Abstract

Based on photon-phonon nonlinear interaction, a scheme of controllable photon-phonon converters is proposed at single-quantum level in a composed quadratically coupled optomechanical system. With the assistance of the mechanical oscillator, the Kerr nonlinear effect between photon and phonon is enhanced so that the single-photon state can be converted into the phonon state with high fidelity even under the current experimental condition that the single-photon coupling rate is much smaller than mechanical frequency (gωm). The state transfer protocols and their transfer fidelity are discussed analytically and numerically. A multi-path photon-phonon converter is designed by combining the optomechanical system with low frequency resonators, which can be controlled by experimentally adjustable parameters. This work provides us a potential platform for quantum state transfer and quantum information.

© 2017 Optical Society of America

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  4. H. Jing, X. Zhao, and L. F. Buchmann, “Quantum optomechanics with a mixture of ultracold atoms”, Phys. Rev. A 86, 065801 (2012)
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  10. K. Zhang, F. Bariani, Y. Dong, W. Zhang, and P. Meystre, “Proposal for an optomechanical microwave sensor at the subphoton level,” Phys. Rev. Lett. 114, 113601 (2015).
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    [Crossref]
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    [Crossref] [PubMed]
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    [PubMed]
  32. M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
    [Crossref]
  33. A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly Efficient Single-Pass Source of Pulsed Single-Mode Twin Beams of Light,” Phys. Rev. Lett. 106, 013603 (2011).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2016 (7)

J. Cheng, W.-Z. Zhang, L. Zhou, and W. Zhang, “Preservation Macroscopic Entanglement of Optomechanical Systems in non-Markovian Environment,” Sci. Rep. 6, 23678 (2016).
[Crossref] [PubMed]

Q. Mu, X. Zhao, and T. Yu, “Memory-effect-induced macroscopic-microscopic entanglement,” Phys. Rev. A 94, 012334 (2016).
[Crossref]

W.-Z. Zhang, J. Cheng, W.-D. Li, and L. Zhou, “Optomechanical cooling in the non-markovian regime,” Phys. Rev. A 93, 063853 (2016).
[Crossref]

J.-Q. Liao and L. Tian, “Macroscopic quantum superposition in cavity optomechanics,” Phys. Rev. Lett. 116, 163602 (2016).
[Crossref] [PubMed]

S. Davuluri and Y. Li, “Absolute rotation detection by Coriolis force measurement using optomechanics,” New Journal of Physics 18, 103047 (2016).
[Crossref]

W. Li, C. Li, and H. Song, “Quantum synchronization in an optomechanical system based on lyapunov control,” Phys. Rev. E 93, 062221 (2016).
[Crossref] [PubMed]

R. Riedinger and et al.,“Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530, 313–316 (2016).
[Crossref] [PubMed]

2015 (6)

L. Tian, “Optoelectromechanical transducer: Reversible conversion between microwave and optical photons,” Annalen der Physik 527, 1–14 (2015).
[Crossref]

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

W.-Z. Zhang, J. Cheng, and L. Zhou, “Quantum control gate in cavity optomechanical system,” Journal of Physics B: Atomic, Molecular and Optical Physics 48, 015502 (2015).
[Crossref]

Y.-C. Liu, Y.-F. Xiao, X. Luan, Q. Gong, and C. W. Wong, “Coupled cavities for motional ground-state cooling and strong optomechanical coupling,” Phys. Rev. A 91, 033818 (2015).
[Crossref]

K. Qu and G. S. Agarwal, “Generating quadrature squeezed light with dissipative optomechanical coupling,” Phys. Rev. A 91, 063815 (2015).
[Crossref]

K. Zhang, F. Bariani, Y. Dong, W. Zhang, and P. Meystre, “Proposal for an optomechanical microwave sensor at the subphoton level,” Phys. Rev. Lett. 114, 113601 (2015).
[Crossref] [PubMed]

2014 (5)

Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
[Crossref] [PubMed]

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

Z. H. Wang, L. Zhou, Y. Li, and C. P. Sun, “Controllable single-photon frequency converter via a one-dimensional waveguide,” Phys. Rev. A 89, 053813 (2014).
[Crossref]

