Abstract

We describe a new approach for on-chip optical non-reciprocity which makes use of strong optomechanical interaction in microring resonators. By optically pumping the ring resonator in one direction, the optomechanical coupling is only enhanced in that direction, and consequently, the system exhibits a non-reciprocal response. For different configurations, this system can function either as an optical isolator or a coherent non-reciprocal phase shifter. We show that the operation of such a device on the level of single-photon could be achieved with existing technology.

© 2012 OSA

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2011 (11)

M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7, 907–912 (2011).
[CrossRef]

R. O. Umucalilar and I. Carusotto, “Artificial gauge field for photons in coupled cavity arrays,” Phys. Rev. A 84, 043804 (2011).
[CrossRef]

E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” arXiv:1107.3761 (2011).

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

D. E. Chang, A.H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys. 13, 023003 (2011).
[CrossRef]

K. Stannigel, P. Rabl, A. S. Sørensen, M. D. Lukin, and P. Zoller, “Optomechanical transducers for quantum information processing,” Phys. Rev. A 84, 042341 (2011).
[CrossRef]

A. H. Safavi-Naeini, T. P. M. 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] [PubMed]

M. S. Kang, A. Butsch, and P. St. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics 5, 549–553 (2011).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. -L. Xu, M. -H. Lu, Y. -F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011).
[CrossRef] [PubMed]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, ”Comment on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38 (2011).
[CrossRef]

P. Rabl, “Photon blockade effect in optomechanical systems,” Phys. Rev. Lett. 107, 063601 (2011).
[CrossRef] [PubMed]

2010 (7)

A. Schliesser and T. J. Kippenberg, “Cavity optomechanics with whispering-gallery mode optical microresonators,” Adv. At., Mol., Opt. Phys. 58, 207–323 (2010).
[CrossRef]

G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A,  81, 041803 (2010).
[CrossRef]

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

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization entangled state measurement on a chip,” Phys. Rev. Lett. 105, 200503 (2010).
[CrossRef]

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency gaas nano-optomechanical disk resonator,” Phys. Rev. Lett. 105, 263903 (2010).
[CrossRef]

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105, 220501 (2010).
[CrossRef]

J. Koch, A. A Houck, K. Le Hur, and S. M. Girvin, “Time-reversal symmetry breaking in circuit-QED based photon lattices,” Phys. Rev. A 82, 043811 (2010).
[CrossRef]

2009 (6)

S. Manipatruni, J. Robinson, and M. Lipson, “Optical nonreciprocity in optomechanical structures,” Phys. Rev. Lett. 102, 213903 (2009).
[CrossRef] [PubMed]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461,772–775 (2009).
[CrossRef] [PubMed]

A. Politi, J. C. F. Matthews, and J. L. O’Brien, “Shor’s quantum factoring algorithm on a photonic chip,” Science 325, 1221 (2009).
[CrossRef] [PubMed]

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
[CrossRef]

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[CrossRef]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
[CrossRef]

2008 (2)

F. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 13904 (2008).
[CrossRef]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 13905 (2008).
[CrossRef]

2007 (6)

T. Carmon and K. Vahala, “Modal spectroscopy of optoexcited vibrations of a micron-scale on-chip resonator at greater than 1 ghz frequency,” Phys. Rev. Lett. 98,123901 (2007).
[CrossRef] [PubMed]

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99, 093901 (2007).
[CrossRef] [PubMed]

F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, “Quantum theory of cavity-assisted sideband cooling of mechanical motion,” Phys. Rev. Lett. 99, 93902 (2007).
[CrossRef]

T. R. Zaman, X. Guo, and R. J. Ram, “Faraday rotation in an InP waveguide,” App. Phys. Lett. 90, 023514 (2007).
[CrossRef]

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counterpropagating whispering-gallery modes by a single rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99, 173603 (2007).
[CrossRef] [PubMed]

D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced mott transitions and xy spin models in coupled cavity arrays,” Phys. Rev. A 76, 31805 (2007).
[CrossRef]

2006 (3)

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).
[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
[CrossRef]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature,  443, 671 (2006).
[CrossRef] [PubMed]

2005 (2)

M. Levy, “Nanomagnetic route to bias-magnet-free, on-chip faraday rotators,” J. Opt. Soc. Am. B 22, 254–260 (2005).
[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys.,  77, 633–673 (2005).
[CrossRef]

2004 (3)

2002 (1)

2001 (1)

K. Gallo, G. Assanto, K. Parameswaran, and M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

1994 (2)

C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A 49,1337–1343 (1994).
[CrossRef] [PubMed]

S. Mancini and P. Tombesi, “Quantum noise reduction by radiation pressure,” Phys. Rev. A 49, 4055–4065 (1994).
[CrossRef] [PubMed]

1985 (1)

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef] [PubMed]

Agarwal, G. S.

