Abstract

We theoretically propose a scheme of an all-optical Kerr switch in a cavity optomechanical system with a Bose–Einstein condensate. It is shown that the nonlinear Kerr response can be easily switched on or off by modulating the pump beam power. We also demonstrate that such a switch can work well under a low power of the pump beam. The scheme proposed here may have potential applications in quantum electronics and quantum information networks.

© 2011 Optical Society of America

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  1. A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Science 308, 672–674(2005).
    [CrossRef] [PubMed]
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    [CrossRef]
  3. J. Zhang, G. Hernandez, and Y. Zhu, “All-optical switching at ultralow light levels,” Opt. Lett. 32, 1317–1319 (2007).
    [CrossRef] [PubMed]
  4. M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. X. Wei, J. Zhang, and Y. Zhu, “All-optical switching in a coupled cavity–atom system,” Phys. Rev. A 82, 033808 (2010).
    [CrossRef]
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  10. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321, 1172–1176 (2008).
    [CrossRef] [PubMed]
  11. M. Ludwig, B. Kubala, and F. Marquardt, “The optomechanical instability in the quantum regime,” New J. Phys. 10, 095013(2008).
    [CrossRef]
  12. C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77, 033804 (2008).
    [CrossRef]
  13. S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
    [CrossRef] [PubMed]
  14. G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81, 041803 (2010).
    [CrossRef]
  15. 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]
  16. J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, “Strong and tunable nonlinear optomechanical coupling in a low-loss system,” Nat. Phys. 6, 707–712 (2010).
    [CrossRef]
  17. F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268–271 (2007).
    [CrossRef] [PubMed]
  18. Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom–field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
    [CrossRef] [PubMed]
  19. F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose–Einstein condensate,” Science 322, 235–238 (2008).
    [CrossRef] [PubMed]
  20. D. Nagy, P. Domokos, A. Vukics, and H. Ritsch, “Nonlinear quantum dynamics of two BEC modes dispersively coupled by an optical cavity,” Eur. Phys. J. D 55, 659–668 (2009).
    [CrossRef]
  21. J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, “Nonlinear dynamics of a cigar-shaped Bose–Einstein condensate in an optical cavity,” Phys. Rev. A 79, 033401 (2009).
    [CrossRef]
  22. S. Ritter, F. Brennecke, K. Baumann, T. Donner, C. Guerlin, and T. Esslinger, “Dynamical coupling between a Bose–Einstein condensate and a cavity optical lattice,” Appl. Phys. B 95, 213–218 (2009).
    [CrossRef]
  23. D. Nagy, G. Kónya, G. Szirmai, and P. Domokos, “Dicke-model phase transition in the quantum motion of a Bose–Einstein condensate in an optical cavity,” Phys. Rev. Lett. 104, 130401(2010).
    [CrossRef] [PubMed]
  24. S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
    [CrossRef] [PubMed]
  25. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
    [CrossRef]
  26. 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 (1985).
    [CrossRef] [PubMed]
  27. C. W. Gardiner and P. Zoller, Quantum Noise (Springer, 2000), pp. 148–153.
  28. R. W. Boyd, Nonlinear Optics (Academic, 2008), p. 207.
    [CrossRef]
  29. A. B. Bhattacherjee, “Cavity quantum optomechanics of ultracold atoms in an optical lattice: normal-mode splitting,” Phys. Rev. A 80, 043607 (2009).
    [CrossRef]
  30. H. J. Kimble, “Strong interactions of single atoms and photons in cavity QED,” Phys. Scr. T76, 127–137 (1998).
    [CrossRef]
  31. G. Szirmai, D. Nagy, and P. Domokos, “Quantum noise of a Bose–Einstein condensate in an optical cavity, correlations, and entanglement,” Phys. Rev. A 81, 043639 (2010).
    [CrossRef]
  32. J. D. Teufel, Dale Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208(2011).
    [CrossRef] [PubMed]
  33. R. W. Keys, “Power dissipation in information processing,” Science 168, 796–801 (1970).
    [CrossRef]

