Abstract

We report a study of optomechanical entanglement under the drive of one or a series of laser pulses with arbitrary detuning and different pulse shapes. Because of the non-existence of system steady state under pulsed driving field, we adopt a different approach from the standard treatment to optomechanical entanglement. The situation of the entanglement evolution in high temperature is also discussed.

© 2015 Optical Society of America

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References

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  1. T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15 (25), 17172–17205 (2007).
    [Crossref] [PubMed]
  2. T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics: backaction at the mesoscale,” Science 321 (5893), 1172–1176 (2008).
    [Crossref] [PubMed]
  3. C. Genes, A. Mari, D. Vitali, and P. Tombesi, “Quantum effects in optomechanical systems,” Adv. At. Mol. Opt. Phys. 57, 33–86 (2009).
    [Crossref]
  4. G. J. Milburn and M. J. Woolley, “An introduction to quantum optomechanics,” Acta Phys. Slovaca 61(5), 483–601 (2011).
    [Crossref]
  5. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
    [Crossref]
  6. H. J. Metcalf and P. Van der Straten, Laser Cooling and Trapping (Springer Science & Business Media, 1999).
    [Crossref]
  7. K. C. Schwab and M. L. Roukes, “Putting mechanics into quantum mechanics,” Phys. Today 58(7), 36–42 (2005).
    [Crossref]
  8. B. Abbott and et al., “Analysis of first LIGO science data for stochastic gravitational waves,” Phys. Rev. D 69(12), 122004 (2004).
    [Crossref]
  9. F. Acernese and et al., “Status of VIRGO,” Class. Quantum Grav. 22(18), S869 (2005).
    [Crossref]
  10. 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 (9), 093902 (2007).
    [Crossref] [PubMed]
  11. I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99 (9), 093901 (2007).
    [Crossref] [PubMed]
  12. F. Marquardt, A. A. Clerk, and S. M. Girvin, “Quantum theory of optomechanical cooling,” J. Mod. Opt. 55(19–20), 3329–3338 (2008).
    [Crossref]
  13. Y. C. Liu, Y. W. Hu, C. W. Wong, and Y. F. Xiao, “Review of cavity optomechanical cooling,” Chin. Phys. B 22(11), 114213 (2013).
    [Crossref]
  14. D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
    [Crossref] [PubMed]
  15. M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
    [Crossref]
  16. D. Vitali, P. Tombesi, M. J. Woolley, A. C. Doherty, and G. J. Milburn, “Entangling a nanomechanical resonator and a superconducting microwave cavity,” Phys. Rev. A 76(4), 042336 (2007).
    [Crossref]
  17. C. Genes, A. Mari, P. Tombesi, and D. Vitali, “Robust entanglement of a micromechanical resonator with output optical fields,” Phys. Rev. A 78(3), 032316 (2008).
    [Crossref]
  18. M. J. Hartmann and M. B. Plenio, “Steady state entanglement in the mechanical vibrations of two dielectric membranes,” Phys. Rev. Lett. 101(20), 200503 (2008).
    [Crossref] [PubMed]
  19. F. Galve, L. A. Pachon, and D. Zueco, “Bringing entanglement to the high temperature limit,” Phys. Rev. Lett. 105(18), 180501 (2010).
    [Crossref]
  20. C. L. Zou, X. B. Zou, F. W. Sun, Z. F. Han, and G. C. Guo, “Room-temperature steady-state optomechanical entanglement on a chip,” Phys. Rev. A 84(3), 032317 (2011).
    [Crossref]
  21. M. Abdi, S. Barzanjeh, P. Tombesi, and D. Vitali, “Effect of phase noise on the generation of stationary entanglement in cavity optomechanics,” Phys. Rev. A 84(3), 032325 (2011).
    [Crossref]
  22. R. Ghobadi, A. R. Bahrampour, and C. Simon, “Quantum optomechanics in the bistable regime,” Phys. Rev. A 84(3), 033846 (2011).
    [Crossref]
  23. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 2000).
  24. B. He, “Quantum optomechanics beyond linearization,” Phys. Rev. A 85(6), 063820 (2012).
    [Crossref]
  25. Q. Lin, B. He, R. Ghobadi, and C. Simon, “Fully quantum approach to optomechanical entanglement,” Phys. Rev. A 90(2), 022309 (2014).
    [Crossref]
  26. O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large quantum superpositions and interference of massive nanometer-sized objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
    [Crossref] [PubMed]
  27. M. R. Vanner, I. Pikovski, G. D. Cole, M. S. Kim, Č. Brukner, K. Hammerer, G. J. Milburn, and M. Aspelmeyer, “Pulsed quantum optomechanics,” Proc. Natl. Acad. Sci. USA 108(39), 16182–16187 (2011).
    [Crossref] [PubMed]
  28. X. T. Wang, S. Vinjanampathy, F. W. Strauch, and K. Jacobs, “Ultraefficient cooling of resonators: beating sideband cooling with quantum control,” Phys. Rev. Lett. 107(17), 177204 (2011).
    [Crossref] [PubMed]
  29. S. G. Hofer, W. Wieczorek, M. Aspelmeyer, and K. Hammerer, “Quantum entanglement and teleportation in pulsed cavity optomechanics,” Phys. Rev. A 84(5), 052327 (2011).
    [Crossref]
  30. M. R. Vanner, “Selective linear or quadratic optomechanical coupling via measurement,” Phys. Rev. X 1(2), 021011 (2011).
  31. S. Machnes, J. Cerrillo, M. Aspelmeyer, W. Wieczorek, M. B. Plenio, and A. Retzker, “Pulsed laser cooling for cavity-optomechanical resonators,” Phys. Rev. Lett. 108(15), 153601 (2012).
    [Crossref] [PubMed]
  32. M. R. Vanner, J. Hofer, G. D. Cole, and M. Aspelmeyer, “Cooling-by-measurement and mechanical state tomography via pulsed optomechanics,” Nat. Commun. 4, 2295 (2013)
    [Crossref] [PubMed]
  33. Q. Y. He and M. D. Reid, “Einstein-Podolsky-Rosen paradox and quantum steering in pulsed optomechanics,” Phys. Rev. A 88(5), 052121 (2013).
    [Crossref]
  34. U. Akram, W. P. Bowen, and G. J. Milburn, “Entangled mechanical cat states via conditional single photon optomechanics,” New J. Phys. 15(9), 093007 (2013).
    [Crossref]
  35. S. Kiesewetter, Q. Y. He, P. D. Drummond, and M. D. Reid, “Scalable quantum simulation of pulsed entanglement and Einstein-Podolsky-Rosen steering in optomechanics,” Phys. Rev. A 90(4), 043805 (2014).
    [Crossref]
  36. C. W. Gardiner and P. Zoller, Quantum Noise (Springer, 2000).
    [Crossref]
  37. A. V. Sharypov and B. He, “Generation of arbitrary symmetric entangled states with conditional linear optical coupling,” Phys. Rev. A 87(3), 032323 (2013).
    [Crossref]
  38. B. He, A. V. Sharypov, J. Sheng, C. Simon, and M. Xiao, “Two-photon dynamics in coherent rydberg atomic ensemble,” Phys. Rev. Lett. 112(13), 133606 (2014).
    [Crossref] [PubMed]
  39. B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91(5), 053832 (2015).
    [Crossref]
  40. G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65(3), 032314 (2002).
    [Crossref]
  41. G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70(2), 022318 (2004).
    [Crossref]
  42. M. B. Plenio, “The logarithmic negativity: A full entanglement monotone that is not convex,” Phys. Rev. Lett. 95(9), 090503 (2005).
    [Crossref] [PubMed]