G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A,  81, 041803 (2010).
[CrossRef]

Alegre, T. P. M.

A. H. Safavi-Naeini, T. P. M. 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] [PubMed]

Angelakis, D. G.

D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced mott transitions and xy spin models in coupled cavity arrays,” Phys. Rev. A 76, 31805 (2007).
[CrossRef]

Aoki, T.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature,  443, 671 (2006).
[CrossRef] [PubMed]

Arcizet, O.

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

Aspelmeyer, M.

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

Assanto, G.

K. Gallo, G. Assanto, K. Parameswaran, and M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
[CrossRef]

Ayache, M.

L. Feng, M. Ayache, J. Huang, Y. -L. Xu, M. -H. Lu, Y. -F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011).
[CrossRef] [PubMed]

Baets, R.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, ”Comment on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38 (2011).
[CrossRef]

Baker, C.

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency gaas nano-optomechanical disk resonator,” Phys. Rev. Lett. 105, 263903 (2010).
[CrossRef]

Benson, O.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counterpropagating whispering-gallery modes by a single rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99, 173603 (2007).
[CrossRef] [PubMed]

Bose, S.

D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced mott transitions and xy spin models in coupled cavity arrays,” Phys. Rev. A 76, 31805 (2007).
[CrossRef]

Botter, T.

D. Brooks, T. Botter, N. Brahms, T. Purdy, S. Schreppler, and D. Stamper-Kurn, “Ponderomotive light squeezing with atomic cavity optomechanics,” arXiv:1107.5609 (2011).

Bourzeix, S.

C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A 49,1337–1343 (1994).
[CrossRef] [PubMed]

Bowen, W. P.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature,  443, 671 (2006).
[CrossRef] [PubMed]

Brahms, N.

D. Brooks, T. Botter, N. Brahms, T. Purdy, S. Schreppler, and D. Stamper-Kurn, “Ponderomotive light squeezing with atomic cavity optomechanics,” arXiv:1107.5609 (2011).

Brandao, F. G. S. L.

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
[CrossRef]

Brinkmeyer, E.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, ”Comment on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38 (2011).
[CrossRef]

Brooks, D.

D. Brooks, T. Botter, N. Brahms, T. Purdy, S. Schreppler, and D. Stamper-Kurn, “Ponderomotive light squeezing with atomic cavity optomechanics,” arXiv:1107.5609 (2011).

Busch, K.

R. B. Wehrspohn, H. S. Kitzerow, and K. Busch. Nanophotonic Materials: Photonic Crystals, Plasmonics, and Metamaterials (Wiley-VCH, 2008).

Butsch, A.

M. S. Kang, A. Butsch, and P. St. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics 5, 549–553 (2011).
[CrossRef]

Cage, M. E.

R. E. Prange, S. M. Girvin, and M. E. Cage. The Quantum Hall Effect. (Springer-Verlag, 1986).

Carmon, T.