2011 (1)

J. D. Teufel, Dale Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208(2011).
[CrossRef] [PubMed]

2010 (8)

G. Szirmai, D. Nagy, and P. Domokos, “Quantum noise of a Bose–Einstein condensate in an optical cavity, correlations, and entanglement,” Phys. Rev. A 81, 043639 (2010).
[CrossRef]

F. Qin, Y. Liu, Z. M. Meng, and Z. Y. Li, “Design of Kerr-effect sensitive microcavity in nonlinear photonic crystal slabs for all-optical switching,” J. Appl. Phys. 108, 053108 (2010).
[CrossRef]

X. Wei, J. Zhang, and Y. Zhu, “All-optical switching in a coupled cavity–atom system,” Phys. Rev. A 82, 033808 (2010).
[CrossRef]

J. Scheuer, A. A. Sukhorukov, and Y. S. Kivshar, “All-optical switching of dark states in nonlinear coupled microring resonators,” Opt. Lett. 35, 3712–3714 (2010).
[CrossRef] [PubMed]

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

J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, “Strong and tunable nonlinear optomechanical coupling in a low-loss system,” Nat. Phys. 6, 707–712 (2010).
[CrossRef]

D. Nagy, G. Kónya, G. Szirmai, and P. Domokos, “Dicke-model phase transition in the quantum motion of a Bose–Einstein condensate in an optical cavity,” Phys. Rev. Lett. 104, 130401(2010).
[CrossRef] [PubMed]

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

2009 (6)

D. Nagy, P. Domokos, A. Vukics, and H. Ritsch, “Nonlinear quantum dynamics of two BEC modes dispersively coupled by an optical cavity,” Eur. Phys. J. D 55, 659–668 (2009).
[CrossRef]

J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, “Nonlinear dynamics of a cigar-shaped Bose–Einstein condensate in an optical cavity,” Phys. Rev. A 79, 033401 (2009).
[CrossRef]

S. Ritter, F. Brennecke, K. Baumann, T. Donner, C. Guerlin, and T. Esslinger, “Dynamical coupling between a Bose–Einstein condensate and a cavity optical lattice,” Appl. Phys. B 95, 213–218 (2009).
[CrossRef]

A. B. Bhattacherjee, “Cavity quantum optomechanics of ultracold atoms in an optical lattice: normal-mode splitting,” Phys. Rev. A 80, 043607 (2009).
[CrossRef]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[CrossRef] [PubMed]

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

2008 (5)

F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose–Einstein condensate,” Science 322, 235–238 (2008).
[CrossRef] [PubMed]

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321, 1172–1176 (2008).
[CrossRef] [PubMed]

M. Ludwig, B. Kubala, and F. Marquardt, “The optomechanical instability in the quantum regime,” New J. Phys. 10, 095013(2008).
[CrossRef]

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77, 033804 (2008).
[CrossRef]

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]

2007 (4)

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom–field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (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, 093901 (2007).
[CrossRef] [PubMed]

J. Zhang, G. Hernandez, and Y. Zhu, “All-optical switching at ultralow light levels,” Opt. Lett. 32, 1317–1319 (2007).
[CrossRef] [PubMed]

2005 (2)

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Science 308, 672–674(2005).
[CrossRef] [PubMed]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[CrossRef]

1999 (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

1998 (1)

H. J. Kimble, “Strong interactions of single atoms and photons in cavity QED,” Phys. Scr. T76, 127–137 (1998).
[CrossRef]

1996 (1)

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 (1985).
[CrossRef] [PubMed]

1970 (1)

R. W. Keys, “Power dissipation in information processing,” Science 168, 796–801 (1970).
[CrossRef]

Agarwal, G. S.

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

Allman, M. S.

J. D. Teufel, Dale Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208(2011).
[CrossRef] [PubMed]

Arcizet, O.

