Abstract

We report a tunable slow and fast light device based on a carbon nanotube resonator, in the presence of a strong pump laser and a weak signal laser. Detailed analysis shows that the signal laser displays the superluminal and ultraslow light characteristics via passing through a suspended carbon nanotube resonator, while the incident pump laser is on- and off-resonant with the exciton frequency, respectively. In particular, the fast and slow light correspond to the negative and positive dispersion, respectively, associating with the vanished absorption. The bandwidth of the signal spectrum is determined by the vibration decay rate of carbon nanotube.

© 2012 OSA

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    [CrossRef]
  33. R. S. Bennink, R. W. Boyd, C. R. Stroud, and V. Wong, “Enhanced self-action effects by electromagnetically induced transparency in the two-level atom,” Phys. Rev. A 63, 033804 (2001).
    [CrossRef]
  34. S. E. Harris, J. E. Field, and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A 46, R29 (1992).
    [CrossRef] [PubMed]
  35. R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]

2011 (6)

H. Farhat, S. Berciaud, M. Kalbac, R. Saito, T. F. Heinz, M. S. Dresselhaus, and J. Kong, “Observation of electronic Raman scattering in metallic carbon nanotubes,” Phys. Rev. Lett. 107, 157401 (2011).
[CrossRef] [PubMed]

J. D. Teufel, D. 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 (2011).
[CrossRef] [PubMed]

J. J. Li and K. D. Zhu, “All-optical Kerr modulator based on a carbon nanotube resonator,” Phys. Rev. B 83, 115445 (2011).
[CrossRef]

S. Yasukochi, T. Murai, S. Moritsubo, T. Shimada, S. Chiashi, S. Maruyama, and Y. K. Kato, “Gate-induced blueshift and quenching of photoluminescence in suspended single-walled carbon nanotubes,” Phys. Rev. B 84, 121409 (2011).
[CrossRef]

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

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[CrossRef] [PubMed]

2010 (7)

B. Gu, N. H. Kwong, R. Binder, and A. L. Smirl, “Slow and fast light associated with polariton interference,” Phys. Rev. B 82, 035313 (2010).
[CrossRef]

V. I. Kovalev, N. E. Kotova, and R. G. Harrison, “Slow light in stimulated Brillouin scattering: on the influence of the spectral width of pump radiation on the group index: reply,” Opt. Express 18, 8055 (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 (2010).
[CrossRef] [PubMed]

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776 (2010).
[CrossRef]

M. Muoth, T. Helbling, L. Durrer, S.-W. Lee, C. Roman, and C. Hierold, “Hysteresis-free operation of suspended carbon nanotube transistors,” Nat. Nanotechnol. 5, 589 (2010).
[CrossRef] [PubMed]

R. Singhal, Z. Orynbayeva, R. V. K. Sundaram, J. J. Niu, S. Bhattacharyya, E. A. Vitol, M. G. Schrlau, E. S. Papazoglou, G. Friedman, and Y. Gogotsi, “Multifunctional carbon-nanotube cellular endoscopes,” Nat. Nanotechnol. 6, 57 (2010)
[CrossRef] [PubMed]

W. Belzig, “Hybrid superconducting devices: bound in a nanotube,” Nat. Phys. 6, 940 (2010).
[CrossRef]

2009 (3)

S. Stepanov and M. P. Sánchez, “Slow and fast light via two-wave mixing in erbium-doped fibers with saturable absorption,” Phys. Rev. A 80, 053830 (2009).
[CrossRef]

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074 (2009).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074 (2009).
[CrossRef] [PubMed]

2008 (2)

P. Avouris, M. Freitag, and V. Perebeinos, “Carbon-nanotube photonics and optoelectronics,” Nat. Photonics 2, 341 (2008).
[CrossRef]

I. Wilson-Rae, “Intrinsic dissipation in nanomechanical resonators due to phonon tunneling,” Phys. Rev. B 77, 245418 (2008).
[CrossRef]

2006 (2)

V. P. Kalosha, L. Chen, and X. Bao, “Slow and fast light via SBS in optical fibers for short pulses and broadband pump,” Opt. Express 14, 12693 (2006).
[CrossRef] [PubMed]

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photon. News 19, 18 (2006).
[CrossRef]

2005 (2)

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

K. L. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum. 76, 061101 (2005).
[CrossRef]

2003 (1)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

2001 (2)

V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Phys. Rev. A 63, 023812 (2001).
[CrossRef]

R. S. Bennink, R. W. Boyd, C. R. Stroud, and V. Wong, “Enhanced self-action effects by electromagnetically induced transparency in the two-level atom,” Phys. Rev. A 63, 033804 (2001).
[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(1999).
[CrossRef]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36 (1997).
[CrossRef]

1992 (1)

S. E. Harris, J. E. Field, and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A 46, R29 (1992).
[CrossRef] [PubMed]

Allman, M. S.