T. Carmon and K. Vahala, “Modal spectroscopy of optoexcited vibrations of a micron-scale on-chip resonator at greater than 1 ghz frequency,” Phys. Rev. Lett. 98,123901 (2007).
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T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature,  443, 671 (2006).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, ”Comment on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38 (2011).
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C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A 49,1337–1343 (1994).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, ”Comment on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38 (2011).
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P. Rabl, “Photon blockade effect in optomechanical systems,” Phys. Rev. Lett. 107, 063601 (2011).
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K. Stannigel, P. Rabl, A. S. Sørensen, M. D. Lukin, and P. Zoller, “Optomechanical transducers for quantum information processing,” Phys. Rev. A 84, 042341 (2011).
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K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105, 220501 (2010).
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F. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 13904 (2008).
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T. R. Zaman, X. Guo, and R. J. Ram, “Faraday rotation in an InP waveguide,” App. Phys. Lett. 90, 023514 (2007).
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L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization entangled state measurement on a chip,” Phys. Rev. Lett. 105, 200503 (2010).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, ”Comment on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38 (2011).
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C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A 49,1337–1343 (1994).
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S. Weis, R. Riviere, S. Deleglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science,  330,1520–1523 (2010).
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A. H. Safavi-Naeini, T. P. M. 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).
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D. E. Chang, A.H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys. 13, 023003 (2011).
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A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counterpropagating whispering-gallery modes by a single rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99, 173603 (2007).
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Sansoni, L.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization entangled state measurement on a chip,” Phys. Rev. Lett. 105, 200503 (2010).
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D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced mott transitions and xy spin models in coupled cavity arrays,” Phys. Rev. A 76, 31805 (2007).
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L. Feng, M. Ayache, J. Huang, Y. -L. Xu, M. -H. Lu, Y. -F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011).
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E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” arXiv:1107.3761 (2011).

S. Weis, R. Riviere, S. Deleglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science,  330,1520–1523 (2010).
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A. Schliesser and T. J. Kippenberg, “Cavity optomechanics with whispering-gallery mode optical microresonators,” Adv. At., Mol., Opt. Phys. 58, 207–323 (2010).
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D. Brooks, T. Botter, N. Brahms, T. Purdy, S. Schreppler, and D. Stamper-Kurn, “Ponderomotive light squeezing with atomic cavity optomechanics,” arXiv:1107.5609 (2011).

Sciarrino, F.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization entangled state measurement on a chip,” Phys. Rev. Lett. 105, 200503 (2010).
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L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency gaas nano-optomechanical disk resonator,” Phys. Rev. Lett. 105, 263903 (2010).
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Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461,772–775 (2009).
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Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 13905 (2008).
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K. Stannigel, P. Rabl, A. S. Sørensen, M. D. Lukin, and P. Zoller, “Optomechanical transducers for quantum information processing,” Phys. Rev. A 84, 042341 (2011).
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K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105, 220501 (2010).
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Stamper-Kurn, D.

D. Brooks, T. Botter, N. Brahms, T. Purdy, S. Schreppler, and D. Stamper-Kurn, “Ponderomotive light squeezing with atomic cavity optomechanics,” arXiv:1107.5609 (2011).

Stannigel, K.

K. Stannigel, P. Rabl, A. S. Sørensen, M. D. Lukin, and P. Zoller, “Optomechanical transducers for quantum information processing,” Phys. Rev. A 84, 042341 (2011).
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K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105, 220501 (2010).
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J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
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A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).
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M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7, 907–912 (2011).
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R. O. Umucalilar and I. Carusotto, “Artificial gauge field for photons in coupled cavity arrays,” Phys. Rev. A 84, 043804 (2011).
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T. Carmon and K. Vahala, “Modal spectroscopy of optoexcited vibrations of a micron-scale on-chip resonator at greater than 1 ghz frequency,” Phys. Rev. Lett. 98,123901 (2007).
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T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature,  443, 671 (2006).
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L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization entangled state measurement on a chip,” Phys. Rev. Lett. 105, 200503 (2010).
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S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, ”Comment on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38 (2011).
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E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” arXiv:1107.3761 (2011).

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J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
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Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461,772–775 (2009).
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Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 13905 (2008).
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E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” arXiv:1107.3761 (2011).

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

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T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature,  443, 671 (2006).
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I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99, 093901 (2007).
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Winger, M.

A. H. Safavi-Naeini, T. P. M. 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).
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L. Feng, M. Ayache, J. Huang, Y. -L. Xu, M. -H. Lu, Y. -F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011).
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Yu, Z.

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, ”Comment on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38 (2011).
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T. R. Zaman, X. Guo, and R. J. Ram, “Faraday rotation in an InP waveguide,” App. Phys. Lett. 90, 023514 (2007).
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Zoller, P.