2015 (1)

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91(5), 053832 (2015).
[Crossref]

2014 (4)

B. He, A. V. Sharypov, J. Sheng, C. Simon, and M. Xiao, “Two-photon dynamics in coherent rydberg atomic ensemble,” Phys. Rev. Lett. 112(13), 133606 (2014).
[Crossref] [PubMed]

S. Kiesewetter, Q. Y. He, P. D. Drummond, and M. D. Reid, “Scalable quantum simulation of pulsed entanglement and Einstein-Podolsky-Rosen steering in optomechanics,” Phys. Rev. A 90(4), 043805 (2014).
[Crossref]

Q. Lin, B. He, R. Ghobadi, and C. Simon, “Fully quantum approach to optomechanical entanglement,” Phys. Rev. A 90(2), 022309 (2014).
[Crossref]

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

2013 (5)

Y. C. Liu, Y. W. Hu, C. W. Wong, and Y. F. Xiao, “Review of cavity optomechanical cooling,” Chin. Phys. B 22(11), 114213 (2013).
[Crossref]

A. V. Sharypov and B. He, “Generation of arbitrary symmetric entangled states with conditional linear optical coupling,” Phys. Rev. A 87(3), 032323 (2013).
[Crossref]

M. R. Vanner, J. Hofer, G. D. Cole, and M. Aspelmeyer, “Cooling-by-measurement and mechanical state tomography via pulsed optomechanics,” Nat. Commun. 4, 2295 (2013)
[Crossref] [PubMed]

Q. Y. He and M. D. Reid, “Einstein-Podolsky-Rosen paradox and quantum steering in pulsed optomechanics,” Phys. Rev. A 88(5), 052121 (2013).
[Crossref]

U. Akram, W. P. Bowen, and G. J. Milburn, “Entangled mechanical cat states via conditional single photon optomechanics,” New J. Phys. 15(9), 093007 (2013).
[Crossref]

2012 (2)

B. He, “Quantum optomechanics beyond linearization,” Phys. Rev. A 85(6), 063820 (2012).
[Crossref]

S. Machnes, J. Cerrillo, M. Aspelmeyer, W. Wieczorek, M. B. Plenio, and A. Retzker, “Pulsed laser cooling for cavity-optomechanical resonators,” Phys. Rev. Lett. 108(15), 153601 (2012).
[Crossref] [PubMed]

2011 (9)

C. L. Zou, X. B. Zou, F. W. Sun, Z. F. Han, and G. C. Guo, “Room-temperature steady-state optomechanical entanglement on a chip,” Phys. Rev. A 84(3), 032317 (2011).
[Crossref]

M. Abdi, S. Barzanjeh, P. Tombesi, and D. Vitali, “Effect of phase noise on the generation of stationary entanglement in cavity optomechanics,” Phys. Rev. A 84(3), 032325 (2011).
[Crossref]

R. Ghobadi, A. R. Bahrampour, and C. Simon, “Quantum optomechanics in the bistable regime,” Phys. Rev. A 84(3), 033846 (2011).
[Crossref]

O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large quantum superpositions and interference of massive nanometer-sized objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
[Crossref] [PubMed]

M. R. Vanner, I. Pikovski, G. D. Cole, M. S. Kim, Č. Brukner, K. Hammerer, G. J. Milburn, and M. Aspelmeyer, “Pulsed quantum optomechanics,” Proc. Natl. Acad. Sci. USA 108(39), 16182–16187 (2011).
[Crossref] [PubMed]

X. T. Wang, S. Vinjanampathy, F. W. Strauch, and K. Jacobs, “Ultraefficient cooling of resonators: beating sideband cooling with quantum control,” Phys. Rev. Lett. 107(17), 177204 (2011).
[Crossref] [PubMed]

S. G. Hofer, W. Wieczorek, M. Aspelmeyer, and K. Hammerer, “Quantum entanglement and teleportation in pulsed cavity optomechanics,” Phys. Rev. A 84(5), 052327 (2011).
[Crossref]

M. R. Vanner, “Selective linear or quadratic optomechanical coupling via measurement,” Phys. Rev. X 1(2), 021011 (2011).

G. J. Milburn and M. J. Woolley, “An introduction to quantum optomechanics,” Acta Phys. Slovaca 61(5), 483–601 (2011).
[Crossref]

2010 (1)

F. Galve, L. A. Pachon, and D. Zueco, “Bringing entanglement to the high temperature limit,” Phys. Rev. Lett. 105(18), 180501 (2010).
[Crossref]

2009 (1)

C. Genes, A. Mari, D. Vitali, and P. Tombesi, “Quantum effects in optomechanical systems,” Adv. At. Mol. Opt. Phys. 57, 33–86 (2009).
[Crossref]

2008 (4)

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics: backaction at the mesoscale,” Science 321 (5893), 1172–1176 (2008).
[Crossref] [PubMed]

F. Marquardt, A. A. Clerk, and S. M. Girvin, “Quantum theory of optomechanical cooling,” J. Mod. Opt. 55(19–20), 3329–3338 (2008).
[Crossref]

C. Genes, A. Mari, P. Tombesi, and D. Vitali, “Robust entanglement of a micromechanical resonator with output optical fields,” Phys. Rev. A 78(3), 032316 (2008).
[Crossref]

M. J. Hartmann and M. B. Plenio, “Steady state entanglement in the mechanical vibrations of two dielectric membranes,” Phys. Rev. Lett. 101(20), 200503 (2008).
[Crossref] [PubMed]

2007 (6)

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
[Crossref]

D. Vitali, P. Tombesi, M. J. Woolley, A. C. Doherty, and G. J. Milburn, “Entangling a nanomechanical resonator and a superconducting microwave cavity,” Phys. Rev. A 76(4), 042336 (2007).
[Crossref]

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 (9), 093902 (2007).
[Crossref] [PubMed]

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99 (9), 093901 (2007).
[Crossref] [PubMed]

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15 (25), 17172–17205 (2007).
[Crossref] [PubMed]

2005 (3)

M. B. Plenio, “The logarithmic negativity: A full entanglement monotone that is not convex,” Phys. Rev. Lett. 95(9), 090503 (2005).
[Crossref] [PubMed]

F. Acernese and et al., “Status of VIRGO,” Class. Quantum Grav. 22(18), S869 (2005).
[Crossref]

K. C. Schwab and M. L. Roukes, “Putting mechanics into quantum mechanics,” Phys. Today 58(7), 36–42 (2005).
[Crossref]

2004 (2)

B. Abbott and et al., “Analysis of first LIGO science data for stochastic gravitational waves,” Phys. Rev. D 69(12), 122004 (2004).
[Crossref]

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70(2), 022318 (2004).
[Crossref]

2002 (1)

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65(3), 032314 (2002).
[Crossref]

Abbott, B.