J. D. Teufel, D. 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 (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 (2010).
[CrossRef] [PubMed]

Avouris, P.

P. Avouris, M. Freitag, and V. Perebeinos, “Carbon-nanotube photonics and optoelectronics,” Nat. Photonics 2, 341 (2008).
[CrossRef]

Bao, X.

Barbour, R.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[CrossRef] [PubMed]

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(1999).
[CrossRef]

Belzig, W.

W. Belzig, “Hybrid superconducting devices: bound in a nanotube,” Nat. Phys. 6, 940 (2010).
[CrossRef]

Bennink, R. S.

R. S. Bennink, R. W. Boyd, C. R. Stroud, and V. Wong, “Enhanced self-action effects by electromagnetically induced transparency in the two-level atom,” Phys. Rev. A 63, 033804 (2001).
[CrossRef]

Berciaud, S.

H. Farhat, S. Berciaud, M. Kalbac, R. Saito, T. F. Heinz, M. S. Dresselhaus, and J. Kong, “Observation of electronic Raman scattering in metallic carbon nanotubes,” Phys. Rev. Lett. 107, 157401 (2011).
[CrossRef] [PubMed]

Bhattacharyya, S.

R. Singhal, Z. Orynbayeva, R. V. K. Sundaram, J. J. Niu, S. Bhattacharyya, E. A. Vitol, M. G. Schrlau, E. S. Papazoglou, G. Friedman, and Y. Gogotsi, “Multifunctional carbon-nanotube cellular endoscopes,” Nat. Nanotechnol. 6, 57 (2010)
[CrossRef] [PubMed]

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

Binder, R.

B. Gu, N. H. Kwong, R. Binder, and A. L. Smirl, “Slow and fast light associated with polariton interference,” Phys. Rev. B 82, 035313 (2010).
[CrossRef]

Boyd, R. W.

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074 (2009).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074 (2009).
[CrossRef] [PubMed]

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photon. News 19, 18 (2006).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

R. S. Bennink, R. W. Boyd, C. R. Stroud, and V. Wong, “Enhanced self-action effects by electromagnetically induced transparency in the two-level atom,” Phys. Rev. A 63, 033804 (2001).
[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic Press, 2008), p. 313.

Burkard, G.

A. Pályi, P. R. Struck, M. Rudner, K. Flensberg, and G. Burkard, “Spin-orbit induced strong coupling of a single spin to a nanomechanical resonator,” ArXiv:1110.4893v1 (2011).

Chan, J.

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

Chang, D. E.

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

Chen, L.

Chiashi, S.

S. Yasukochi, T. Murai, S. Moritsubo, T. Shimada, S. Chiashi, S. Maruyama, and Y. K. Kato, “Gate-induced blueshift and quenching of photoluminescence in suspended single-walled carbon nanotubes,” Phys. Rev. B 84, 121409 (2011).
[CrossRef]

Cicak, K.

J. D. Teufel, D. 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 (2011).
[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 (2010).
[CrossRef] [PubMed]

Dresselhaus, M. S.

H. Farhat, S. Berciaud, M. Kalbac, R. Saito, T. F. Heinz, M. S. Dresselhaus, and J. Kong, “Observation of electronic Raman scattering in metallic carbon nanotubes,” Phys. Rev. Lett. 107, 157401 (2011).
[CrossRef] [PubMed]

Durrer, L.

M. Muoth, T. Helbling, L. Durrer, S.-W. Lee, C. Roman, and C. Hierold, “Hysteresis-free operation of suspended carbon nanotube transistors,” Nat. Nanotechnol. 5, 589 (2010).
[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(1999).
[CrossRef]

Eichenfield, M.

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

Ekinci, K. L.

K. L. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum. 76, 061101 (2005).
[CrossRef]

Farhat, H.

H. Farhat, S. Berciaud, M. Kalbac, R. Saito, T. F. Heinz, M. S. Dresselhaus, and J. Kong, “Observation of electronic Raman scattering in metallic carbon nanotubes,” Phys. Rev. Lett. 107, 157401 (2011).
[CrossRef] [PubMed]

Field, J. E.

S. E. Harris, J. E. Field, and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A 46, R29 (1992).
[CrossRef] [PubMed]

Fiore, V.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[CrossRef] [PubMed]

Fleischhauer, M.

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

Flensberg, K.