K. Stannigel, P. Rabl, A. S. Sørensen, M. D. Lukin, and P. Zoller, “Optomechanical transducers for quantum information processing,” Phys. Rev. A 84, 042341 (2011).
[CrossRef]

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105, 220501 (2010).
[CrossRef]

Zumofen, G.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counterpropagating whispering-gallery modes by a single rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99, 173603 (2007).
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I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99, 093901 (2007).
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Adv. At., Mol., Opt. Phys. (1)

A. Schliesser and T. J. Kippenberg, “Cavity optomechanics with whispering-gallery mode optical microresonators,” Adv. At., Mol., Opt. Phys. 58, 207–323 (2010).
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App. Phys. Lett. (1)

T. R. Zaman, X. Guo, and R. J. Ram, “Faraday rotation in an InP waveguide,” App. Phys. Lett. 90, 023514 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

K. Gallo, G. Assanto, K. Parameswaran, and M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79, 314–316 (2001).
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J. Opt. Soc. Am. B (1)

Nat. Photonics (4)

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).
[CrossRef]

M. S. Kang, A. Butsch, and P. St. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics 5, 549–553 (2011).
[CrossRef]

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
[CrossRef]

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[CrossRef]

Nat. Phys. (3)

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).
[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
[CrossRef]

M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7, 907–912 (2011).
[CrossRef]

Nature (4)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461,772–775 (2009).
[CrossRef] [PubMed]

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

A. H. Safavi-Naeini, T. P. M. 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] [PubMed]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature,  443, 671 (2006).
[CrossRef] [PubMed]

New J. Phys. (1)

D. E. Chang, A.H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys. 13, 023003 (2011).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (8)

D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced mott transitions and xy spin models in coupled cavity arrays,” Phys. Rev. A 76, 31805 (2007).
[CrossRef]

S. Mancini and P. Tombesi, “Quantum noise reduction by radiation pressure,” Phys. Rev. A 49, 4055–4065 (1994).
[CrossRef] [PubMed]

K. Stannigel, P. Rabl, A. S. Sørensen, M. D. Lukin, and P. Zoller, “Optomechanical transducers for quantum information processing,” Phys. Rev. A 84, 042341 (2011).
[CrossRef]

C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A 49,1337–1343 (1994).
[CrossRef] [PubMed]

R. O. Umucalilar and I. Carusotto, “Artificial gauge field for photons in coupled cavity arrays,” Phys. Rev. A 84, 043804 (2011).
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J. Koch, A. A Houck, K. Le Hur, and S. M. Girvin, “Time-reversal symmetry breaking in circuit-QED based photon lattices,” Phys. Rev. A 82, 043811 (2010).
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G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A,  81, 041803 (2010).
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Phys. Rev. Lett. (11)

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization entangled state measurement on a chip,” Phys. Rev. Lett. 105, 200503 (2010).
[CrossRef]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100, 13905 (2008).
[CrossRef]

S. Manipatruni, J. Robinson, and M. Lipson, “Optical nonreciprocity in optomechanical structures,” Phys. Rev. Lett. 102, 213903 (2009).
[CrossRef] [PubMed]

F. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 13904 (2008).
[CrossRef]

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99, 093901 (2007).
[CrossRef] [PubMed]

F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, “Quantum theory of cavity-assisted sideband cooling of mechanical motion,” Phys. Rev. Lett. 99, 93902 (2007).
[CrossRef]

T. Carmon and K. Vahala, “Modal spectroscopy of optoexcited vibrations of a micron-scale on-chip resonator at greater than 1 ghz frequency,” Phys. Rev. Lett. 98,123901 (2007).
[CrossRef] [PubMed]

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency gaas nano-optomechanical disk resonator,” Phys. Rev. Lett. 105, 263903 (2010).
[CrossRef]

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105, 220501 (2010).
[CrossRef]

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counterpropagating whispering-gallery modes by a single rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99, 173603 (2007).
[CrossRef] [PubMed]

P. Rabl, “Photon blockade effect in optomechanical systems,” Phys. Rev. Lett. 107, 063601 (2011).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

R. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004).
[CrossRef]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys.,  77, 633–673 (2005).
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Science (4)

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

A. Politi, J. C. F. Matthews, and J. L. O’Brien, “Shor’s quantum factoring algorithm on a photonic chip,” Science 325, 1221 (2009).
[CrossRef] [PubMed]

L. Feng, M. Ayache, J. Huang, Y. -L. Xu, M. -H. Lu, Y. -F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011).
[CrossRef] [PubMed]

S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, ”Comment on Nonreciprocal light propagation in a silicon photonic circuit,” Science 335, 38 (2011).
[CrossRef]

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R. B. Wehrspohn, H. S. Kitzerow, and K. Busch. Nanophotonic Materials: Photonic Crystals, Plasmonics, and Metamaterials (Wiley-VCH, 2008).