X.-W. Xu and Y. Li, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a weakly nonlinear cavity,” Phys. Rev. A 90, 033832 (2014).
[Crossref]

M. Lee and et al., “Three-dimensional imaging of cavity vacuum with single atoms localized by a nanohole array,” Nat. Commun. 5, 3441 (2014).
[PubMed]

2013 (6)

S. A. McGee, D. Meiser, C. A. Regal, K. W. Lehnert, and M. J. Holland, “Mechanical resonators for storage and transfer of electrical and optical quantum states,” Phys. Rev. A 87, 053818 (2013).
[Crossref]

W.-B. Yan, J.-F. Huang, and H. Fan, “Tunable single-photon frequency conversion in a Sagnac interferometer,” Sci. Rep. 3, 3555 (2013).
[Crossref] [PubMed]

H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013).
[Crossref]

A. Mari, A. Farace, N. Didier, V. Giovannetti, and R. Fazio, “Measures of quantum synchronization in continuous variable systems,” Phys. Rev. Lett. 111, 103605 (2013).
[Crossref]

M. Ludwig and F. Marquardt, “Quantum many-body dynamics in optomechanical arrays,” Phys. Rev. Lett. 111, 073603 (2013).
[Crossref] [PubMed]

I. Mahboob, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi, “Phonon lasing in an electromechanical resonator,” Phys. Rev. Lett. 110, 127202 (2013).
[Crossref] [PubMed]

2012 (4)

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, L.-J. Xie, Z.-Y. Wang, and L.-M. Kuang, “Photonic two-qubit parity gate with tiny cross-kerr nonlinearity,” Phys. Rev. A 85, 052326 (2012).
[Crossref]

S. Singh, H. Jing, E. M. Wright, and P. Meystre, “Quantum-state transfer between a bose-einstein condensate and an optomechanical mirror,” Phys. Rev. A 86, 021801 (2012).
[Crossref]

H. Jing, X. Zhao, and L. F. Buchmann, “Quantum optomechanics with a mixture of ultracold atoms”, Phys. Rev. A 86, 065801 (2012)
[Crossref]

K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
[Crossref] [PubMed]

2011 (2)

H. Jing, D. S. Goldbaum, L. Buchmann, and P. Meystre, “Quantum Optomechanics of a Bose-Einstein Antiferromagnet”, Phys. Rev. Lett. 106, 223601 (2011).
[Crossref] [PubMed]

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly Efficient Single-Pass Source of Pulsed Single-Mode Twin Beams of Light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

2010 (2)

Y.-x. Liu, A. Miranowicz, Y. B. Gao, J. c. v. Bajer, C. P. Sun, and F. Nori, “Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators,” Phys. Rev. A 82, 032101 (2010).
[Crossref]

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

2008 (2)

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

L. Tian, M. S. Allman, and R. W. Simmonds, “Parametric coupling between macroscopic quantum resonators,” New Journal of Physics 10, 115001 (2008).
[Crossref]

2006 (1)

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

2005 (2)

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
[Crossref]

A. Zhang and M. S. Demokan, “Broadband wavelength converter based on four-wave mixing in a highly nonlinear photonic crystal fiber,” Opt. Lett. 30, 2375–2377 (2005).
[Crossref] [PubMed]

2003 (1)

J. Zhang, K. Peng, and S. L. Braunstein, “Quantum-state transfer from light to macroscopic oscillators,” Phys. Rev. A 68, 013808 (2003).
[Crossref]

2002 (1)

P. Bertet and et al.,“Direct Measurement of the Wigner Function of a One-Photon Fock State in a Cavity,” Phys. Rev. Lett. 89, 200402 (2002).
[Crossref] [PubMed]

Agarwal, G. S.

K. Qu and G. S. Agarwal, “Generating quadrature squeezed light with dissipative optomechanical coupling,” Phys. Rev. A 91, 063815 (2015).
[Crossref]

Allman, M. S.

L. Tian, M. S. Allman, and R. W. Simmonds, “Parametric coupling between macroscopic quantum resonators,” New Journal of Physics 10, 115001 (2008).
[Crossref]

Ansmann, M.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Arcizet, O.

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

Aspelmeyer, M.

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

Bajer, J. c. v.