A. Pályi, P. R. Struck, M. Rudner, K. Flensberg, and G. Burkard, “Spin-orbit induced strong coupling of a single spin to a nanomechanical resonator,” ArXiv:1110.4893v1 (2011).

Freitag, M.

P. Avouris, M. Freitag, and V. Perebeinos, “Carbon-nanotube photonics and optoelectronics,” Nat. Photonics 2, 341 (2008).
[CrossRef]

Friedman, G.

R. Singhal, Z. Orynbayeva, R. V. K. Sundaram, J. J. Niu, S. Bhattacharyya, E. A. Vitol, M. G. Schrlau, E. S. Papazoglou, G. Friedman, and Y. Gogotsi, “Multifunctional carbon-nanotube cellular endoscopes,” Nat. Nanotechnol. 6, 57 (2010)
[CrossRef] [PubMed]

Gaeta, A. L.

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photon. News 19, 18 (2006).
[CrossRef]

Galland, C.

I. Wilson-Rae, C. Galland, W. Zwerger, and A. Imamoğlu, “Nano-optomechanics with localized carbon nanotube excitons,” arXiv:0911.1330 (2009).

Gardiner, C. W.

C. W. Gardiner and P. Zoller, Quantum Noise, 2nd ed. (Springer, 2000) pp. 425–433.

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074 (2009).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074 (2009).
[CrossRef] [PubMed]

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photon. News 19, 18 (2006).
[CrossRef]

Gavartin, E.

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

Giovannetti, V.

V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Phys. Rev. A 63, 023812 (2001).
[CrossRef]

Gogotsi, Y.

R. Singhal, Z. Orynbayeva, R. V. K. Sundaram, J. J. Niu, S. Bhattacharyya, E. A. Vitol, M. G. Schrlau, E. S. Papazoglou, G. Friedman, and Y. Gogotsi, “Multifunctional carbon-nanotube cellular endoscopes,” Nat. Nanotechnol. 6, 57 (2010)
[CrossRef] [PubMed]

Graff, K. F.

K. F. Graff, Wave Motion in Elastic Solids (Dover, 1991) pp. 539–564.

Gu, B.

B. Gu, N. H. Kwong, R. Binder, and A. L. Smirl, “Slow and fast light associated with polariton interference,” Phys. Rev. B 82, 035313 (2010).
[CrossRef]

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(1999).
[CrossRef]

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36 (1997).
[CrossRef]

S. E. Harris, J. E. Field, and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A 46, R29 (1992).
[CrossRef] [PubMed]

Harrison, R. G.

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(1999).
[CrossRef]

Hawkins, A. R.

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776 (2010).
[CrossRef]

Heinz, T. F.

H. Farhat, S. Berciaud, M. Kalbac, R. Saito, T. F. Heinz, M. S. Dresselhaus, and J. Kong, “Observation of electronic Raman scattering in metallic carbon nanotubes,” Phys. Rev. Lett. 107, 157401 (2011).
[CrossRef] [PubMed]

Helbling, T.

M. Muoth, T. Helbling, L. Durrer, S.-W. Lee, C. Roman, and C. Hierold, “Hysteresis-free operation of suspended carbon nanotube transistors,” Nat. Nanotechnol. 5, 589 (2010).
[CrossRef] [PubMed]

Hierold, C.

M. Muoth, T. Helbling, L. Durrer, S.-W. Lee, C. Roman, and C. Hierold, “Hysteresis-free operation of suspended carbon nanotube transistors,” Nat. Nanotechnol. 5, 589 (2010).
[CrossRef] [PubMed]

Hill, J. T.

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

Hulbert, J. F.

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776 (2010).
[CrossRef]

Hurd, K.

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776 (2010).
[CrossRef]

Imamoglu, A.

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

I. Wilson-Rae, C. Galland, W. Zwerger, and A. Imamoğlu, “Nano-optomechanics with localized carbon nanotube excitons,” arXiv:0911.1330 (2009).

Kalbac, M.

H. Farhat, S. Berciaud, M. Kalbac, R. Saito, T. F. Heinz, M. S. Dresselhaus, and J. Kong, “Observation of electronic Raman scattering in metallic carbon nanotubes,” Phys. Rev. Lett. 107, 157401 (2011).
[CrossRef] [PubMed]

Kalosha, V. P.

Kasapi, A.

S. E. Harris, J. E. Field, and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A 46, R29 (1992).
[CrossRef] [PubMed]

Kato, Y. K.

S. Yasukochi, T. Murai, S. Moritsubo, T. Shimada, S. Chiashi, S. Maruyama, and Y. K. Kato, “Gate-induced blueshift and quenching of photoluminescence in suspended single-walled carbon nanotubes,” Phys. Rev. B 84, 121409 (2011).
[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 (2010).
[CrossRef] [PubMed]

Kong, J.