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

Aspelmeyer, M.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[CrossRef] [PubMed]

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77, 033804 (2008).
[CrossRef]

Bajcsy, M.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Balic, V.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Baumann, K.

S. Ritter, F. Brennecke, K. Baumann, T. Donner, C. Guerlin, and T. Esslinger, “Dynamical coupling between a Bose–Einstein condensate and a cavity optical lattice,” Appl. Phys. B 95, 213–218 (2009).
[CrossRef]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Bhattacherjee, A. B.

A. B. Bhattacherjee, “Cavity quantum optomechanics of ultracold atoms in an optical lattice: normal-mode splitting,” Phys. Rev. A 80, 043607 (2009).
[CrossRef]

Bourdel, T.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2008), p. 207.
[CrossRef]

Brennecke, F.

S. Ritter, F. Brennecke, K. Baumann, T. Donner, C. Guerlin, and T. Esslinger, “Dynamical coupling between a Bose–Einstein condensate and a cavity optical lattice,” Appl. Phys. B 95, 213–218 (2009).
[CrossRef]

F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose–Einstein condensate,” Science 322, 235–238 (2008).
[CrossRef] [PubMed]

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

Cicak, K.

J. D. Teufel, Dale Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208(2011).
[CrossRef] [PubMed]

Clark, S. M.

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Science 308, 672–674(2005).
[CrossRef] [PubMed]

Collett, M. J.

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 (1985).
[CrossRef] [PubMed]

Colombe, Y.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom–field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[CrossRef] [PubMed]

Cui, F. C.

J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, “Nonlinear dynamics of a cigar-shaped Bose–Einstein condensate in an optical cavity,” Phys. Rev. A 79, 033401 (2009).
[CrossRef]

Dawes, A. M. C.

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Science 308, 672–674(2005).
[CrossRef] [PubMed]

Deléglise, S.

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

Domokos, P.

G. Szirmai, D. Nagy, and P. Domokos, “Quantum noise of a Bose–Einstein condensate in an optical cavity, correlations, and entanglement,” Phys. Rev. A 81, 043639 (2010).
[CrossRef]

D. Nagy, G. Kónya, G. Szirmai, and P. Domokos, “Dicke-model phase transition in the quantum motion of a Bose–Einstein condensate in an optical cavity,” Phys. Rev. Lett. 104, 130401(2010).
[CrossRef] [PubMed]

D. Nagy, P. Domokos, A. Vukics, and H. Ritsch, “Nonlinear quantum dynamics of two BEC modes dispersively coupled by an optical cavity,” Eur. Phys. J. D 55, 659–668 (2009).
[CrossRef]

Donner, T.

S. Ritter, F. Brennecke, K. Baumann, T. Donner, C. Guerlin, and T. Esslinger, “Dynamical coupling between a Bose–Einstein condensate and a cavity optical lattice,” Appl. Phys. B 95, 213–218 (2009).
[CrossRef]

F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose–Einstein condensate,” Science 322, 235–238 (2008).
[CrossRef] [PubMed]

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

Dubois, G.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom–field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[CrossRef] [PubMed]

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Esslinger, T.

S. Ritter, F. Brennecke, K. Baumann, T. Donner, C. Guerlin, and T. Esslinger, “Dynamical coupling between a Bose–Einstein condensate and a cavity optical lattice,” Appl. Phys. B 95, 213–218 (2009).
[CrossRef]

F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose–Einstein condensate,” Science 322, 235–238 (2008).
[CrossRef] [PubMed]

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

Gardiner, C. W.

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 (1985).
[CrossRef] [PubMed]

C. W. Gardiner and P. Zoller, Quantum Noise (Springer, 2000), pp. 148–153.

Gauthier, D. J.

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Science 308, 672–674(2005).
[CrossRef] [PubMed]

Gavartin, E.

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

Genes, C.

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77, 033804 (2008).
[CrossRef]

Gigan, S.

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77, 033804 (2008).
[CrossRef]

Girvin, S. M.