Y.-x. Liu, A. Miranowicz, Y. B. Gao, J. c. v. Bajer, C. P. Sun, and F. Nori, “Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators,” Phys. Rev. A 82, 032101 (2010).
[Crossref]

Banaszek, K.

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005).
[Crossref]

Bariani, F.

K. Zhang, F. Bariani, Y. Dong, W. Zhang, and P. Meystre, “Proposal for an optomechanical microwave sensor at the subphoton level,” Phys. Rev. Lett. 114, 113601 (2015).
[Crossref] [PubMed]

Barzanjeh, S.

S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

Bennett, S. D.

K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
[Crossref] [PubMed]

Bertet, P.

P. Bertet and et al.,“Direct Measurement of the Wigner Function of a One-Photon Fock State in a Cavity,” Phys. Rev. Lett. 89, 200402 (2002).
[Crossref] [PubMed]

Bialczak, R. C.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Blair, D. G.

Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
[Crossref] [PubMed]

Braunstein, S. L.

J. Zhang, K. Peng, and S. L. Braunstein, “Quantum-state transfer from light to macroscopic oscillators,” Phys. Rev. A 68, 013808 (2003).
[Crossref]

Briant, T.

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

Buchmann, L.

H. Jing, D. S. Goldbaum, L. Buchmann, and P. Meystre, “Quantum Optomechanics of a Bose-Einstein Antiferromagnet”, Phys. Rev. Lett. 106, 223601 (2011).
[Crossref] [PubMed]

Buchmann, L. F.

H. Jing, X. Zhao, and L. F. Buchmann, “Quantum optomechanics with a mixture of ultracold atoms”, Phys. Rev. A 86, 065801 (2012)
[Crossref]

Chang, C.-Y.

H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013).
[Crossref]

Chang, E. Y.

H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013).
[Crossref]

Chen, Y.

Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
[Crossref] [PubMed]

Cheng, J.

J. Cheng, W.-Z. Zhang, L. Zhou, and W. Zhang, “Preservation Macroscopic Entanglement of Optomechanical Systems in non-Markovian Environment,” Sci. Rep. 6, 23678 (2016).
[Crossref] [PubMed]

W.-Z. Zhang, J. Cheng, W.-D. Li, and L. Zhou, “Optomechanical cooling in the non-markovian regime,” Phys. Rev. A 93, 063853 (2016).
[Crossref]

W.-Z. Zhang, J. Cheng, and L. Zhou, “Quantum control gate in cavity optomechanical system,” Journal of Physics B: Atomic, Molecular and Optical Physics 48, 015502 (2015).
[Crossref]

Christ, A.

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly Efficient Single-Pass Source of Pulsed Single-Mode Twin Beams of Light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref] [PubMed]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000), Chap.7.

Cleland, a. N.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Cohadon, P.-F.

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

Danilishin, S. L.

Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
[Crossref] [PubMed]

Davuluri, S.

S. Davuluri and Y. Li, “Absolute rotation detection by Coriolis force measurement using optomechanics,” New Journal of Physics 18, 103047 (2016).
[Crossref]

Demokan, M. S.

Didier, N.

A. Mari, A. Farace, N. Didier, V. Giovannetti, and R. Fazio, “Measures of quantum synchronization in continuous variable systems,” Phys. Rev. Lett. 111, 103605 (2013).
[Crossref]

Dong, Y.

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A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and a. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
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Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
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H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013).
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W.-B. Yan, J.-F. Huang, and H. Fan, “Tunable single-photon frequency conversion in a Sagnac interferometer,” Sci. Rep. 3, 3555 (2013).
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Q. Mu, X. Zhao, and T. Yu, “Memory-effect-induced macroscopic-microscopic entanglement,” Phys. Rev. A 94, 012334 (2016).
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J. Cheng, W.-Z. Zhang, L. Zhou, and W. Zhang, “Preservation Macroscopic Entanglement of Optomechanical Systems in non-Markovian Environment,” Sci. Rep. 6, 23678 (2016).
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K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
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L. Tian, “Optoelectromechanical transducer: Reversible conversion between microwave and optical photons,” Annalen der Physik 527, 1–14 (2015).
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Journal of Physics B: Atomic, Molecular and Optical Physics (1)