H. Farhat, S. Berciaud, M. Kalbac, R. Saito, T. F. Heinz, M. S. Dresselhaus, and J. Kong, “Observation of electronic Raman scattering in metallic carbon nanotubes,” Phys. Rev. Lett. 107, 157401 (2011).
[CrossRef] [PubMed]

Kotova, N. E.

Kovalev, V. I.

Kuzyk, M. C.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[CrossRef] [PubMed]

Kwong, N. H.

B. Gu, N. H. Kwong, R. Binder, and A. L. Smirl, “Slow and fast light associated with polariton interference,” Phys. Rev. B 82, 035313 (2010).
[CrossRef]

Lee, S.-W.

M. Muoth, T. Helbling, L. Durrer, S.-W. Lee, C. Roman, and C. Hierold, “Hysteresis-free operation of suspended carbon nanotube transistors,” Nat. Nanotechnol. 5, 589 (2010).
[CrossRef] [PubMed]

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

Li, D.

J. D. Teufel, D. 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 (2011).
[CrossRef] [PubMed]

Li, J. J.

J. J. Li and K. D. Zhu, “All-optical Kerr modulator based on a carbon nanotube resonator,” Phys. Rev. B 83, 115445 (2011).
[CrossRef]

Lin, Q.

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

Lunt, E. J.

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776 (2010).
[CrossRef]

Marangos, J. P.

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

Maruyama, S.

S. Yasukochi, T. Murai, S. Moritsubo, T. Shimada, S. Chiashi, S. Maruyama, and Y. K. Kato, “Gate-induced blueshift and quenching of photoluminescence in suspended single-walled carbon nanotubes,” Phys. Rev. B 84, 121409 (2011).
[CrossRef]

Mayer Alegre, T. P.

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

Milburn, G. J.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994) pp. 245–265.

Moritsubo, S.

S. Yasukochi, T. Murai, S. Moritsubo, T. Shimada, S. Chiashi, S. Maruyama, and Y. K. Kato, “Gate-induced blueshift and quenching of photoluminescence in suspended single-walled carbon nanotubes,” Phys. Rev. B 84, 121409 (2011).
[CrossRef]

Muoth, M.

M. Muoth, T. Helbling, L. Durrer, S.-W. Lee, C. Roman, and C. Hierold, “Hysteresis-free operation of suspended carbon nanotube transistors,” Nat. Nanotechnol. 5, 589 (2010).
[CrossRef] [PubMed]

Murai, T.

S. Yasukochi, T. Murai, S. Moritsubo, T. Shimada, S. Chiashi, S. Maruyama, and Y. K. Kato, “Gate-induced blueshift and quenching of photoluminescence in suspended single-walled carbon nanotubes,” Phys. Rev. B 84, 121409 (2011).
[CrossRef]

Niu, J. J.

R. Singhal, Z. Orynbayeva, R. V. K. Sundaram, J. J. Niu, S. Bhattacharyya, E. A. Vitol, M. G. Schrlau, E. S. Papazoglou, G. Friedman, and Y. Gogotsi, “Multifunctional carbon-nanotube cellular endoscopes,” Nat. Nanotechnol. 6, 57 (2010)
[CrossRef] [PubMed]

Ohm, C.

C. Ohm, C. Stampfer, J. Splettstoesser, and M. R. Wegewijs, “Readout of carbon nanotube vibrations based on spin-phonon coupling,” ArXiv:1110.5165v1 (2011).

Orynbayeva, Z.

R. Singhal, Z. Orynbayeva, R. V. K. Sundaram, J. J. Niu, S. Bhattacharyya, E. A. Vitol, M. G. Schrlau, E. S. Papazoglou, G. Friedman, and Y. Gogotsi, “Multifunctional carbon-nanotube cellular endoscopes,” Nat. Nanotechnol. 6, 57 (2010)
[CrossRef] [PubMed]

Painter, O.

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

Pályi, A.

A. Pályi, P. R. Struck, M. Rudner, K. Flensberg, and G. Burkard, “Spin-orbit induced strong coupling of a single spin to a nanomechanical resonator,” ArXiv:1110.4893v1 (2011).

Papazoglou, E. S.

R. Singhal, Z. Orynbayeva, R. V. K. Sundaram, J. J. Niu, S. Bhattacharyya, E. A. Vitol, M. G. Schrlau, E. S. Papazoglou, G. Friedman, and Y. Gogotsi, “Multifunctional carbon-nanotube cellular endoscopes,” Nat. Nanotechnol. 6, 57 (2010)
[CrossRef] [PubMed]

Perebeinos, V.