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]

Gröblacher, S.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[CrossRef] [PubMed]

Guerlin, C.

S. Ritter, F. Brennecke, K. Baumann, T. Donner, C. Guerlin, and T. Esslinger, “Dynamical coupling between a Bose–Einstein condensate and a cavity optical lattice,” Appl. Phys. B 95, 213–218 (2009).
[CrossRef]

Hafezi, M.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Hammerer, K.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[CrossRef] [PubMed]

Harris, J. G. E.

J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, “Strong and tunable nonlinear optomechanical coupling in a low-loss system,” Nat. Phys. 6, 707–712 (2010).
[CrossRef]

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]

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Hernandez, G.

Hofferberth, S.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Huang, S.

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

Hunger, D.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom–field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[CrossRef] [PubMed]

Illing, L.

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Science 308, 672–674(2005).
[CrossRef] [PubMed]

Imamogdlu, A.

Jayich, A. M.

J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, “Strong and tunable nonlinear optomechanical coupling in a low-loss system,” Nat. Phys. 6, 707–712 (2010).
[CrossRef]

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]

Keys, R. W.

R. W. Keys, “Power dissipation in information processing,” Science 168, 796–801 (1970).
[CrossRef]

Kimble, H. J.

H. J. Kimble, “Strong interactions of single atoms and photons in cavity QED,” Phys. Scr. T76, 127–137 (1998).
[CrossRef]

Kippenberg, T. J.

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

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321, 1172–1176 (2008).
[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, 093901 (2007).
[CrossRef] [PubMed]

Kivshar, Y. S.

Köhl, M.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

Kónya, G.

D. Nagy, G. Kónya, G. Szirmai, and P. Domokos, “Dicke-model phase transition in the quantum motion of a Bose–Einstein condensate in an optical cavity,” Phys. Rev. Lett. 104, 130401(2010).
[CrossRef] [PubMed]

Kubala, B.

M. Ludwig, B. Kubala, and F. Marquardt, “The optomechanical instability in the quantum regime,” New J. Phys. 10, 095013(2008).
[CrossRef]

Kuramochi, E.

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[CrossRef]

Li, Dale

J. D. Teufel, Dale Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208(2011).
[CrossRef] [PubMed]

Li, Z. Y.

F. Qin, Y. Liu, Z. M. Meng, and Z. Y. Li, “Design of Kerr-effect sensitive microcavity in nonlinear photonic crystal slabs for all-optical switching,” J. Appl. Phys. 108, 053108 (2010).
[CrossRef]

Linke, F.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom–field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[CrossRef] [PubMed]

Liu, W. M.

J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, “Nonlinear dynamics of a cigar-shaped Bose–Einstein condensate in an optical cavity,” Phys. Rev. A 79, 033401 (2009).
[CrossRef]

Liu, Y.

F. Qin, Y. Liu, Z. M. Meng, and Z. Y. Li, “Design of Kerr-effect sensitive microcavity in nonlinear photonic crystal slabs for all-optical switching,” J. Appl. Phys. 108, 053108 (2010).
[CrossRef]

Ludwig, M.

M. Ludwig, B. Kubala, and F. Marquardt, “The optomechanical instability in the quantum regime,” New J. Phys. 10, 095013(2008).
[CrossRef]

Lukin, M. D.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Marquardt, F.

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]

M. Ludwig, B. Kubala, and F. Marquardt, “The optomechanical instability in the quantum regime,” New J. Phys. 10, 095013(2008).
[CrossRef]

Meng, Z. M.

F. Qin, Y. Liu, Z. M. Meng, and Z. Y. Li, “Design of Kerr-effect sensitive microcavity in nonlinear photonic crystal slabs for all-optical switching,” J. Appl. Phys. 108, 053108 (2010).
[CrossRef]

Mitsugi, S.

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[CrossRef]

Nagy, D.