B. Abbott and et al., “Analysis of first LIGO science data for stochastic gravitational waves,” Phys. Rev. D 69(12), 122004 (2004).
[Crossref]

Abdi, M.

M. Abdi, S. Barzanjeh, P. Tombesi, and D. Vitali, “Effect of phase noise on the generation of stationary entanglement in cavity optomechanics,” Phys. Rev. A 84(3), 032325 (2011).
[Crossref]

Acernese, F.

F. Acernese and et al., “Status of VIRGO,” Class. Quantum Grav. 22(18), S869 (2005).
[Crossref]

Adesso, G.

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70(2), 022318 (2004).
[Crossref]

Akram, U.

U. Akram, W. P. Bowen, and G. J. Milburn, “Entangled mechanical cat states via conditional single photon optomechanics,” New J. Phys. 15(9), 093007 (2013).
[Crossref]

Aspelmeyer, M.

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

M. R. Vanner, J. Hofer, G. D. Cole, and M. Aspelmeyer, “Cooling-by-measurement and mechanical state tomography via pulsed optomechanics,” Nat. Commun. 4, 2295 (2013)
[Crossref] [PubMed]

S. Machnes, J. Cerrillo, M. Aspelmeyer, W. Wieczorek, M. B. Plenio, and A. Retzker, “Pulsed laser cooling for cavity-optomechanical resonators,” Phys. Rev. Lett. 108(15), 153601 (2012).
[Crossref] [PubMed]

S. G. Hofer, W. Wieczorek, M. Aspelmeyer, and K. Hammerer, “Quantum entanglement and teleportation in pulsed cavity optomechanics,” Phys. Rev. A 84(5), 052327 (2011).
[Crossref]

M. R. Vanner, I. Pikovski, G. D. Cole, M. S. Kim, Č. Brukner, K. Hammerer, G. J. Milburn, and M. Aspelmeyer, “Pulsed quantum optomechanics,” Proc. Natl. Acad. Sci. USA 108(39), 16182–16187 (2011).
[Crossref] [PubMed]

O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large quantum superpositions and interference of massive nanometer-sized objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
[Crossref] [PubMed]

M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
[Crossref]

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

Bahrampour, A. R.

R. Ghobadi, A. R. Bahrampour, and C. Simon, “Quantum optomechanics in the bistable regime,” Phys. Rev. A 84(3), 033846 (2011).
[Crossref]

Barzanjeh, S.

M. Abdi, S. Barzanjeh, P. Tombesi, and D. Vitali, “Effect of phase noise on the generation of stationary entanglement in cavity optomechanics,” Phys. Rev. A 84(3), 032325 (2011).
[Crossref]

Blaser, F.

O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large quantum superpositions and interference of massive nanometer-sized objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
[Crossref] [PubMed]

Böhm, H. R.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

Bowen, W. P.

U. Akram, W. P. Bowen, and G. J. Milburn, “Entangled mechanical cat states via conditional single photon optomechanics,” New J. Phys. 15(9), 093007 (2013).
[Crossref]

Brukner, C.

M. R. Vanner, I. Pikovski, G. D. Cole, M. S. Kim, Č. Brukner, K. Hammerer, G. J. Milburn, and M. Aspelmeyer, “Pulsed quantum optomechanics,” Proc. Natl. Acad. Sci. USA 108(39), 16182–16187 (2011).
[Crossref] [PubMed]

M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
[Crossref]

Cerrillo, J.

S. Machnes, J. Cerrillo, M. Aspelmeyer, W. Wieczorek, M. B. Plenio, and A. Retzker, “Pulsed laser cooling for cavity-optomechanical resonators,” Phys. Rev. Lett. 108(15), 153601 (2012).
[Crossref] [PubMed]

Chen, J. P.

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 (9), 093902 (2007).
[Crossref] [PubMed]

Cirac, J. I.

O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large quantum superpositions and interference of massive nanometer-sized objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
[Crossref] [PubMed]

Clerk, A. A.

F. Marquardt, A. A. Clerk, and S. M. Girvin, “Quantum theory of optomechanical cooling,” J. Mod. Opt. 55(19–20), 3329–3338 (2008).
[Crossref]

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 (9), 093902 (2007).
[Crossref] [PubMed]

Cole, G. D.

M. R. Vanner, J. Hofer, G. D. Cole, and M. Aspelmeyer, “Cooling-by-measurement and mechanical state tomography via pulsed optomechanics,” Nat. Commun. 4, 2295 (2013)
[Crossref] [PubMed]

M. R. Vanner, I. Pikovski, G. D. Cole, M. S. Kim, Č. Brukner, K. Hammerer, G. J. Milburn, and M. Aspelmeyer, “Pulsed quantum optomechanics,” Proc. Natl. Acad. Sci. USA 108(39), 16182–16187 (2011).
[Crossref] [PubMed]

Doherty, A. C.

D. Vitali, P. Tombesi, M. J. Woolley, A. C. Doherty, and G. J. Milburn, “Entangling a nanomechanical resonator and a superconducting microwave cavity,” Phys. Rev. A 76(4), 042336 (2007).
[Crossref]

Drummond, P. D.

S. Kiesewetter, Q. Y. He, P. D. Drummond, and M. D. Reid, “Scalable quantum simulation of pulsed entanglement and Einstein-Podolsky-Rosen steering in optomechanics,” Phys. Rev. A 90(4), 043805 (2014).
[Crossref]

Eisert, J.

M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
[Crossref]

Ferreira, A.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

Galve, F.

F. Galve, L. A. Pachon, and D. Zueco, “Bringing entanglement to the high temperature limit,” Phys. Rev. Lett. 105(18), 180501 (2010).
[Crossref]

Gardiner, C. W.

C. W. Gardiner and P. Zoller, Quantum Noise (Springer, 2000).
[Crossref]

Genes, C.

C. Genes, A. Mari, D. Vitali, and P. Tombesi, “Quantum effects in optomechanical systems,” Adv. At. Mol. Opt. Phys. 57, 33–86 (2009).
[Crossref]

C. Genes, A. Mari, P. Tombesi, and D. Vitali, “Robust entanglement of a micromechanical resonator with output optical fields,” Phys. Rev. A 78(3), 032316 (2008).
[Crossref]

Ghobadi, R.