P. Avouris, M. Freitag, and V. Perebeinos, “Carbon-nanotube photonics and optoelectronics,” Nat. Photonics 2, 341 (2008).
[CrossRef]

Rivière, R.

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

Roman, C.

M. Muoth, T. Helbling, L. Durrer, S.-W. Lee, C. Roman, and C. Hierold, “Hysteresis-free operation of suspended carbon nanotube transistors,” Nat. Nanotechnol. 5, 589 (2010).
[CrossRef] [PubMed]

Roukes, M. L.

K. L. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum. 76, 061101 (2005).
[CrossRef]

Rudner, M.

A. Pályi, P. R. Struck, M. Rudner, K. Flensberg, and G. Burkard, “Spin-orbit induced strong coupling of a single spin to a nanomechanical resonator,” ArXiv:1110.4893v1 (2011).

Safavi-Naeini, A. H.

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

Saito, R.

H. Farhat, S. Berciaud, M. Kalbac, R. Saito, T. F. Heinz, M. S. Dresselhaus, and J. Kong, “Observation of electronic Raman scattering in metallic carbon nanotubes,” Phys. Rev. Lett. 107, 157401 (2011).
[CrossRef] [PubMed]

Sánchez, M. P.

S. Stepanov and M. P. Sánchez, “Slow and fast light via two-wave mixing in erbium-doped fibers with saturable absorption,” Phys. Rev. A 80, 053830 (2009).
[CrossRef]

Schliesser, A.

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

Schmidt, H.

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776 (2010).
[CrossRef]

Schrlau, M. G.

R. Singhal, Z. Orynbayeva, R. V. K. Sundaram, J. J. Niu, S. Bhattacharyya, E. A. Vitol, M. G. Schrlau, E. S. Papazoglou, G. Friedman, and Y. Gogotsi, “Multifunctional carbon-nanotube cellular endoscopes,” Nat. Nanotechnol. 6, 57 (2010)
[CrossRef] [PubMed]

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge Iniversity Press, 1997).

Shimada, T.

S. Yasukochi, T. Murai, S. Moritsubo, T. Shimada, S. Chiashi, S. Maruyama, and Y. K. Kato, “Gate-induced blueshift and quenching of photoluminescence in suspended single-walled carbon nanotubes,” Phys. Rev. B 84, 121409 (2011).
[CrossRef]

Simmonds, R. W.

J. D. Teufel, D. 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 (2011).
[CrossRef] [PubMed]

Singhal, R.

R. Singhal, Z. Orynbayeva, R. V. K. Sundaram, J. J. Niu, S. Bhattacharyya, E. A. Vitol, M. G. Schrlau, E. S. Papazoglou, G. Friedman, and Y. Gogotsi, “Multifunctional carbon-nanotube cellular endoscopes,” Nat. Nanotechnol. 6, 57 (2010)
[CrossRef] [PubMed]

Sirois, A. J.

J. D. Teufel, D. 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 (2011).
[CrossRef] [PubMed]

Smirl, A. L.

B. Gu, N. H. Kwong, R. Binder, and A. L. Smirl, “Slow and fast light associated with polariton interference,” Phys. Rev. B 82, 035313 (2010).
[CrossRef]

Splettstoesser, J.

C. Ohm, C. Stampfer, J. Splettstoesser, and M. R. Wegewijs, “Readout of carbon nanotube vibrations based on spin-phonon coupling,” ArXiv:1110.5165v1 (2011).

Stampfer, C.

C. Ohm, C. Stampfer, J. Splettstoesser, and M. R. Wegewijs, “Readout of carbon nanotube vibrations based on spin-phonon coupling,” ArXiv:1110.5165v1 (2011).

Stepanov, S.

S. Stepanov and M. P. Sánchez, “Slow and fast light via two-wave mixing in erbium-doped fibers with saturable absorption,” Phys. Rev. A 80, 053830 (2009).
[CrossRef]

Stroud, C. R.

R. S. Bennink, R. W. Boyd, C. R. Stroud, and V. Wong, “Enhanced self-action effects by electromagnetically induced transparency in the two-level atom,” Phys. Rev. A 63, 033804 (2001).
[CrossRef]

Struck, P. R.

A. Pályi, P. R. Struck, M. Rudner, K. Flensberg, and G. Burkard, “Spin-orbit induced strong coupling of a single spin to a nanomechanical resonator,” ArXiv:1110.4893v1 (2011).

Sundaram, R. V. K.