G. Szirmai, D. Nagy, and P. Domokos, “Quantum noise of a Bose–Einstein condensate in an optical cavity, correlations, and entanglement,” Phys. Rev. A 81, 043639 (2010).
[CrossRef]

D. Nagy, G. Kónya, G. Szirmai, and P. Domokos, “Dicke-model phase transition in the quantum motion of a Bose–Einstein condensate in an optical cavity,” Phys. Rev. Lett. 104, 130401(2010).
[CrossRef] [PubMed]

D. Nagy, P. Domokos, A. Vukics, and H. Ritsch, “Nonlinear quantum dynamics of two BEC modes dispersively coupled by an optical cavity,” Eur. Phys. J. D 55, 659–668 (2009).
[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, 093901 (2007).
[CrossRef] [PubMed]

Notomi, M.

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[CrossRef]

Peyronel, T.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Qin, F.

F. Qin, Y. Liu, Z. M. Meng, and Z. Y. Li, “Design of Kerr-effect sensitive microcavity in nonlinear photonic crystal slabs for all-optical switching,” J. Appl. Phys. 108, 053108 (2010).
[CrossRef]

Reichel, J.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom–field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[CrossRef] [PubMed]

Ritsch, H.

D. Nagy, P. Domokos, A. Vukics, and H. Ritsch, “Nonlinear quantum dynamics of two BEC modes dispersively coupled by an optical cavity,” Eur. Phys. J. D 55, 659–668 (2009).
[CrossRef]

Ritter, S.

S. Ritter, F. Brennecke, K. Baumann, T. Donner, C. Guerlin, and T. Esslinger, “Dynamical coupling between a Bose–Einstein condensate and a cavity optical lattice,” Appl. Phys. B 95, 213–218 (2009).
[CrossRef]

F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose–Einstein condensate,” Science 322, 235–238 (2008).
[CrossRef] [PubMed]

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

Rivière, R.

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

Sankey, J. C.

J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, “Strong and tunable nonlinear optomechanical coupling in a low-loss system,” Nat. Phys. 6, 707–712 (2010).
[CrossRef]

Scheuer, J.

Schliesser, A.

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

Schmidt, H.

Shinya, A.

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[CrossRef]

Simmonds, R. W.

J. D. Teufel, Dale Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208(2011).
[CrossRef] [PubMed]

Sirois, A. J.

J. D. Teufel, Dale Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208(2011).
[CrossRef] [PubMed]

Steinmetz, T.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom–field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[CrossRef] [PubMed]

Sukhorukov, A. A.

Szirmai, G.

G. Szirmai, D. Nagy, and P. Domokos, “Quantum noise of a Bose–Einstein condensate in an optical cavity, correlations, and entanglement,” Phys. Rev. A 81, 043639 (2010).
[CrossRef]

D. Nagy, G. Kónya, G. Szirmai, and P. Domokos, “Dicke-model phase transition in the quantum motion of a Bose–Einstein condensate in an optical cavity,” Phys. Rev. Lett. 104, 130401(2010).
[CrossRef] [PubMed]

Tanabe, T.

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[CrossRef]

Teufel, J. D.

J. D. Teufel, Dale Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208(2011).
[CrossRef] [PubMed]

Thompson, J. D.

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]

Tombesi, P.

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77, 033804 (2008).
[CrossRef]

Vahala, K. J.

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321, 1172–1176 (2008).
[CrossRef] [PubMed]

Vanner, M. R.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[CrossRef] [PubMed]

Vitali, D.

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77, 033804 (2008).
[CrossRef]

Vukics, A.

D. Nagy, P. Domokos, A. Vukics, and H. Ritsch, “Nonlinear quantum dynamics of two BEC modes dispersively coupled by an optical cavity,” Eur. Phys. J. D 55, 659–668 (2009).
[CrossRef]

Vuletic, V.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Wei, X.

X. Wei, J. Zhang, and Y. Zhu, “All-optical switching in a coupled cavity–atom system,” Phys. Rev. A 82, 033808 (2010).
[CrossRef]

Weis, S.