Q. Lin, B. He, R. Ghobadi, and C. Simon, “Fully quantum approach to optomechanical entanglement,” Phys. Rev. A 90(2), 022309 (2014).
[Crossref]

R. Ghobadi, A. R. Bahrampour, and C. Simon, “Quantum optomechanics in the bistable regime,” Phys. Rev. A 84(3), 033846 (2011).
[Crossref]

Gigan, S.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
[Crossref]

Girvin, S. M.

F. Marquardt, A. A. Clerk, and S. M. Girvin, “Quantum theory of optomechanical cooling,” J. Mod. Opt. 55(19–20), 3329–3338 (2008).
[Crossref]

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 (9), 093902 (2007).
[Crossref] [PubMed]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 2000).

Guerreiro, A.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

Guo, G. C.

C. L. Zou, X. B. Zou, F. W. Sun, Z. F. Han, and G. C. Guo, “Room-temperature steady-state optomechanical entanglement on a chip,” Phys. Rev. A 84(3), 032317 (2011).
[Crossref]

Hammerer, K.

S. G. Hofer, W. Wieczorek, M. Aspelmeyer, and K. Hammerer, “Quantum entanglement and teleportation in pulsed cavity optomechanics,” Phys. Rev. A 84(5), 052327 (2011).
[Crossref]

M. R. Vanner, I. Pikovski, G. D. Cole, M. S. Kim, Č. Brukner, K. Hammerer, G. J. Milburn, and M. Aspelmeyer, “Pulsed quantum optomechanics,” Proc. Natl. Acad. Sci. USA 108(39), 16182–16187 (2011).
[Crossref] [PubMed]

Han, Z. F.

C. L. Zou, X. B. Zou, F. W. Sun, Z. F. Han, and G. C. Guo, “Room-temperature steady-state optomechanical entanglement on a chip,” Phys. Rev. A 84(3), 032317 (2011).
[Crossref]

Hartmann, M. J.

M. J. Hartmann and M. B. Plenio, “Steady state entanglement in the mechanical vibrations of two dielectric membranes,” Phys. Rev. Lett. 101(20), 200503 (2008).
[Crossref] [PubMed]

He, B.

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91(5), 053832 (2015).
[Crossref]

Q. Lin, B. He, R. Ghobadi, and C. Simon, “Fully quantum approach to optomechanical entanglement,” Phys. Rev. A 90(2), 022309 (2014).
[Crossref]

B. He, A. V. Sharypov, J. Sheng, C. Simon, and M. Xiao, “Two-photon dynamics in coherent rydberg atomic ensemble,” Phys. Rev. Lett. 112(13), 133606 (2014).
[Crossref] [PubMed]

A. V. Sharypov and B. He, “Generation of arbitrary symmetric entangled states with conditional linear optical coupling,” Phys. Rev. A 87(3), 032323 (2013).
[Crossref]

B. He, “Quantum optomechanics beyond linearization,” Phys. Rev. A 85(6), 063820 (2012).
[Crossref]

He, Q. Y.

S. Kiesewetter, Q. Y. He, P. D. Drummond, and M. D. Reid, “Scalable quantum simulation of pulsed entanglement and Einstein-Podolsky-Rosen steering in optomechanics,” Phys. Rev. A 90(4), 043805 (2014).
[Crossref]

Q. Y. He and M. D. Reid, “Einstein-Podolsky-Rosen paradox and quantum steering in pulsed optomechanics,” Phys. Rev. A 88(5), 052121 (2013).
[Crossref]

Hofer, J.

M. R. Vanner, J. Hofer, G. D. Cole, and M. Aspelmeyer, “Cooling-by-measurement and mechanical state tomography via pulsed optomechanics,” Nat. Commun. 4, 2295 (2013)
[Crossref] [PubMed]

Hofer, S. G.

S. G. Hofer, W. Wieczorek, M. Aspelmeyer, and K. Hammerer, “Quantum entanglement and teleportation in pulsed cavity optomechanics,” Phys. Rev. A 84(5), 052327 (2011).
[Crossref]

Hu, Y. W.

Y. C. Liu, Y. W. Hu, C. W. Wong, and Y. F. Xiao, “Review of cavity optomechanical cooling,” Chin. Phys. B 22(11), 114213 (2013).
[Crossref]

Illuminati, F.

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70(2), 022318 (2004).
[Crossref]

Jacobs, K.

X. T. Wang, S. Vinjanampathy, F. W. Strauch, and K. Jacobs, “Ultraefficient cooling of resonators: beating sideband cooling with quantum control,” Phys. Rev. Lett. 107(17), 177204 (2011).
[Crossref] [PubMed]

Kaltenbaek, R.

O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large quantum superpositions and interference of massive nanometer-sized objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
[Crossref] [PubMed]

Kiesel, N.

O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large quantum superpositions and interference of massive nanometer-sized objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
[Crossref] [PubMed]

Kiesewetter, S.

S. Kiesewetter, Q. Y. He, P. D. Drummond, and M. D. Reid, “Scalable quantum simulation of pulsed entanglement and Einstein-Podolsky-Rosen steering in optomechanics,” Phys. Rev. A 90(4), 043805 (2014).
[Crossref]

Kim, M. S.

M. R. Vanner, I. Pikovski, G. D. Cole, M. S. Kim, Č. Brukner, K. Hammerer, G. J. Milburn, and M. Aspelmeyer, “Pulsed quantum optomechanics,” Proc. Natl. Acad. Sci. USA 108(39), 16182–16187 (2011).
[Crossref] [PubMed]

M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
[Crossref]

Kippenberg, T. J.

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

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics: backaction at the mesoscale,” Science 321 (5893), 1172–1176 (2008).
[Crossref] [PubMed]

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15 (25), 17172–17205 (2007).
[Crossref] [PubMed]

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99 (9), 093901 (2007).
[Crossref] [PubMed]

Lin, Q.

Q. Lin, B. He, R. Ghobadi, and C. Simon, “Fully quantum approach to optomechanical entanglement,” Phys. Rev. A 90(2), 022309 (2014).
[Crossref]

Liu, Y. C.

Y. C. Liu, Y. W. Hu, C. W. Wong, and Y. F. Xiao, “Review of cavity optomechanical cooling,” Chin. Phys. B 22(11), 114213 (2013).
[Crossref]

Machnes, S.

S. Machnes, J. Cerrillo, M. Aspelmeyer, W. Wieczorek, M. B. Plenio, and A. Retzker, “Pulsed laser cooling for cavity-optomechanical resonators,” Phys. Rev. Lett. 108(15), 153601 (2012).
[Crossref] [PubMed]

Mari, A.