R. Singhal, Z. Orynbayeva, R. V. K. Sundaram, J. J. Niu, S. Bhattacharyya, E. A. Vitol, M. G. Schrlau, E. S. Papazoglou, G. Friedman, and Y. Gogotsi, “Multifunctional carbon-nanotube cellular endoscopes,” Nat. Nanotechnol. 6, 57 (2010)
[CrossRef] [PubMed]

Teufel, J. D.

J. D. Teufel, D. 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 (2011).
[CrossRef] [PubMed]

Tian, L.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[CrossRef] [PubMed]

Vitali, D.

V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Phys. Rev. A 63, 023812 (2001).
[CrossRef]

Vitol, E. A.

R. Singhal, Z. Orynbayeva, R. V. K. Sundaram, J. J. Niu, S. Bhattacharyya, E. A. Vitol, M. G. Schrlau, E. S. Papazoglou, G. Friedman, and Y. Gogotsi, “Multifunctional carbon-nanotube cellular endoscopes,” Nat. Nanotechnol. 6, 57 (2010)
[CrossRef] [PubMed]

Walls, D. F.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994) pp. 245–265.

Wang, H.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[CrossRef] [PubMed]

Wegewijs, M. R.

C. Ohm, C. Stampfer, J. Splettstoesser, and M. R. Wegewijs, “Readout of carbon nanotube vibrations based on spin-phonon coupling,” ArXiv:1110.5165v1 (2011).

Weis, S.

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

Whittaker, J. D.

J. D. Teufel, D. 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 (2011).
[CrossRef] [PubMed]

Wilson-Rae, I.

I. Wilson-Rae, “Intrinsic dissipation in nanomechanical resonators due to phonon tunneling,” Phys. Rev. B 77, 245418 (2008).
[CrossRef]

I. Wilson-Rae, C. Galland, W. Zwerger, and A. Imamoğlu, “Nano-optomechanics with localized carbon nanotube excitons,” arXiv:0911.1330 (2009).

Winger, M.

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

Wong, V.

R. S. Bennink, R. W. Boyd, C. R. Stroud, and V. Wong, “Enhanced self-action effects by electromagnetically induced transparency in the two-level atom,” Phys. Rev. A 63, 033804 (2001).
[CrossRef]

Wu, B.

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776 (2010).
[CrossRef]

Yang, Y.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[CrossRef] [PubMed]

Yasukochi, S.

S. Yasukochi, T. Murai, S. Moritsubo, T. Shimada, S. Chiashi, S. Maruyama, and Y. K. Kato, “Gate-induced blueshift and quenching of photoluminescence in suspended single-walled carbon nanotubes,” Phys. Rev. B 84, 121409 (2011).
[CrossRef]

Zhu, K. D.

J. J. Li and K. D. Zhu, “All-optical Kerr modulator based on a carbon nanotube resonator,” Phys. Rev. B 83, 115445 (2011).
[CrossRef]

Zoller, P.

C. W. Gardiner and P. Zoller, Quantum Noise, 2nd ed. (Springer, 2000) pp. 425–433.

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge Iniversity Press, 1997).

Zwerger, W.

I. Wilson-Rae, C. Galland, W. Zwerger, and A. Imamoğlu, “Nano-optomechanics with localized carbon nanotube excitons,” arXiv:0911.1330 (2009).

Nat. Nanotechnol. (2)

M. Muoth, T. Helbling, L. Durrer, S.-W. Lee, C. Roman, and C. Hierold, “Hysteresis-free operation of suspended carbon nanotube transistors,” Nat. Nanotechnol. 5, 589 (2010).
[CrossRef] [PubMed]

R. Singhal, Z. Orynbayeva, R. V. K. Sundaram, J. J. Niu, S. Bhattacharyya, E. A. Vitol, M. G. Schrlau, E. S. Papazoglou, G. Friedman, and Y. Gogotsi, “Multifunctional carbon-nanotube cellular endoscopes,” Nat. Nanotechnol. 6, 57 (2010)
[CrossRef] [PubMed]

Nat. Photonics (2)

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776 (2010).
[CrossRef]

P. Avouris, M. Freitag, and V. Perebeinos, “Carbon-nanotube photonics and optoelectronics,” Nat. Photonics 2, 341 (2008).
[CrossRef]

Nat. Phys. (1)

W. Belzig, “Hybrid superconducting devices: bound in a nanotube,” Nat. Phys. 6, 940 (2010).
[CrossRef]

Nature (3)

J. D. Teufel, D. 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 (2011).
[CrossRef] [PubMed]

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69 (2011).
[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(1999).
[CrossRef]

Opt. Express (2)

Opt. Photon. News (1)

