref]

Z. Shen, C.-H. Dong, Y. Chen, Y.-F. Xiao, F.-W. Sun, and G.-C. Guo, “Compensation of the Kerr effect for transient optomechanically induced transparency in a silica microsphere,” Opt. Lett. 41, 1249–1252 (2016).
[Crossref]

M. Asano, Ş. K. Özdemir, W. Chen, R. Ikuta, L. Yang, N. Imoto, and T. Yamamoto, “Controlling slow and fast light and dynamic pulse-splitting with tunable optical gain in a whispering-gallery-mode microcavity,” Appl. Phys. Lett. 108, 181105 (2016).
[Crossref]

Y. Jiao, H. Lü, J. Qian, Y. Li, and H. Jing, “Nonlinear optomechanics with gain and loss: amplifying higher-order sideband and group delay,” New J. Phys. 18, 083034 (2016).
[Crossref]

G. Li, T. Zentgraf, and S. Zhang, “Rotational Doppler effect in nonlinear optics,” Nat. Phys. 12, 736–740 (2016).
[Crossref]

2015 (5)

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref]

L. Fan, K. Y. Fong, M. Poot, and H. X. Tang, “Cascaded optical transparency in multimode-cavity optomechanical systems,” Nat. Commun. 6, 5850 (2015).
[Crossref]

H. Jing, Ş. K. Özdemir, Z. Geng, J. Zhang, X.-Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanically-induced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5, 9663 (2015).
[Crossref]

S. Davuluri and S. Zhu, “Controlling optomechanically induced transparency through rotation,” Europhys. Lett. 112, 64002 (2015).
[Crossref]

C.-H. Dong, Z. Shen, C.-L. Zou, Y.-L. Zhang, W. Fu, and G.-C. Guo, “Brillouin-scattering-induced transparency and non-reciprocal light storage,” Nat. Commun. 6, 6193 (2015).
[Crossref]

2014 (8)

D. Sofikitis, L. Bougas, G. E. Katsoprinakis, A. K. Spiliotis, B. Loppinet, and T. P. Rakitzis, “Evanescent-wave and ambient chiral sensing by signal-reversing cavity ringdown polarimetry,” Nature 514, 76–79 (2014).
[Crossref]

L. Ge, R. Sarma, and H. Cao, “Rotation-induced mode coupling in open wavelength-scale microcavities,” Phys. Rev. A 90, 013809 (2014).
[Crossref]

R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, “Sound isolation and giant linear nonreciprocity in a compact acoustic circulator,” Science 343, 516–519 (2014).
[Crossref]

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

M. Metcalfe, “Applications of cavity optomechanics,” Appl. Phys. Rev. 1, 031105 (2014).
[Crossref]

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

H. Jing, S. K. Özdemir, X.-Y. Lü, J. Zhang, L. Yang, and F. Nori, “PT-symmetric phonon laser,” Phys. Rev. Lett. 113, 053604 (2014).
[Crossref]

I. M. Mirza and S. J. van Enk, “Single-photon time-dependent spectra in quantum optomechanics,” Phys. Rev. A 90, 043831 (2014).
[Crossref]

2013 (5)

J.-Q. Liao and C. K. Law, “Correlated two-photon scattering in cavity optomechanics,” Phys. Rev. A 87, 043809 (2013).
[Crossref]

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref]

A. Kronwald and F. Marquardt, “Optomechanically induced transparency in the nonlinear quantum regime,” Phys. Rev. Lett. 111, 133601 (2013).
[Crossref]

X. Zhou, F. Hocke, A. Schliesser, A. Marx, H. Huebl, R. Gross, and T. J. Kippenberg, “Slowing, advancing and switching of microwave signals using circuit nanoelectromechanics,” Nat. Phys. 9, 179–184 (2013).
[Crossref]

S. Davuluri and Y. V. Rostovtsev, “Quantum optical mouse to detect Coriolis force,” Europhys. Lett. 103, 24001 (2013).
[Crossref]

2012 (2)

H. Xiong, L.-G. Si, A.-S. Zheng, X. Yang, and Y. Wu, “Higher-order sidebands in optomechanically induced transparency,” Phys. Rev. A 86, 013815 (2012).
[Crossref]

E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7, 509–514 (2012).
[Crossref]

2011 (3)

A. Nunnenkamp, K. Brkje, and S. M. Girvin, “Single-photon optomechanics,” Phys. Rev. Lett. 107, 063602 (2011).
[Crossref]

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

S. Franke-Arnold, G. Gibson, R. W. Boyd, and M. J. Padgett, “Rotary photon drag enhanced by a slow-light medium,” Science 333, 65–67 (2011).
[Crossref]

2010 (3)

C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Photonic technologies for angular velocity sensing,” Adv. Opt. Photon. 2, 370–404 (2010).
[Crossref]

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref]

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104, 083901 (2010).
[Crossref]