C. Genes, A. Mari, D. Vitali, and P. Tombesi, “Quantum effects in optomechanical systems,” Adv. At. Mol. Opt. Phys. 57, 33–86 (2009).
[Crossref]

C. Genes, A. Mari, P. Tombesi, and D. Vitali, “Robust entanglement of a micromechanical resonator with output optical fields,” Phys. Rev. A 78(3), 032316 (2008).
[Crossref]

Marquardt, F.

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

F. Marquardt, A. A. Clerk, and S. M. Girvin, “Quantum theory of optomechanical cooling,” J. Mod. Opt. 55(19–20), 3329–3338 (2008).
[Crossref]

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 (9), 093902 (2007).
[Crossref] [PubMed]

Metcalf, H. J.

H. J. Metcalf and P. Van der Straten, Laser Cooling and Trapping (Springer Science & Business Media, 1999).
[Crossref]

Milburn, G. J.

U. Akram, W. P. Bowen, and G. J. Milburn, “Entangled mechanical cat states via conditional single photon optomechanics,” New J. Phys. 15(9), 093007 (2013).
[Crossref]

G. J. Milburn and M. J. Woolley, “An introduction to quantum optomechanics,” Acta Phys. Slovaca 61(5), 483–601 (2011).
[Crossref]

M. R. Vanner, I. Pikovski, G. D. Cole, M. S. Kim, Č. Brukner, K. Hammerer, G. J. Milburn, and M. Aspelmeyer, “Pulsed quantum optomechanics,” Proc. Natl. Acad. Sci. USA 108(39), 16182–16187 (2011).
[Crossref] [PubMed]

D. Vitali, P. Tombesi, M. J. Woolley, A. C. Doherty, and G. J. Milburn, “Entangling a nanomechanical resonator and a superconducting microwave cavity,” Phys. Rev. A 76(4), 042336 (2007).
[Crossref]

Nooshi, N.

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99 (9), 093901 (2007).
[Crossref] [PubMed]

Pachon, L. A.

F. Galve, L. A. Pachon, and D. Zueco, “Bringing entanglement to the high temperature limit,” Phys. Rev. Lett. 105(18), 180501 (2010).
[Crossref]

Paternostro, M.

M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
[Crossref]

Pflanzer, A. C.

O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large quantum superpositions and interference of massive nanometer-sized objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
[Crossref] [PubMed]

Pikovski, I.

M. R. Vanner, I. Pikovski, G. D. Cole, M. S. Kim, Č. Brukner, K. Hammerer, G. J. Milburn, and M. Aspelmeyer, “Pulsed quantum optomechanics,” Proc. Natl. Acad. Sci. USA 108(39), 16182–16187 (2011).
[Crossref] [PubMed]

Plenio, M. B.

S. Machnes, J. Cerrillo, M. Aspelmeyer, W. Wieczorek, M. B. Plenio, and A. Retzker, “Pulsed laser cooling for cavity-optomechanical resonators,” Phys. Rev. Lett. 108(15), 153601 (2012).
[Crossref] [PubMed]

M. J. Hartmann and M. B. Plenio, “Steady state entanglement in the mechanical vibrations of two dielectric membranes,” Phys. Rev. Lett. 101(20), 200503 (2008).
[Crossref] [PubMed]

M. B. Plenio, “The logarithmic negativity: A full entanglement monotone that is not convex,” Phys. Rev. Lett. 95(9), 090503 (2005).
[Crossref] [PubMed]

Reid, M. D.

S. Kiesewetter, Q. Y. He, P. D. Drummond, and M. D. Reid, “Scalable quantum simulation of pulsed entanglement and Einstein-Podolsky-Rosen steering in optomechanics,” Phys. Rev. A 90(4), 043805 (2014).
[Crossref]

Q. Y. He and M. D. Reid, “Einstein-Podolsky-Rosen paradox and quantum steering in pulsed optomechanics,” Phys. Rev. A 88(5), 052121 (2013).
[Crossref]

Retzker, A.

S. Machnes, J. Cerrillo, M. Aspelmeyer, W. Wieczorek, M. B. Plenio, and A. Retzker, “Pulsed laser cooling for cavity-optomechanical resonators,” Phys. Rev. Lett. 108(15), 153601 (2012).
[Crossref] [PubMed]

Romero-Isart, O.

O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large quantum superpositions and interference of massive nanometer-sized objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
[Crossref] [PubMed]

Roukes, M. L.

K. C. Schwab and M. L. Roukes, “Putting mechanics into quantum mechanics,” Phys. Today 58(7), 36–42 (2005).
[Crossref]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 2000).

Schwab, K. C.

K. C. Schwab and M. L. Roukes, “Putting mechanics into quantum mechanics,” Phys. Today 58(7), 36–42 (2005).
[Crossref]

Serafini, A.

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70(2), 022318 (2004).
[Crossref]

Sharypov, A. V.

B. He, A. V. Sharypov, J. Sheng, C. Simon, and M. Xiao, “Two-photon dynamics in coherent rydberg atomic ensemble,” Phys. Rev. Lett. 112(13), 133606 (2014).
[Crossref] [PubMed]

A. V. Sharypov and B. He, “Generation of arbitrary symmetric entangled states with conditional linear optical coupling,” Phys. Rev. A 87(3), 032323 (2013).
[Crossref]

Sheng, J.

B. He, A. V. Sharypov, J. Sheng, C. Simon, and M. Xiao, “Two-photon dynamics in coherent rydberg atomic ensemble,” Phys. Rev. Lett. 112(13), 133606 (2014).
[Crossref] [PubMed]

Simon, C.

B. He, A. V. Sharypov, J. Sheng, C. Simon, and M. Xiao, “Two-photon dynamics in coherent rydberg atomic ensemble,” Phys. Rev. Lett. 112(13), 133606 (2014).
[Crossref] [PubMed]

Q. Lin, B. He, R. Ghobadi, and C. Simon, “Fully quantum approach to optomechanical entanglement,” Phys. Rev. A 90(2), 022309 (2014).
[Crossref]

R. Ghobadi, A. R. Bahrampour, and C. Simon, “Quantum optomechanics in the bistable regime,” Phys. Rev. A 84(3), 033846 (2011).
[Crossref]

Strauch, F. W.

X. T. Wang, S. Vinjanampathy, F. W. Strauch, and K. Jacobs, “Ultraefficient cooling of resonators: beating sideband cooling with quantum control,” Phys. Rev. Lett. 107(17), 177204 (2011).
[Crossref] [PubMed]

Sun, F. W.

C. L. Zou, X. B. Zou, F. W. Sun, Z. F. Han, and G. C. Guo, “Room-temperature steady-state optomechanical entanglement on a chip,” Phys. Rev. A 84(3), 032317 (2011).
[Crossref]

Tombesi, P.