R. W. Boyd, D. J. Gauthier, and A. L. Gaeta, “Applications of slow light in telecommunications,” Opt. Photon. News 19, 18 (2006).
[CrossRef]

Phys. Rev. A (4)

V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Phys. Rev. A 63, 023812 (2001).
[CrossRef]

R. S. Bennink, R. W. Boyd, C. R. Stroud, and V. Wong, “Enhanced self-action effects by electromagnetically induced transparency in the two-level atom,” Phys. Rev. A 63, 033804 (2001).
[CrossRef]

S. E. Harris, J. E. Field, and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A 46, R29 (1992).
[CrossRef] [PubMed]

S. Stepanov and M. P. Sánchez, “Slow and fast light via two-wave mixing in erbium-doped fibers with saturable absorption,” Phys. Rev. A 80, 053830 (2009).
[CrossRef]

Phys. Rev. B (4)

J. J. Li and K. D. Zhu, “All-optical Kerr modulator based on a carbon nanotube resonator,” Phys. Rev. B 83, 115445 (2011).
[CrossRef]

S. Yasukochi, T. Murai, S. Moritsubo, T. Shimada, S. Chiashi, S. Maruyama, and Y. K. Kato, “Gate-induced blueshift and quenching of photoluminescence in suspended single-walled carbon nanotubes,” Phys. Rev. B 84, 121409 (2011).
[CrossRef]

I. Wilson-Rae, “Intrinsic dissipation in nanomechanical resonators due to phonon tunneling,” Phys. Rev. B 77, 245418 (2008).
[CrossRef]

B. Gu, N. H. Kwong, R. Binder, and A. L. Smirl, “Slow and fast light associated with polariton interference,” Phys. Rev. B 82, 035313 (2010).
[CrossRef]

Phys. Rev. Lett. (3)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[CrossRef] [PubMed]

H. Farhat, S. Berciaud, M. Kalbac, R. Saito, T. F. Heinz, M. S. Dresselhaus, and J. Kong, “Observation of electronic Raman scattering in metallic carbon nanotubes,” Phys. Rev. Lett. 107, 157401 (2011).
[CrossRef] [PubMed]

Phys. Today (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36 (1997).
[CrossRef]

Rev. Mod. Phys. (1)

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

Rev. Sci. Instrum. (1)

K. L. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum. 76, 061101 (2005).
[CrossRef]

Science (3)

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074 (2009).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074 (2009).
[CrossRef] [PubMed]

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

Other (8)

I. Wilson-Rae, C. Galland, W. Zwerger, and A. Imamoğlu, “Nano-optomechanics with localized carbon nanotube excitons,” arXiv:0911.1330 (2009).

K. F. Graff, Wave Motion in Elastic Solids (Dover, 1991) pp. 539–564.

C. W. Gardiner and P. Zoller, Quantum Noise, 2nd ed. (Springer, 2000) pp. 425–433.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994) pp. 245–265.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge Iniversity Press, 1997).

A. Pályi, P. R. Struck, M. Rudner, K. Flensberg, and G. Burkard, “Spin-orbit induced strong coupling of a single spin to a nanomechanical resonator,” ArXiv:1110.4893v1 (2011).

C. Ohm, C. Stampfer, J. Splettstoesser, and M. R. Wegewijs, “Readout of carbon nanotube vibrations based on spin-phonon coupling,” ArXiv:1110.5165v1 (2011).

R. W. Boyd, Nonlinear Optics (Academic Press, 2008), p. 313.

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Figures (4)

Fig. 1
Fig. 1

Schematic of a suspended carbon nanotube resonator with a localized exciton. This system is driven by a strong pump laser and probed by a weak signal laser. The inset describes the energy level of exciton while dressing with the vibration modes of carbon nanotube resonator.

Fig. 2
Fig. 2

(a) The absorption spectrum of a signal field as a function of signal-pump detuning for the case Ω R 2 = 2,ωn0 = 6, Δp0 = 0, γn0 = 0.003, and η = 0.17. (b) The energy levels of localized exciton while dressing with the vibrational modes of nanotube resonator. The transition 1,2,3 correspond to the characteristic parts shown in (a), respectively.

Fig. 3
Fig. 3

A tunable device of slow and fast light using a carbon nanotube resonator. (a) The dimensionless imaginary part and real part of the linear optical susceptibility (in units of Σ1) as a function of the signal-exciton detuning for Δp = 0; (b) The group velocity index ng of superluminal light (in units of Σ) as a function of pump Rabi frequency Ω2; (c) The same plots with (a) except Δp = ωn; (d) The group velocity index ng(= c/vg) of slow light (in units of Σ) as a function of the pump Rabi frequency Ω2. The other parameters used in plot(a)–(d) are Ω2 = 0.1(GHz)2, ωn = 0.725GHz, γn = 0.8MHz, and η = 0.17.