W.-Z. Zhang, J. Cheng, and L. Zhou, “Quantum control gate in cavity optomechanical system,” Journal of Physics B: Atomic, Molecular and Optical Physics 48, 015502 (2015).
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R. Riedinger and et al.,“Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530, 313–316 (2016).
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J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
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H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nature Phys. 9, 480–484 (2013).
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L. Tian, M. S. Allman, and R. W. Simmonds, “Parametric coupling between macroscopic quantum resonators,” New Journal of Physics 10, 115001 (2008).
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S. Davuluri and Y. Li, “Absolute rotation detection by Coriolis force measurement using optomechanics,” New Journal of Physics 18, 103047 (2016).
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J. Zhang, K. Peng, and S. L. Braunstein, “Quantum-state transfer from light to macroscopic oscillators,” Phys. Rev. A 68, 013808 (2003).
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S. Singh, H. Jing, E. M. Wright, and P. Meystre, “Quantum-state transfer between a bose-einstein condensate and an optomechanical mirror,” Phys. Rev. A 86, 021801 (2012).
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S. A. McGee, D. Meiser, C. A. Regal, K. W. Lehnert, and M. J. Holland, “Mechanical resonators for storage and transfer of electrical and optical quantum states,” Phys. Rev. A 87, 053818 (2013).
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H. Jing, X. Zhao, and L. F. Buchmann, “Quantum optomechanics with a mixture of ultracold atoms”, Phys. Rev. A 86, 065801 (2012)
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Q. Mu, X. Zhao, and T. Yu, “Memory-effect-induced macroscopic-microscopic entanglement,” Phys. Rev. A 94, 012334 (2016).
[Crossref]

W.-Z. Zhang, J. Cheng, W.-D. Li, and L. Zhou, “Optomechanical cooling in the non-markovian regime,” Phys. Rev. A 93, 063853 (2016).
[Crossref]

Y.-C. Liu, Y.-F. Xiao, X. Luan, Q. Gong, and C. W. Wong, “Coupled cavities for motional ground-state cooling and strong optomechanical coupling,” Phys. Rev. A 91, 033818 (2015).
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K. Qu and G. S. Agarwal, “Generating quadrature squeezed light with dissipative optomechanical coupling,” Phys. Rev. A 91, 063815 (2015).
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Z. H. Wang, L. Zhou, Y. Li, and C. P. Sun, “Controllable single-photon frequency converter via a one-dimensional waveguide,” Phys. Rev. A 89, 053813 (2014).
[Crossref]

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X.-W. Xu and Y. Li, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a weakly nonlinear cavity,” Phys. Rev. A 90, 033832 (2014).
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Phys. Rev. E (1)

W. Li, C. Li, and H. Song, “Quantum synchronization in an optomechanical system based on lyapunov control,” Phys. Rev. E 93, 062221 (2016).
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I. Mahboob, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi, “Phonon lasing in an electromechanical resonator,” Phys. Rev. Lett. 110, 127202 (2013).
[Crossref] [PubMed]

K. Zhang, F. Bariani, Y. Dong, W. Zhang, and P. Meystre, “Proposal for an optomechanical microwave sensor at the subphoton level,” Phys. Rev. Lett. 114, 113601 (2015).
[Crossref] [PubMed]

Y. Ma, S. L. Danilishin, C. Zhao, H. Miao, W. Z. Korth, Y. Chen, R. L. Ward, and D. G. Blair, “Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction,” Phys. Rev. Lett. 113, 151102 (2014).
[Crossref] [PubMed]

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S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, “Microwave quantum illumination,” Phys. Rev. Lett. 114, 080503 (2015).
[Crossref] [PubMed]

K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
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Sci. Rep. (2)

J. Cheng, W.-Z. Zhang, L. Zhou, and W. Zhang, “Preservation Macroscopic Entanglement of Optomechanical Systems in non-Markovian Environment,” Sci. Rep. 6, 23678 (2016).
[Crossref] [PubMed]

W.-B. Yan, J.-F. Huang, and H. Fan, “Tunable single-photon frequency conversion in a Sagnac interferometer,” Sci. Rep. 3, 3555 (2013).
[Crossref] [PubMed]

Other (1)

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000), Chap.7.