M. Abdi, S. Barzanjeh, P. Tombesi, and D. Vitali, “Effect of phase noise on the generation of stationary entanglement in cavity optomechanics,” Phys. Rev. A 84(3), 032325 (2011).
[Crossref]

C. Genes, A. Mari, D. Vitali, and P. Tombesi, “Quantum effects in optomechanical systems,” Adv. At. Mol. Opt. Phys. 57, 33–86 (2009).
[Crossref]

C. Genes, A. Mari, P. Tombesi, and D. Vitali, “Robust entanglement of a micromechanical resonator with output optical fields,” Phys. Rev. A 78(3), 032316 (2008).
[Crossref]

D. Vitali, P. Tombesi, M. J. Woolley, A. C. Doherty, and G. J. Milburn, “Entangling a nanomechanical resonator and a superconducting microwave cavity,” Phys. Rev. A 76(4), 042336 (2007).
[Crossref]

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

Vahala, K. J.

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics: backaction at the mesoscale,” Science 321 (5893), 1172–1176 (2008).
[Crossref] [PubMed]

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15 (25), 17172–17205 (2007).
[Crossref] [PubMed]

Van der Straten, P.

H. J. Metcalf and P. Van der Straten, Laser Cooling and Trapping (Springer Science & Business Media, 1999).
[Crossref]

Vanner, M. R.

M. R. Vanner, J. Hofer, G. D. Cole, and M. Aspelmeyer, “Cooling-by-measurement and mechanical state tomography via pulsed optomechanics,” Nat. Commun. 4, 2295 (2013)
[Crossref] [PubMed]

M. R. Vanner, “Selective linear or quadratic optomechanical coupling via measurement,” Phys. Rev. X 1(2), 021011 (2011).

M. R. Vanner, I. Pikovski, G. D. Cole, M. S. Kim, Č. Brukner, K. Hammerer, G. J. Milburn, and M. Aspelmeyer, “Pulsed quantum optomechanics,” Proc. Natl. Acad. Sci. USA 108(39), 16182–16187 (2011).
[Crossref] [PubMed]

Vedral, V.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

Vidal, G.

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65(3), 032314 (2002).
[Crossref]

Vinjanampathy, S.

X. T. Wang, S. Vinjanampathy, F. W. Strauch, and K. Jacobs, “Ultraefficient cooling of resonators: beating sideband cooling with quantum control,” Phys. Rev. Lett. 107(17), 177204 (2011).
[Crossref] [PubMed]

Vitali, D.

M. Abdi, S. Barzanjeh, P. Tombesi, and D. Vitali, “Effect of phase noise on the generation of stationary entanglement in cavity optomechanics,” Phys. Rev. A 84(3), 032325 (2011).
[Crossref]

C. Genes, A. Mari, D. Vitali, and P. Tombesi, “Quantum effects in optomechanical systems,” Adv. At. Mol. Opt. Phys. 57, 33–86 (2009).
[Crossref]

C. Genes, A. Mari, P. Tombesi, and D. Vitali, “Robust entanglement of a micromechanical resonator with output optical fields,” Phys. Rev. A 78(3), 032316 (2008).
[Crossref]

M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
[Crossref]

D. Vitali, P. Tombesi, M. J. Woolley, A. C. Doherty, and G. J. Milburn, “Entangling a nanomechanical resonator and a superconducting microwave cavity,” Phys. Rev. A 76(4), 042336 (2007).
[Crossref]

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

Wang, J.

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91(5), 053832 (2015).
[Crossref]

Wang, X. T.

X. T. Wang, S. Vinjanampathy, F. W. Strauch, and K. Jacobs, “Ultraefficient cooling of resonators: beating sideband cooling with quantum control,” Phys. Rev. Lett. 107(17), 177204 (2011).
[Crossref] [PubMed]

Werner, R. F.

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65(3), 032314 (2002).
[Crossref]

Wieczorek, W.

S. Machnes, J. Cerrillo, M. Aspelmeyer, W. Wieczorek, M. B. Plenio, and A. Retzker, “Pulsed laser cooling for cavity-optomechanical resonators,” Phys. Rev. Lett. 108(15), 153601 (2012).
[Crossref] [PubMed]

S. G. Hofer, W. Wieczorek, M. Aspelmeyer, and K. Hammerer, “Quantum entanglement and teleportation in pulsed cavity optomechanics,” Phys. Rev. A 84(5), 052327 (2011).
[Crossref]

Wilson-Rae, I.

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99 (9), 093901 (2007).
[Crossref] [PubMed]

Wong, C. W.

Y. C. Liu, Y. W. Hu, C. W. Wong, and Y. F. Xiao, “Review of cavity optomechanical cooling,” Chin. Phys. B 22(11), 114213 (2013).
[Crossref]

Woolley, M. J.

G. J. Milburn and M. J. Woolley, “An introduction to quantum optomechanics,” Acta Phys. Slovaca 61(5), 483–601 (2011).
[Crossref]

D. Vitali, P. Tombesi, M. J. Woolley, A. C. Doherty, and G. J. Milburn, “Entangling a nanomechanical resonator and a superconducting microwave cavity,” Phys. Rev. A 76(4), 042336 (2007).
[Crossref]

Xiao, M.

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91(5), 053832 (2015).
[Crossref]

B. He, A. V. Sharypov, J. Sheng, C. Simon, and M. Xiao, “Two-photon dynamics in coherent rydberg atomic ensemble,” Phys. Rev. Lett. 112(13), 133606 (2014).
[Crossref] [PubMed]

Xiao, Y. F.

Y. C. Liu, Y. W. Hu, C. W. Wong, and Y. F. Xiao, “Review of cavity optomechanical cooling,” Chin. Phys. B 22(11), 114213 (2013).
[Crossref]

Yan, S. B.

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91(5), 053832 (2015).
[Crossref]

Zeilinger, A.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

Zoller, P.

C. W. Gardiner and P. Zoller, Quantum Noise (Springer, 2000).
[Crossref]

Zou, C. L.

C. L. Zou, X. B. Zou, F. W. Sun, Z. F. Han, and G. C. Guo, “Room-temperature steady-state optomechanical entanglement on a chip,” Phys. Rev. A 84(3), 032317 (2011).
[Crossref]

Zou, X. B.

C. L. Zou, X. B. Zou, F. W. Sun, Z. F. Han, and G. C. Guo, “Room-temperature steady-state optomechanical entanglement on a chip,” Phys. Rev. A 84(3), 032317 (2011).
[Crossref]

Zueco, D.

F. Galve, L. A. Pachon, and D. Zueco, “Bringing entanglement to the high temperature limit,” Phys. Rev. Lett. 105(18), 180501 (2010).
[Crossref]

Zwerger, W.