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

Whittaker, J. D.

J. D. Teufel, Dale Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208(2011).
[CrossRef] [PubMed]

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, 093901 (2007).
[CrossRef] [PubMed]

Yang, C.

J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, “Strong and tunable nonlinear optomechanical coupling in a low-loss system,” Nat. Phys. 6, 707–712 (2010).
[CrossRef]

Zhang, J.

X. Wei, J. Zhang, and Y. Zhu, “All-optical switching in a coupled cavity–atom system,” Phys. Rev. A 82, 033808 (2010).
[CrossRef]

J. Zhang, G. Hernandez, and Y. Zhu, “All-optical switching at ultralow light levels,” Opt. Lett. 32, 1317–1319 (2007).
[CrossRef] [PubMed]

Zhang, J. M.

J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, “Nonlinear dynamics of a cigar-shaped Bose–Einstein condensate in an optical cavity,” Phys. Rev. A 79, 033401 (2009).
[CrossRef]

Zhou, D. L.

J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, “Nonlinear dynamics of a cigar-shaped Bose–Einstein condensate in an optical cavity,” Phys. Rev. A 79, 033401 (2009).
[CrossRef]

Zhu, Y.

X. Wei, J. Zhang, and Y. Zhu, “All-optical switching in a coupled cavity–atom system,” Phys. Rev. A 82, 033808 (2010).
[CrossRef]

J. Zhang, G. Hernandez, and Y. Zhu, “All-optical switching at ultralow light levels,” Opt. Lett. 32, 1317–1319 (2007).
[CrossRef] [PubMed]

Zibrov, A. S.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Zoller, P.

C. W. Gardiner and P. Zoller, Quantum Noise (Springer, 2000), pp. 148–153.

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, 093901 (2007).
[CrossRef] [PubMed]

Zwickl, B. M.

J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, “Strong and tunable nonlinear optomechanical coupling in a low-loss system,” Nat. Phys. 6, 707–712 (2010).
[CrossRef]

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]

Appl. Phys. B (1)

S. Ritter, F. Brennecke, K. Baumann, T. Donner, C. Guerlin, and T. Esslinger, “Dynamical coupling between a Bose–Einstein condensate and a cavity optical lattice,” Appl. Phys. B 95, 213–218 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[CrossRef]

Eur. Phys. J. D (1)

D. Nagy, P. Domokos, A. Vukics, and H. Ritsch, “Nonlinear quantum dynamics of two BEC modes dispersively coupled by an optical cavity,” Eur. Phys. J. D 55, 659–668 (2009).
[CrossRef]

J. Appl. Phys. (1)

F. Qin, Y. Liu, Z. M. Meng, and Z. Y. Li, “Design of Kerr-effect sensitive microcavity in nonlinear photonic crystal slabs for all-optical switching,” J. Appl. Phys. 108, 053108 (2010).
[CrossRef]

Nat. Phys. (1)

J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, “Strong and tunable nonlinear optomechanical coupling in a low-loss system,” Nat. Phys. 6, 707–712 (2010).
[CrossRef]

Nature (6)

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom–field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[CrossRef] [PubMed]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[CrossRef] [PubMed]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

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]

J. D. Teufel, Dale Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature 471, 204–208(2011).
[CrossRef] [PubMed]

New J. Phys. (1)

M. Ludwig, B. Kubala, and F. Marquardt, “The optomechanical instability in the quantum regime,” New J. Phys. 10, 095013(2008).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (7)

X. Wei, J. Zhang, and Y. Zhu, “All-optical switching in a coupled cavity–atom system,” Phys. Rev. A 82, 033808 (2010).
[CrossRef]

G. Szirmai, D. Nagy, and P. Domokos, “Quantum noise of a Bose–Einstein condensate in an optical cavity, correlations, and entanglement,” Phys. Rev. A 81, 043639 (2010).
[CrossRef]