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Figures (6)

Fig. 1
Fig. 1 The quadratically coupled optomechanical system consists of a membrane in the middle of the cavity. The membrane is interacted to a low frequency resonator with the coupling strength V via a capacitance C.
Fig. 2
Fig. 2 The effective frequency of the mechanical oscillator ωeff, effective coupling strength geff, the ratio of | g eff ω eff | and effective damping rate γeff is a function of mechanical coupling strength V, corresponding to (a), (b) and (c), respectively. (d), (e) and (f) show these effective parameters changing with the frequency difference Δωm = ωm1ωm2 (. For (a), (b) and (c), the parameters are g/ωm1 = 10−4, ωm2/ωm1 = 0.998, γm1/ωm1 = 10−6, γm1/γm2 = 102, while for (d), (e) and (f), the parameters are g/ωm1 = 10−4, γm1/ωm1 = 10−6, V/ωm1 = 5 × 10−2, γm1/γm2 = 102.
Fig. 3
Fig. 3 (a) The comparison of analytical and numerical solution of fidelity Fcp. The mechanical coupling rate V/ωm1 = 3.16 × 10−2. The fidelity Fcp as a function of time t with different mechanical coupling strength V/ωm1 = 1.35 × 10−2, 2.58 × 10−2, 3.16 × 10−2, corresponding to (b), (c) and (d), respectively. The corresponding ratio | g eff ω eff | = 0.01, 0.05, 0.1, and the maximal fidelity Fcpmax ≈ 0.83, 0.94, 0.97. For all of the figures, κ/g = 0.5, nth = 1, and the other parameters are the same with Fig. 2.
Fig. 4
Fig. 4 Quantum circuit of photon-phonon convertor. After performing single-qubit operation according to the measure result, we can obtain the state we want in mechanical mode.
Fig. 5
Fig. 5 Schematic diagram of multi-controlled phase gate and quantum circuit of photon-phonon conveter.
Fig. 6
Fig. 6 The dynamic of the conversion fidelity with different effective coupling rate ge2. The blue line denotes the conversion fidelity of output port 1, the green line denotes the conversion fidelity of output port 2. Other parameters are ωe1 = ωe2, κ1 = κ2 = 0.1ωe1, J1/ωe1 = 0.1, γ1 = 10γ2 = 10−5ωe1, nth1 = nth2 = 5.

Equations (36)