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99 (9), 093901 (2007).
[Crossref] [PubMed]

Acta Phys. Slovaca (1)

G. J. Milburn and M. J. Woolley, “An introduction to quantum optomechanics,” Acta Phys. Slovaca 61(5), 483–601 (2011).
[Crossref]

Adv. At. Mol. Opt. Phys. (1)

C. Genes, A. Mari, D. Vitali, and P. Tombesi, “Quantum effects in optomechanical systems,” Adv. At. Mol. Opt. Phys. 57, 33–86 (2009).
[Crossref]

Chin. Phys. B (1)

Y. C. Liu, Y. W. Hu, C. W. Wong, and Y. F. Xiao, “Review of cavity optomechanical cooling,” Chin. Phys. B 22(11), 114213 (2013).
[Crossref]

Class. Quantum Grav. (1)

F. Acernese and et al., “Status of VIRGO,” Class. Quantum Grav. 22(18), S869 (2005).
[Crossref]

J. Mod. Opt. (1)

F. Marquardt, A. A. Clerk, and S. M. Girvin, “Quantum theory of optomechanical cooling,” J. Mod. Opt. 55(19–20), 3329–3338 (2008).
[Crossref]

Nat. Commun. (1)

M. R. Vanner, J. Hofer, G. D. Cole, and M. Aspelmeyer, “Cooling-by-measurement and mechanical state tomography via pulsed optomechanics,” Nat. Commun. 4, 2295 (2013)
[Crossref] [PubMed]

New J. Phys. (1)

U. Akram, W. P. Bowen, and G. J. Milburn, “Entangled mechanical cat states via conditional single photon optomechanics,” New J. Phys. 15(9), 093007 (2013).
[Crossref]

Opt. Express (1)

Phys. Rev. A (14)

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91(5), 053832 (2015).
[Crossref]

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65(3), 032314 (2002).
[Crossref]

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70(2), 022318 (2004).
[Crossref]

S. Kiesewetter, Q. Y. He, P. D. Drummond, and M. D. Reid, “Scalable quantum simulation of pulsed entanglement and Einstein-Podolsky-Rosen steering in optomechanics,” Phys. Rev. A 90(4), 043805 (2014).
[Crossref]

A. V. Sharypov and B. He, “Generation of arbitrary symmetric entangled states with conditional linear optical coupling,” Phys. Rev. A 87(3), 032323 (2013).
[Crossref]

Q. Y. He and M. D. Reid, “Einstein-Podolsky-Rosen paradox and quantum steering in pulsed optomechanics,” Phys. Rev. A 88(5), 052121 (2013).
[Crossref]

S. G. Hofer, W. Wieczorek, M. Aspelmeyer, and K. Hammerer, “Quantum entanglement and teleportation in pulsed cavity optomechanics,” Phys. Rev. A 84(5), 052327 (2011).
[Crossref]

B. He, “Quantum optomechanics beyond linearization,” Phys. Rev. A 85(6), 063820 (2012).
[Crossref]

Q. Lin, B. He, R. Ghobadi, and C. Simon, “Fully quantum approach to optomechanical entanglement,” Phys. Rev. A 90(2), 022309 (2014).
[Crossref]

D. Vitali, P. Tombesi, M. J. Woolley, A. C. Doherty, and G. J. Milburn, “Entangling a nanomechanical resonator and a superconducting microwave cavity,” Phys. Rev. A 76(4), 042336 (2007).
[Crossref]

C. Genes, A. Mari, P. Tombesi, and D. Vitali, “Robust entanglement of a micromechanical resonator with output optical fields,” Phys. Rev. A 78(3), 032316 (2008).
[Crossref]

C. L. Zou, X. B. Zou, F. W. Sun, Z. F. Han, and G. C. Guo, “Room-temperature steady-state optomechanical entanglement on a chip,” Phys. Rev. A 84(3), 032317 (2011).
[Crossref]

M. Abdi, S. Barzanjeh, P. Tombesi, and D. Vitali, “Effect of phase noise on the generation of stationary entanglement in cavity optomechanics,” Phys. Rev. A 84(3), 032325 (2011).
[Crossref]

R. Ghobadi, A. R. Bahrampour, and C. Simon, “Quantum optomechanics in the bistable regime,” Phys. Rev. A 84(3), 033846 (2011).
[Crossref]

Phys. Rev. D (1)

B. Abbott and et al., “Analysis of first LIGO science data for stochastic gravitational waves,” Phys. Rev. D 69(12), 122004 (2004).
[Crossref]

Phys. Rev. Lett. (11)

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 (9), 093902 (2007).
[Crossref] [PubMed]

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99 (9), 093901 (2007).
[Crossref] [PubMed]

M. J. Hartmann and M. B. Plenio, “Steady state entanglement in the mechanical vibrations of two dielectric membranes,” Phys. Rev. Lett. 101(20), 200503 (2008).
[Crossref] [PubMed]

F. Galve, L. A. Pachon, and D. Zueco, “Bringing entanglement to the high temperature limit,” Phys. Rev. Lett. 105(18), 180501 (2010).
[Crossref]

O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Large quantum superpositions and interference of massive nanometer-sized objects,” Phys. Rev. Lett. 107(2), 020405 (2011).
[Crossref] [PubMed]

X. T. Wang, S. Vinjanampathy, F. W. Strauch, and K. Jacobs, “Ultraefficient cooling of resonators: beating sideband cooling with quantum control,” Phys. Rev. Lett. 107(17), 177204 (2011).
[Crossref] [PubMed]

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
[Crossref]

B. He, A. V. Sharypov, J. Sheng, C. Simon, and M. Xiao, “Two-photon dynamics in coherent rydberg atomic ensemble,” Phys. Rev. Lett. 112(13), 133606 (2014).
[Crossref] [PubMed]

M. B. Plenio, “The logarithmic negativity: A full entanglement monotone that is not convex,” Phys. Rev. Lett. 95(9), 090503 (2005).
[Crossref] [PubMed]

S. Machnes, J. Cerrillo, M. Aspelmeyer, W. Wieczorek, M. B. Plenio, and A. Retzker, “Pulsed laser cooling for cavity-optomechanical resonators,” Phys. Rev. Lett. 108(15), 153601 (2012).
[Crossref] [PubMed]

Phys. Rev. X (1)

M. R. Vanner, “Selective linear or quadratic optomechanical coupling via measurement,” Phys. Rev. X 1(2), 021011 (2011).

Phys. Today (1)

K. C. Schwab and M. L. Roukes, “Putting mechanics into quantum mechanics,” Phys. Today 58(7), 36–42 (2005).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

M. R. Vanner, I. Pikovski, G. D. Cole, M. S. Kim, Č. Brukner, K. Hammerer, G. J. Milburn, and M. Aspelmeyer, “Pulsed quantum optomechanics,” Proc. Natl. Acad. Sci. USA 108(39), 16182–16187 (2011).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

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

Science (1)

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics: backaction at the mesoscale,” Science 321 (5893), 1172–1176 (2008).
[Crossref] [PubMed]

Other (3)

H. J. Metcalf and P. Van der Straten, Laser Cooling and Trapping (Springer Science & Business Media, 1999).
[Crossref]

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 2000).