2006 (2)

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Franais, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref]

W. M. Zhang and G. Meng, “Stability, bifurcation and chaos analyses of a high-speed micro-rotor system with rub-impact,” Sens. Actuators A 127, 163–178 (2006).
[Crossref]

2000 (1)

G. B. Malykin, “The Sagnac effect: correct and incorrect explanations,” Phys. Usp. 43, 1229–1252 (2000).
[Crossref]

1999 (1)

R. Kurose and S. Komori, “Drag and lift forces on a rotating sphere in a linear shear flow,” J. Fluid Mech. 384, 183–206 (1999).
[Crossref]

1985 (1)

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[Crossref]

1967 (1)

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39, 475–493 (1967).
[Crossref]

Alù, A.

F. Ruesink, M.-A. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nat. Commun. 7, 13662 (2016).
[Crossref]

R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, “Sound isolation and giant linear nonreciprocity in a compact acoustic circulator,” Science 343, 516–519 (2014).
[Crossref]

Appel, J.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

Arcizet, O.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref]

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Franais, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref]

Armenise, M. N.

Asano, M.

M. Asano, Ş. K. Özdemir, W. Chen, R. Ikuta, L. Yang, N. Imoto, and T. Yamamoto, “Controlling slow and fast light and dynamic pulse-splitting with tunable optical gain in a whispering-gallery-mode microcavity,” Appl. Phys. Lett. 108, 181105 (2016).
[Crossref]

Aspelmeyer, M.

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

Aumentado, J.

F. Lecocq, J. B. Clark, R. W. Simmonds, J. Aumentado, and J. D. Teufel, “Mechanically mediated microwave frequency conversion in the quantum regime,” Phys. Rev. Lett. 116, 043601 (2016).
[Crossref]

Bagci, T.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

Barnett, S. M.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref]

Bougas, L.

D. Sofikitis, L. Bougas, G. E. Katsoprinakis, A. K. Spiliotis, B. Loppinet, and T. P. Rakitzis, “Evanescent-wave and ambient chiral sensing by signal-reversing cavity ringdown polarimetry,” Nature 514, 76–79 (2014).
[Crossref]

Boyd, R. W.

S. Franke-Arnold, G. Gibson, R. W. Boyd, and M. J. Padgett, “Rotary photon drag enhanced by a slow-light medium,” Science 333, 65–67 (2011).
[Crossref]

Brasch, V.

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, 94–102 (2017).
[Crossref]

Briant, T.

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Figures (3)

Fig. 1.
Fig. 1. Optomechanics in a rotating microresonator coupled to a stationary tapered fiber. The resonator contains a mechanical mode at frequency ωm, driven by a pump field at frequency ωl, and the frequency of rotation is positive (Ω>0) for the CW direction.
Fig. 2.
Fig. 2. (a, c, d) Transmission of the probe light as a function of the optical detuning Δp and (b) rotation speed |Ω|. The rotation speed is set as (a, b) 40 kHz and (c, d) 100 kHz.
Fig. 3.
Fig. 3. (a) Group delay of the probe light τg at Δp=0, as a function of the rotation speed |Ω|. (b) Enhancement factor of the group delay D as a function of the probe detuning Δp and rotation speed |Ω|.

Equations (14)

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ωaωa+Δsag,
Δsag=nrΩωac(11n2λndndλ),
H=Δ+aaξxaa+p22m+12mωm2x2+pθ22mr2+iγexϵl(aeiωltaeiωlt)+iγexϵp(aeiωptaeiωpt),
a˙=(iΔ+iξx+β)a+γexϵl+γexϵpeiηt,x¨+γmx˙+ωm2x=ξmaa+pθ2m2r3,θ˙=pθmr2,p˙θ=0,
a¯=γexϵlβ+iΔ+iξx¯,x¯=γexξ|ϵl|2mωm2[β2+(Δ+ξx¯)2]2+r(Ωωm)2,
a=a¯+δaeiηt+δa+eiηt,x=x¯+δxeiηt+δx*eiηt.
(β+iΔ+iξx¯iη)δaiξa¯δx=γexϵp,(βiΔ++iξx¯iη)δa+*+iξa¯*δx=0,(ωm2η2iηγm)δx=ξm(a¯*δa+a¯δa+*).
δa=γexϵph1(η)[1+i|a¯|2ξ2χ(η)h1(η)2|a¯|2ξ2χ(η)h2(η)],
h1(η)=β+iΔ+iξx¯iη,h2(η)=Δ+ξx¯βiΔ++iξx¯iη,χ(η)=1m(ωm2η2iγmη).
aout=ainγexδa,
T=|tp|2=|aoutain|2=|1γexϵpδa|2.
f=T(Ω0)T(Ω=0)|Δp=01.
τg=darg(tp)dΔp.
D=τg(Ω0)τg(Ω=0)1.

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