Abstract

We propose a cooling scheme for a trapped atom using the phenomenon of cavity-induced double electromagnetically induced transparency (EIT), where the atom comprising of four levels in tripod configuration is confined inside a high-finesse optical cavity. By exploiting one cavity-induced EIT, which involves one cavity photon and two laser photons, carrier transition can be eliminated due to the quantum destructive interference of excitation paths. Heating process originated from blue-sideband transition mediated by cavity field can also be prohibited due to the destructive quantum interference with the additional transition between the additional ground state and the excited state. As a consequence, the trapped atom can be cooled to the motional ground state in the leading order of the Lamb-Dicke parameters. In addition, the cooling rate is of the same order of magnitude as that obtained in the cavity-induced single EIT scheme.

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  1. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl Inst. Stand. Technol.103259–328 (1998).
    [CrossRef]
  2. A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A62, 042305 (2000).
    [CrossRef]
  3. E. Buks and B. Yurke, “Mass detection with a nonlinear nanomechanical resonator,” Phys. Rev. E74, 046619 (2006).
    [CrossRef]
  4. J. J. Bollinger, J. D. Prestage, W. M. Itano, and D. J. Wineland, “Laser-Cooled-Atomic Frequency Standard,” Phys. Rev. Lett.54, 1000–1003 (1985).
    [CrossRef] [PubMed]
  5. F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Laser Cooling to the Zero-Point Energy of Motion,” Phys. Rev. Lett.62, 403–406 (1989).
    [CrossRef] [PubMed]
  6. C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, “Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy,” Phys. Rev. Lett.75, 4011–4014 (1995).
    [CrossRef] [PubMed]
  7. G. Morigi, J. Eschner, and C. H. Keitel, “Ground State Laser Cooling Using Electromagnetically Induced Transparency,” Phys. Rev. Lett.85, 4458–4461 (2000).
    [CrossRef] [PubMed]
  8. P. Horak, G. Hechenblaikner, K.M. Gheri, H. Stecher, and H. Ritsch, “Cavity-Induced Atom Cooling in the Strong Coupling Regime,” Phys. Rev. Lett.79, 4974–4977 (1997).
    [CrossRef]
  9. V. Vuletić and S. Chu, “Laser Cooling of Atoms, Ions, or Molecules by Coherent Scattering,” Phys. Rev. Lett.84, 3787–3790 (2000).
    [CrossRef]
  10. P. R. Berman, Cavity Quantum Electrodynamics (Academic Press, New York) (1994).
  11. P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B20, 1098–1130 (2003).
    [CrossRef]
  12. P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Cavity cooling of a single atom,” Nature428, 50–52 (2004).
    [CrossRef] [PubMed]
  13. D. R. Leibrandt, J. Labaziewicz, V. Vuletić, and I. L. Chuang, “Cavity Sideband Cooling of a Single Trapped Ion,” Phys. Rev. Lett.103, 103001 (2009).
    [CrossRef] [PubMed]
  14. M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature465, 755–758 (2010).
    [CrossRef] [PubMed]
  15. A. Reiserer, C. Nölleke, S. Ritter, and G. Rempe, “Ground-state cooling of a single atom at the center of an optical cavity,” arXiv:1212.5295v1 (2012).
  16. G. Morigi, P. W. H. Pinkse, M. Kowalewski, and R. de Vivie-Riedle, “Cavity Cooling of Internal Molecular Motion,” Phys. Rev. Lett.99, 073001 (2007).
    [CrossRef] [PubMed]
  17. M. Kowalewski, G. Morigi, P. W. H. Pinkse, and R. de Vivie-Riedle, “Cavity cooling of translational and ro-vibrational motion of molecules: ab initio-based simulations for OH and NO,” Appl. Phys. B89, 459–467 (2007).
    [CrossRef]
  18. S. Rebić, A. S. Parkins, and S. M. Tan, “Photon statistics of a single-atom intracavity system involving electromagnetically induced transparency,” Phys. Rev. A65, 063804 (2002).
    [CrossRef]
  19. M. D. Lukin, M. Fleischhauer, M. O. Scully, and V. L. Velichansky, “Intracavity electromagnetically induced transparency,” Opt. Lett.23, 295–297 (1998).
    [CrossRef]
  20. G. Nikoghosyan and M. Fleischhauer, “Photon-Number Selective Group Delay in Cavity Induced Transparency,” Phys. Rev. Lett.105, 013601 (2010).
    [CrossRef] [PubMed]
  21. M. Bienert and G. Morigi, “Cavity cooling of a trapped atom using electromagnetically induced transparency,” New J. Phys.14, 023002 (2012).
    [CrossRef]
  22. J. Evers and C. H. Keitel, “Double-EIT ground-state laser coupling without bue-sideband heating,” Europhys. Lett.68, 370–376 (2004).
    [CrossRef]
  23. J. Cerrillo, A. Retzker, and M. B. Plenio, “Fast and Robust Laser Cooling of Trapped Systems,” Phys. Rev. Lett.104, 043003 (2010).
    [CrossRef] [PubMed]
  24. S. Zhang, C. W. Wu, and P. X. Chen, “Dark-state laser cooling of a trapped ion using standing waves,” Phys. Rev. A85, 053420 (2012).
    [CrossRef]
  25. S. Zippilli and G. Morigi, “Mechanical effects of optical resonators on driven trapped atoms: Ground-state cooling in a high-finesse cavity,” Phys. Rev. A72, 053408 (2005).
    [CrossRef]
  26. T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “EIT-control of single-atom motion in an optical cavity,” arXiv:1212.3814v1 (2012).
  27. M. D. Lukin, S. F. Yelin, M. Fleichhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A603225–3228 (1999).
    [CrossRef]
  28. C. Y. Ye, A. S. Zibrov, Yu. V. Rostovtsev, and M. O. Scully, “Unexpected Doppler-free resonance in generalized double dark states,” Phys. Rev. A65043805 (2002).
    [CrossRef]
  29. T. Kampschulte, W. Alt, S. Brakhane, M. Eckstein, R. Reimann, A. Widera, and D. Meschede, “Optical Control of the Refractive Index of a Single Atom,” Phys. Rev. Lett.105153603 (2010).
    [CrossRef]
  30. J.-H. Li, J.-B. Liu, A.-X. Chen, and Ch.-Ch. Qi, “Spontaneous emission spectra and simulating multiple spontaneous generation coherence in a five-level atomic medium,” Phys. Rev. A74033816 (2006).
    [CrossRef]
  31. Y. Wu, J. Saldana, and Y. F. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A67, 013811 (2003).
    [CrossRef]
  32. S. Stenholm, “The semiclassical theory of laser cooling,” Rev. Mod. Phys.58, 699–739 (1986).
    [CrossRef]
  33. F. Schmidt-Kaler, J. Eschner, G. Morigi, C. F. Roos, D. Leibfried, A. Mundt, and R. Blatt, “Laser cooling with electromagnetically induced transparency: Application to trapped samples of ions or neutral atoms,” Appl. Phys. B73, 807–814 (2001).
    [CrossRef]
  34. J. Javanainen, M. Lindberg, and S. Stenholm, “Laser cooling of trapped ions: dynamics of the final stages,” J. Opt. Soc. Am. B1, 111–115 (1984).
    [CrossRef]
  35. J. I. Cirac, R. Blatt, P. Zoller, and W. D. Phillips, “Laser cooling of trapped ions in a standing wave,” Phys. Rev. A46, 2668–2681 (1992).
    [CrossRef] [PubMed]
  36. J. S. Peng and G. X. Li, Introduction to Modern Quantum Optics (Singapore: World Scientific) (1998).
  37. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge1997).
  38. Z. Yi, W. J. Gu, and G. X. Li, “Sideband cooling of atoms with the help of an auxiliary transition,” Phys. Rev. A86, 055401 (2012).
    [CrossRef]
  39. P. Rabl, “Cooling of mechanical motion with a two-level system: The high-temperature regime,” Phys. Rev. B82, 165320 (2010).
    [CrossRef]
  40. H. J. Kimble, in Cavity Quantum Electrodynamics, ed. P. R. Berman, (Academic Press, New York) (1994).
  41. P. F. Zhang, Y. Q. Guo, Zh. H. Li, Y. C. Zhang, Y. F. Zhang, J. J. Du, G. Li, J. M. Wang, and T. C. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A83, 031804(R) (2011).
    [CrossRef]