E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” arXiv:1107.3761 (2011).

D. Brooks, T. Botter, N. Brahms, T. Purdy, S. Schreppler, and D. Stamper-Kurn, “Ponderomotive light squeezing with atomic cavity optomechanics,” arXiv:1107.5609 (2011).

R. E. Prange, S. M. Girvin, and M. E. Cage. The Quantum Hall Effect. (Springer-Verlag, 1986).

A. Comtet, T. Jolicoeur, S. Ouvry, and F. David, editors, The Quantum Hall Effect: Novel Excitations and Broken Symmetries (Spinger-Verlag, 2000).

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Figures (7)

Fig. 1
Fig. 1

Non-reciprocal optomechanical device. (a) A strong pump field enhances the optomechanical coupling between an isolated vibrational mode and the right-circulating optical mode inside a ring resonator. This results in different transmission properties for right-and left-moving fields in the waveguide. (b) Optical isolation. (c) Non-reciprocal phase shifter.

Fig. 2
Fig. 2

(a) Transmission |tR/L|2 of the OM system when operated as an optical isolator (κin = κ). Within the resonator bandwidth, the left-moving field is attenuated while the right-moving field is almost completely transmitted. For this plot GR = 5κ. (b) Non-reciprocal phase shifter (κin = 0.01κ). Both the left and the right input field are almost completely transmitted (> 98%), but acquire different phases, Δθ = θRθL. Black lines show the location of resonances. For these plots γm = 0.

Fig. 3
Fig. 3

General add-drop configuration, which can be employed for non-reciprocal photon routing between the upper and lower waveguide. It reduces to the resonator coupled to a single waveguide, if the coupling to the lower waveguide is absent (κ′ = 0).

Fig. 4
Fig. 4

Mean photon number in the left and right circulating modes in the presence of a finite mode coupling β and as a function of the pump detuning Δ = ωL ωc. For this plot we have assumed that the pump field only drives the right-circulating mode and that the resonator is coupled to a single waveguide (κ′ = 0). The other parameters are (β,κin)/κ = (4,1). At the normal mode frequencies ω ≃ ±β, the left- and right-circulating modes are almost equally populated, while everywhere else, there is an intensity imbalance between left- and right-circulating modes. (b) The diagram shows the relation between the relevant frequencies in the system. In the presence of the mode coupling, the sidebands (±β) are located around the bare resonator frequency ωc and the resonator is pumped at the mechanical red sideband.

Fig. 5
Fig. 5

Transmittance for light propagating in a waveguide coupled to a resonator (AFP), in the presence of (a) weak (β = 2κ) and (b) strong (β = 8κ) mode mixing. For these plots we have assumed (ωm, GR,κin,γm)/κ = (20,5,1,0) and Δ = −ωm.

Fig. 6
Fig. 6

Operational bandwidth of an optical diode in the presence of a finite mode coupling β and different values of the enhanced OM coupling GR. For this plot we have assumed GL = 0 and (ωminm)/κ = (20,1,0), Δ = −ωm. In the absence of the mode coupling the bandwidth is 4κ, which for a finite β can be recovered by using a strong pump to enhance |GR|.

Fig. 7
Fig. 7

Ratio between phase sensitive squeezing terms (η) and the phase-insensitive transmission amplitudes (α). For this plot we have assumed Δ = −ωm and (G,κinm)/κ = (5,.5,0).

Equations (32)