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H = H sys + H d
H sys = ω c a a g a a ( b 1 + b 1 ) 2 + j = 1 , 2 ( ω m j b j b j + V b j b 3 j ) ,
H d = ε ( a e i ω d t + a e i ω d t ) ,
H eff = Δ a a + ω eff b 2 b 2 + g eff a a b 2 b 2 ,
Δ 1 = ω c ω d g ,
ω eff = ω m 2 V 2 ( ω m 1 ω m 2 ) | A | 2 ,
g eff = 2 g V 2 | A | 2 ,
A = i ( ω m 1 ω m 2 ) + ( γ 1 γ 2 ) / 2 .
| ψ = α | 0 c | 0 m + β | 0 c | 1 m + γ | 1 c | 0 m + δ | 1 c | 1 m ,
| Φ = α | 0 c | 0 m + β | 0 c | 1 m + γ | 1 c | 0 m δ | 1 c | 1 m .
| ψ f = α | 0 c | 0 m + β e i θ 01 | 0 c | 1 m + γ e i ω 10 | 1 c | 0 m + δ e i θ 11 | 1 c | 1 m ,
F c p = | α 2 e i θ 00 + β 2 e i θ 01 + γ 2 e i θ 10 δ 2 e i θ 11 | ,
θ 01 = ω eff t = 2 n 1 π , θ 10 = Δ t = 2 n 2 π , θ 11 = ( ω eff + Δ g eff ) t = ( 2 n 3 + 1 ) π , n i ( i = 1 , 2 , 3 ) ,
ρ ˙ = i [ ρ , H ] + κ 𝒟 [ a ] ρ + j = 1 , 2 γ j ( n t h j + 1 ) 𝒟 [ b j ] ρ + γ j n t h j 𝒟 [ b j ] ρ ,
1 2 | 0 1 ( α | 0 2 + β | 1 2 ) + | 1 1 ( α | 0 2 β | 1 2 ) ,
H = j = 1 n ω j a j a j + ω m j b j b j + ω A j b A j b A j + g j a j a j ( b j + b j ) 2 + V j ( b j b A j + b j b A j ) + s = 1 n 1 J s ( a 1 a s + 1 + a 1 a s + 1 ) ,
H eff = j = 1 n Δ j a j a j + ω e j b A j b A j + g e j a j a j b A j b A j + s = 1 n 1 J s ( a 1 a s + 1 + a 1 a s + 1 ) ,
F Cj = F Gj F Sj = ( ψ f | ρ j | ψ f ψ 0 | ρ a j | ψ 0 ) 1 / 4 ,
H sys = ω c a a g a a ( b 1 b 1 + b 1 b 1 ) + j = 1 , 2 ( ω m j b j b j + V b j b 3 j ) .
a ˙ = ( i Δ + κ / 2 ) a + 2 i g a b 1 b 1 + κ a in ,
b ˙ 1 = ( i ω m 1 + γ 1 / 2 ) b 1 + 2 i g b 1 a 1 a 1 i V b 2 + γ 1 b in , 1 ,
b ˙ 2 = ( i ω m 2 + γ 2 / 2 ) b 2 i V b 1 + γ 2 b in , 2 ,
a ˙ = ( i Δ + κ / 2 ) a + 2 i g a N b + κ a in ,
b ˙ 1 = ( i ω m 1 + γ 1 / 2 ) b 1 + 2 i g b 1 N a i V b 2 + γ 1 b in , 1 ,
b ˙ 2 = ( i ω m 2 + γ 2 / 2 ) b 2 i V b 1 + γ 2 b in , 2 ,
N ˙ a = κ 1 N a ,
a 1 ( t ) = a ( 0 ) e ( i Δ + κ / 2 ) t e 0 t d τ 2 i g N b ( τ ) + 0 t d τ e ( i Δ + κ / 2 ) ( t τ ) e τ t d τ 2 i g N b ( τ ) κ a in ( τ ) ] ,
b 1 ( t ) = b 1 ( 0 ) e ( i ω m 1 + γ 1 / 2 ) t e 0 t d τ 2 i g N a ( τ ) + 0 t d τ e ( i ω m 1 + γ 1 / 2 ) ( t τ ) e τ t d τ 2 i g N a ( τ ) [ i V b 2 ( τ ) + γ 1 b in , 1 ( τ ) ] ,
b 2 ( t ) = b 2 ( 0 ) e ( i ω m 2 + γ 2 / 2 ) t + 0 t d τ e ( i ω m 2 + γ 2 / 2 ) ( t τ ) [ i V b 1 ( τ ) + γ 2 b in , 2 ( τ ) ] ,
b 2 ( 0 ) ( t ) b 2 ( 0 ) e ( i ω m 2 + γ 2 / 2 ) t + B in , 2 ( t ) ,
b 1 ( t ) b 1 ( 0 ) e ( i ω m 1 + γ 1 / 2 2 i g N a t ) + 0 t d τ e ( i ω m 1 + γ 1 / 2 2 i g N a ) ( t τ ) × [ i V b 2 ( 0 ) e ( i ω m 2 + γ 2 / 2 ) τ i V B in , 2 ( τ ) + γ 1 b in , 1 ( τ ) ] .
b 1 ( t ) i V b 2 ( t ) i ( ω m 1 ω m 2 ) + ( γ 1 γ 2 ) / 2 2 i g N a + B in , 1
b 1 ( t ) i V b 2 ( t ) A [ 1 + i ( ω m 1 ω m 2 ) + ( γ 1 γ 2 / 2 ) 2 i g N a | A | 2 ] + B in , 1 ( t )
a ˙ = ( i Δ + κ / 2 ) a + i g eff a b 2 b 2 + κ a in ,
b ˙ 2 = ( i ω eff + γ eff / 2 ) b 2 + i g eff b 2 a a + γ eff B in , 2 ,
H eff = Δ a a + ω eff b 2 b 2 + g eff a a b 2 b 2 .

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