A. B. Bhattacherjee, “Cavity quantum optomechanics of ultracold atoms in an optical lattice: normal-mode splitting,” Phys. Rev. A 80, 043607 (2009).
[CrossRef]

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77, 033804 (2008).
[CrossRef]

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 (1985).
[CrossRef] [PubMed]

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

J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, “Nonlinear dynamics of a cigar-shaped Bose–Einstein condensate in an optical cavity,” Phys. Rev. A 79, 033401 (2009).
[CrossRef]

Phys. Rev. Lett. (3)

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, 093901 (2007).
[CrossRef] [PubMed]

D. Nagy, G. Kónya, G. Szirmai, and P. Domokos, “Dicke-model phase transition in the quantum motion of a Bose–Einstein condensate in an optical cavity,” Phys. Rev. Lett. 104, 130401(2010).
[CrossRef] [PubMed]

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Phys. Scr. (1)

H. J. Kimble, “Strong interactions of single atoms and photons in cavity QED,” Phys. Scr. T76, 127–137 (1998).
[CrossRef]

Science (5)

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

R. W. Keys, “Power dissipation in information processing,” Science 168, 796–801 (1970).
[CrossRef]

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Science 308, 672–674(2005).
[CrossRef] [PubMed]

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321, 1172–1176 (2008).
[CrossRef] [PubMed]

F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose–Einstein condensate,” Science 322, 235–238 (2008).
[CrossRef] [PubMed]

Other (2)

C. W. Gardiner and P. Zoller, Quantum Noise (Springer, 2000), pp. 148–153.

R. W. Boyd, Nonlinear Optics (Academic, 2008), p. 207.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram for a coupled BEC cavity system in the simultaneous presence of a pump laser and a weak probe laser.

Fig. 2
Fig. 2

Mean photon number ω 0 of the intracavity as a function of cavity-pump detuning Δ c for E pu = 0.4 , 1.5, 2.8, and 4.5 MHz . The other parameters used are N = 1.2 × 10 5 , g 0 = 2 π × 10.9 MHz , κ = 2 π × 1.3 MHz , Δ a = 2 π × 32 GHz , γ m = 2 π × 0.4 kHz , and ω rec = 2 π × 3.8 kHz .

Fig. 3
Fig. 3

(a) Relative transmitted intensity T out and (b) phase ϕ T corresponding to the cross-Kerr response as a function of the effective probe-cavity detuning Δ prc = ω pr ω c with Δ c = ω m and E pu = 0.4 MHz . The other parameters used are N = 1.2 × 10 5 , g 0 = 2 π × 10.9 MHz , κ = 2 π × 1.3 MHz , Δ a = 2 π × 32 GHz , γ m = 2 π × 0.4 kHz , and ω rec = 2 π × 3.8 kHz .

Fig. 4
Fig. 4

Relative cross-Kerr transmitted intensity T out as a function of the effective probe-cavity detuning Δ prc = ω pr ω c with Δ c = ω m and E pu = 0.4 MHz for three different effective cou pling strengths (g). The other parameters used are N = 1.2 × 10 5 , g 0 = 2 π × 10.9 MHz , κ = 2 π × 1.3 MHz , Δ a = 2 π × 32 GHz , γ m = 2 π × 0.4 kHz , and ω rec = 2 π × 3.8 kHz .

Fig. 5
Fig. 5

Relative cross-Kerr transmitted intensity T out as a function of the effective probe-cavity detuning Δ prc = ω pr ω c with Δ c = ω m for E pu = 0.0 , 0.4, 0.5, and 0.6 MHz . The other parameters used are N = 1.2 × 10 5 , g 0 = 2 π × 10.9 MHz , κ = 2 π × 1.3 MHz , Δ a = 2 π × 32 GHz , γ m = 2 π × 0.4 kHz , and ω rec = 2 π × 3.8 kHz .