C. W. Gardiner and P. Zoller, Quantum Noise (Springer, 2000).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Entanglement evolution under Gaussian pulse drive with different widths (displayed on the top). Long dashed (green) curve is for Δω/ωm = 0.4, short dashed (black) curve for Δω/ωm = 0.8, thin solid (red) curve for Δω/ωm = 4/3, and thick solid (blue) curve for Δω/ωm = 4, respectively. The corresponding detuning Δ0/ωm for Figs. 1(a)–1(d) are Δ0/ωm = −1, −0.5, 0.5, 1, respectively. The other parameters are g/κ = 10−6, ωm = 2.5, ωmm = 107, and T = 0.
Fig. 2
Fig. 2 Entanglement evolution under pulse drive with different profiles (displayed on the top). (a) The detuning is Δ0/ωm = −1. (b) The detuning is Δ0/ωm = 1. The other parameters are the same as in Fig. 1.
Fig. 3
Fig. 3 Entanglement evolution under a series of Gaussian pulses with the detuning Δ0/ωm = −1. The left two figures are for the pulses and the right ones are for the entanglement evolution. The gap time of the pulse centers in (a) and (b) are Δ(κt) = 8 and Δ(κt) = 5, respectively. The width for thin (blue) curve is Δω/ωm = 4, while that for thick (red) curve is Δω/ωm = 4/3. The other parameters are the same as in Fig. 1.
Fig. 4
Fig. 4 Entanglement evolution under Gaussian pulse drive with the temperature nm = 104. The other parameters are the same to Fig. 1.

Equations (19)

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H S ( t ) = g { b ^ e i ω m t + b ^ e i ω m t } a ^ a ^ + i ( j E j ( t ) a ^ e i Δ 0 ( t j t 0 ) j E j * ( t ) a ^ e i Δ 0 ( t j t 0 ) )
H D ( t ) = i ( κ a ^ ξ ^ c ( t ) + γ m b ^ ξ ^ m ( t ) ) + H . c .
T e i 0 t d τ ( H 1 ( τ ) + H 2 ( τ ) ) = { T e i 0 t d τ H 1 ( τ ) T e i 0 t d τ V 1 ( τ , 0 ) H 2 ( τ ) V 1 ( τ , 0 ) ; Left Factorization T e i 0 t d τ V 2 ( t , τ ) H 1 ( τ ) V 2 ( t , τ ) T e i 0 t d τ H 2 ( τ ) ; Right Factorization
U S ( t , 0 ) = T exp { i 0 t d τ U D ( t , τ ) H S ( τ ) U D ( t , τ ) } T exp { i 0 t d τ H D ( τ ) } .
U D ( t , τ ) a ^ U D ( t , τ ) = e κ 2 ( t τ ) a ^ + n ^ c ( t , τ ) A ^ ( t , τ ) , U D ( t , τ ) b ^ U D ( t , τ ) = e γ m 2 ( t τ ) b ^ + n ^ m ( t , τ ) B ^ ( t , τ ) ,
Γ c ( t , τ ) = [ n ^ c ( t , t ) , n ^ c ( t , τ ) ] = e κ ( τ t ) / 2 e κ ( t τ ) / 2 e κ ( t t ) / 2 , Γ m ( t , τ ) = [ n ^ m ( t , t ) , n ^ m ( t , τ ) ] = e γ m ( τ t ) / 2 e γ m ( t τ ) / 2 e γ m ( t t ) / 2 .
U E ( τ , 0 ) A ^ ( t , τ ) U E ( τ , 0 ) = A ^ ( t , τ ) + j [ e κ 2 ( t τ ) 0 τ d t E j ( t ) e i Δ 0 ( t j t 0 ) e κ 2 ( t t ) + 0 τ d t Γ c ( t , τ ) E j ( t ) e i Δ 0 ( t j t 0 ) ] A ^ ( t , τ ) + j D j ( τ ) ,
H ˜ O M ( τ ) = g [ B ^ ( t , τ ) e i ω m t + B ^ ( t , τ ) e i ω m t ] × [ j A ^ ( t , τ ) D j * ( τ ) + k A ^ ( t , τ ) D k ( τ ) + j k D j * ( τ ) D k ( τ ) ] .
U S ( t , 0 ) = U E ( t , 0 ) U O M ( t , 0 ) U C ( t , 0 ) U D ( t , 0 ) .
χ ( 0 ) = ρ ( 0 ) R ( 0 ) = | 0 c 0 | n = 0 n m n ( 1 + n m ) n + 1 | n m n | R ( 0 ) ,
Tr S { O ^ ρ ( t ) } = Tr S { O ^ Tr R { U S ( t , 0 ) ρ ( 0 ) R ( 0 ) U S ( t , 0 ) } } = Tr S R { U O M ( t , 0 ) U E ( t , 0 ) O ^ U E ( t , 0 ) U O M ( t , 0 ) ρ ( 0 ) R ( 0 ) } .
V ^ = ( A ^ C ^ C ^ T B ^ ) .
E 𝒩 = max [ 0 , ln 2 η ] ,
η = 1 2 Σ Σ 2 det V ^
Σ = det A ^ + det B ^ 2 det C ^ .
i d a ^ d τ = g e ( κ + γ m ) ( t τ ) / 2 j D j ( τ ) ( b ^ e i ω m τ + b ^ e i ω m τ ) + g e κ ( t τ ) / 2 j D j ( τ ) [ n ^ m ( t , τ ) e i ω m τ + n ^ m ( t , τ ) e i ω m τ ] i d b ^ d τ = g e ( κ + γ m ) ( t τ / 2 ) e i ω m τ j [ D j * ( τ ) a ^ + D j ( τ ) a ^ ] + g e i ω m τ γ m 2 ( t τ ) j [ n ^ c ( t , τ ) D j * ( τ ) + n ^ c ( t , τ ) D j ( τ ) ] + g e i ω m τ γ m 2 ( t τ ) j k D j * ( τ ) D k ( τ ) .
d d τ u ^ = M ^ ( t , τ ) u ^ ,
M ^ ( t , τ ) = ( 0 0 cos ( ω m τ ) sin ( ω m τ ) 0 0 cos ( ω m τ ) sin ( ω m τ ) sin ( ω m τ ) sin ( ω m τ ) 0 0 cos ( ω m τ ) cos ( ω m τ ) 0 0 ) ,
u ^ ( t ) = e 0 t d τ M ^ ( t , τ ) u ^ ( 0 ) = ( cosh ( m ( t , 0 ) I ^ + sinh ( m ( t , 0 ) ) m ( t , 0 ) K ^ ( t , 0 ) ) ) u ^ ( 0 ) ,

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