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H om = ω m b b + i = L , R ω c a i a i + g 0 a i a i ( b + b ) .
H om lin = Δ ( a R a R + a L a L ) + ω m b b + ( G R a R + G R * a R ) ( b + b ) ,
f R / L , out ( t ) = f R / L , in ( t ) + 2 κ a R / L ( t ) ,
a ˙ R = ( i Δ κ in κ ) a R i G R ( b + b ) 2 κ f R , in ,
a ˙ L = ( i Δ κ in κ ) a L 2 κ f L , in ,
b ˙ = ( i ω m γ m ) b i G R * a R i G R a R ,
( f R , out ( δ ) f L , out ( δ ) ) = ( t R ( δ ) r L ( δ ) r R ( δ ) t L ( δ ) ) ( f R , in ( δ ) f L , in ( δ ) ) ,
t L = κ in κ i δ κ in + κ i δ , t R = 1 2 ( γ m / 2 i δ ) κ | G R | 2 + ( γ m / 2 i δ ) ( κ + κ in i δ ) .
( f R , out ( δ ) f L , out ( δ ) ) ( 1 0 0 0 ) ( f R , in ( δ ) f L , in ( δ ) ) .
( f R , out ( δ ) f L , out ( δ ) ) ( e i θ R ( δ ) 0 0 e i θ L ( δ ) ) ( f R , in ( δ ) f L , in ( δ ) ) .
H = H om + β a L a R + β * a R a L .
a ˙ i ( t ) = i [ H , a i ( t ) ] κ t a i ( t ) 2 κ f i , in 1 ( t ) 2 κ f i , in 2 ( t ) 2 κ in f i , 0 ( t ) ,
b ˙ ( t ) = i [ H , b ( t ) ] γ m 2 b ( t ) γ m ξ ( t ) ,
a ˙ R = ( i Δ 0 i g 0 b + b κ t ) a R i β * a L 2 κ ,
a ˙ L = ( i Δ 0 i g 0 b + b κ t ) a L i β a R ,
b ˙ = i ω m b i g 0 ( | a R | 2 + | a L | 2 ) .
0 = ( i Δ κ t ) a R i β * a L 2 κ ,
0 = ( i Δ κ t ) a L i β a R .
a R = 2 κ ( i Δ κ t ) ( i Δ κ t ) 2 + | β | 2 , a L = i β i Δ κ t a R ,
H = ω m b b i = R , L Δ a i a i + β a L a R + β * a R a L + i = R , L ( G i a i + G i * a i ) ( b + b ) ,
t v ( t ) = M v ( t ) 2 κ I 1 ( t ) 2 κ I 2 ( t ) γ m I m ( t ) .
M = i ( ω m i γ m / 2 G R * G L * 0 G R G L G R Δ i κ t β * G R 0 0 G L β Δ i κ t G L 0 0 0 G R * G L * ω m i γ m / 2 G R G L G R * 0 0 G R * Δ i κ t β G L * 0 0 G L * β * Δ i κ t ) ,
v ˜ ( ω ) = ( M + i ω 𝕀 ) 1 ( 2 κ I ˜ 1 ( ω ) + 2 κ I ˜ 2 ( ω ) + γ m I ˜ m ( ω ) ) .
O ˜ 1 ( ω ) = ( 0 , f ˜ R , out 1 ( ω ) , f ˜ L , out 1 ( ω ) , 0 , f ˜ R , out 1 ( ω ) , f ˜ L , out 1 ( ω ) ) T ,
O ˜ 1 ( ω ) = 2 κ diag ( 0 , 1 , 1 , 0 , 1 , 1 ) v ˜ ( ω ) + I ˜ 1 ( ω ) ,
α R = 2 κ ( i Δ κ t ) ( i Δ κ t ) 2 + | β | 2 , α L = 2 i β κ | β | 2 + ( i Δ κ t ) 2 ,
P noise = h ¯ ω c × B d ω 2 π f ˜ R , out 1 ( ω ) f ˜ R , out 1 ( ω ) ,
P noise h ¯ ω c B d ω 2 π 2 γ m N th κ G R 2 G R 4 2 G R 2 ( ω ω m ) 2 + ( κ t 2 + ( ω ω m ) 2 ) ( ω ω m ) 2 .
P noise h ¯ ω c × γ m N th × κ Δ B G R 2 .
( f R , out 1 ( ω ) f R , out 1 ( ω ) ) = ( α ( ω ) η ( ω ) η * ( ω ) α * ( ω ) ) ( f R , in 1 ( ω ) f R , in 1 ( ω ) ) ,
α ( ω ) = 4 | G | 2 ω m ( ω m + i κ ) ( ω 2 ω m 2 ) ( ( ω + i κ in ) 2 ( ω m + i κ ) 2 ) ( 4 | G | 2 ω m 2 + ( ω 2 ω m 2 ) ( ( κ + κ in i ω ) 2 + ω m 2 ) ) ,
η ( ω ) = 4 i G 2 κ ω m ( 4 | G | 2 ω m 2 + ( ω 2 ω m 2 ) ( ( κ + κ in i ω ) 2 + ω m 2 ) ) .

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