Fig. 6
Fig. 6

Peak value of the relative cross-Kerr transmitted intensity T out as a function of the pump power P pu with Δ c = ω m . The other parameters used are N = 1.2 × 10 5 , g 0 = 2 π × 10.9 MHz , κ = 2 π × 1.3 MHz , Δ a = 2 π × 32 GHz , γ m = 2 π × 0.4 kHz , ω rec = 2 π × 3.8 kHz , and λ pu = 780 nm .

Fig. 7
Fig. 7

Relative cross-Kerr transmitted intensity T out as a function of the effective probe-cavity detuning Δ prc = ω pr ω c for two different oscillation frequencies ( ω m and ω m = ω m 2 π × 1.37 kHz ) with Δ c = ω m ( ω m ) and E pu = 0.4 MHz . The magnified peak of the relative cross-Kerr transmitted intensity is presented in the inset. The other parameters used are N = 1.2 × 10 5 , g 0 = 2 π × 10.9 MHz , κ = 2 π × 1.3 MHz , Δ a = 2 π × 32 GHz , γ m = 2 π × 0.4 kHz , and ω rec = 2 π × 3.8 kHz .

Equations (17)

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H = Ψ ( x ) ( 2 2 m d 2 d x 2 + V ext ( x ) + U 0 cos 2 ( k x ) c c ) Ψ ( x ) d x + H A A + ω c c c + E pu ( c e i ω pu t + c e i ω pu t ) + E pr ( c e i ω pr t + c e i ω pr t ) .
Ψ ( x ) = 1 L a 0 + 2 L cos ( 2 k x ) a 2 ,
H = ω m a a + Δ c c c + g ( a + a ) c c + E pu ( c + c ) + E pr ( c e i δ t + c e i δ t ) ,
d c d t = ( i Δ c + κ ) c i 2 g X c i E pu i E pr e i δ t ,
d 2 X d t 2 + γ m d X d t + ω m 2 X = ω m g 2 c c ,
c ( t ) = c 0 + c + e i δ t + c e i δ t ,
X ( t ) = X 0 + X + e i δ t + X e i δ t .
{ ( i Δ c + i 2 g X 0 + κ ) c 0 = i E pu , c + = i E pr i 2 g X + c 0 i 2 g X 0 + i Δ c + κ i δ , c = i 2 g X c 0 i 2 g X 0 + i Δ c + κ + i δ ,
{ X 0 = g 2 ω m | c 0 | 2 , X + = ω m g 2 ω m 2 i δ γ m δ 2 ( c 0 * c + + c * c 0 ) , X = ω m g 2 ω m 2 + i δ γ m δ 2 ( c 0 * c + c + * c 0 ) .
c + = E pr [ δ + Δ c C + i κ ( κ i δ ) 2 + ( Δ c C ) 2 D ] ,
c = A B * ω m E pr E pu 2 ( κ + i δ ) 2 + ( Δ c C * ) 2 D * · 1 ( i Δ c i A ω m ω 0 + κ ) 2 ,
ω 0 [ κ 2 + ( Δ c 2 g 2 ω m ω 0 ) 2 ] = E pu 2 ,
c out ( t ) = c in ( t ) 2 κ c ( t ) = ( E pu / 2 κ 2 κ c 0 ) + ( E pr / 2 κ 2 κ c + ) e i δ t 2 κ c e i δ t .
c out ( t ) = c out 0 + c out + e i δ t + c out e i δ t .
c out + = E pr 2 κ [ 1 2 κ ( δ + Δ c C + i κ ) D ( κ i δ ) 2 ( Δ c C ) 2 ] ,
c out = E pu 2 E pr ( i Δ c i A ω m ω 0 + κ ) 2 · 2 κ A B * ω m D * ( κ + i δ ) 2 ( Δ c C * ) 2 .
T out = | c out E pr / 2 κ | 2 = | E pu 2 ( i Δ c i A ω m ω 0 + κ ) 2 · 2 κ A B * ω m D * ( κ + i δ ) 2 ( Δ c C * ) 2 | 2 .

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