Fig. 4
Fig. 4

The absorption spectrum of a signal field as a function of the detuning Δs with three different decay rates of CNT resonator. The other parameters used are Ω2 = 0.1(GHz)2, ωn = 0.725GHz, Δp = 0.725GHz, and η = 0.17. The inset shows the amplification of the most remarkable region of transparency.

Equations (19)

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H = H ex + H n + H ex n + H ex o = h ¯ ω ex S z + h ¯ ω n b + b + h ¯ ω n η S z ( b + + b ) μ ( S + E p e i ω p t + S E p * e i ω p t ) μ ( S + E s e i ω s t + S E s * e i ω s t ) ,
H = h ¯ Δ p S z + h ¯ ω n b + b + h ¯ ω n η S z ( b + + b ) h ¯ ( Ω S + + Ω * S ) μ ( S + E s e i δ t + S E s * e i δ t ) ,
d d t S z = Γ 1 ( S z + 1 2 ) + i Ω S + i Ω * S + i μ E s e i δ t h ¯ S + i μ E s * e i δ t h ¯ S ,
d d t S = ( i Δ p + Γ 2 ) S i ω n η Q S 2 i Ω S z 2 i μ E s e i δ t h ¯ S z + F ^ e ,
d 2 d t 2 Q + 1 τ n d d t Q + ω n 2 Q = 2 ω n 2 η S z + ξ ^ ,
ξ ^ + ( t ) ξ ^ ( t ) = γ n ω n d ω 2 π ω e i ω ( t t ) [ 1 + coth ( h ¯ ω 2 k B T ) ] .
S 0 = 2 Ω S 0 z ( Δ p + ω n η Q 0 ) i Γ 2 , Q 0 = 2 η S 0 z ,
S = S 0 + δ S , S z = S 0 z + δ S z , Q = Q 0 + δ Q .
δ S ˙ z = Γ 1 δ S z + i Ω δ ( S ) * i Ω * δ S + i μ E s e i δ t h ¯ δ ( S ) * i μ E s * e i δ t h ¯ δ S ,
δ S ˙ = ( i Δ p + Γ 2 ) δ S i ω n η ( δ S Q 0 + S 0 δ Q ) 2 i Ω δ S z 2 i μ E s e i δ t h ¯ δ S z ,
δ ¨ Q + 1 τ n δ ˙ Q + ω n 2 δ Q = 2 ω n 2 η δ S z .
χ ( 1 ) ( ω s ) eff = ρ μ S + ɛ 0 E s = ρ μ 2 ɛ 0 h ¯ Γ 2 χ ( 1 ) ( ω s ) = Σ 1 χ ( 1 ) ( ω s ) ,
χ ( 1 ) ( ω s ) = w 0 f ( δ 0 ) × { 2 e 1 Ω R 2 ( e 1 + δ 0 ) ( e 2 + ω n 0 η 2 w 0 ζ ) e 1 e 2 [ 2 Ω R 2 ( e 1 + ω n 0 η 2 w 0 ζ ) e 1 ( 2 i + δ 0 ) ( e 1 + δ 0 ) ] } ,
ζ ( δ 0 ) = ω n 0 2 ω n 0 2 i δ 0 γ n 0 δ 0 2 ,
f ( δ 0 ) = e 1 e 2 ( e 1 δ 0 ) [ 2 Ω R 2 ( e 1 + ω n 0 η 2 w 0 ζ ) e 1 ( 2 i + δ 0 ) ( e 1 + δ 0 ) ] 2 e 1 2 Ω R 2 ( e 1 + δ 0 ) ( e 2 + ω n 0 η 2 w 0 ζ ) .
( w 0 + 1 ) [ ( Δ p 0 ω n 0 η 2 w 0 ) 2 + 1 ] + 2 Ω R 2 w 0 = 0.
v g = c n + ω s ( d n / d ω s ) ,
c v g = 1 + 2 π R e χ eff ( 1 ) ( ω s ) ω s = ω ex + 2 π ω s R e ( d χ eff ( 1 ) d ω s ) ω s = ω ex .
n g = c v g 1 = c v g v g = 2 π ω ex ρ μ 2 h ¯ Γ 2 R e ( d χ ( 1 ) ( ω s ) d ω s ) ω s = ω e x = Γ 2 Σ R e ( d χ ( 1 ) ( ω s ) d ω s ) ω s = ω ex ,

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