2012 (3)

M. Bienert and G. Morigi, “Cavity cooling of a trapped atom using electromagnetically induced transparency,” New J. Phys.14, 023002 (2012).
[CrossRef]

S. Zhang, C. W. Wu, and P. X. Chen, “Dark-state laser cooling of a trapped ion using standing waves,” Phys. Rev. A85, 053420 (2012).
[CrossRef]

Z. Yi, W. J. Gu, and G. X. Li, “Sideband cooling of atoms with the help of an auxiliary transition,” Phys. Rev. A86, 055401 (2012).
[CrossRef]

2011 (1)

P. F. Zhang, Y. Q. Guo, Zh. H. Li, Y. C. Zhang, Y. F. Zhang, J. J. Du, G. Li, J. M. Wang, and T. C. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A83, 031804(R) (2011).
[CrossRef]

2010 (5)

P. Rabl, “Cooling of mechanical motion with a two-level system: The high-temperature regime,” Phys. Rev. B82, 165320 (2010).
[CrossRef]

T. Kampschulte, W. Alt, S. Brakhane, M. Eckstein, R. Reimann, A. Widera, and D. Meschede, “Optical Control of the Refractive Index of a Single Atom,” Phys. Rev. Lett.105153603 (2010).
[CrossRef]

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature465, 755–758 (2010).
[CrossRef] [PubMed]

J. Cerrillo, A. Retzker, and M. B. Plenio, “Fast and Robust Laser Cooling of Trapped Systems,” Phys. Rev. Lett.104, 043003 (2010).
[CrossRef] [PubMed]

G. Nikoghosyan and M. Fleischhauer, “Photon-Number Selective Group Delay in Cavity Induced Transparency,” Phys. Rev. Lett.105, 013601 (2010).
[CrossRef] [PubMed]

2009 (1)

D. R. Leibrandt, J. Labaziewicz, V. Vuletić, and I. L. Chuang, “Cavity Sideband Cooling of a Single Trapped Ion,” Phys. Rev. Lett.103, 103001 (2009).
[CrossRef] [PubMed]

2007 (2)

G. Morigi, P. W. H. Pinkse, M. Kowalewski, and R. de Vivie-Riedle, “Cavity Cooling of Internal Molecular Motion,” Phys. Rev. Lett.99, 073001 (2007).
[CrossRef] [PubMed]

M. Kowalewski, G. Morigi, P. W. H. Pinkse, and R. de Vivie-Riedle, “Cavity cooling of translational and ro-vibrational motion of molecules: ab initio-based simulations for OH and NO,” Appl. Phys. B89, 459–467 (2007).
[CrossRef]

2006 (2)

J.-H. Li, J.-B. Liu, A.-X. Chen, and Ch.-Ch. Qi, “Spontaneous emission spectra and simulating multiple spontaneous generation coherence in a five-level atomic medium,” Phys. Rev. A74033816 (2006).
[CrossRef]

E. Buks and B. Yurke, “Mass detection with a nonlinear nanomechanical resonator,” Phys. Rev. E74, 046619 (2006).
[CrossRef]

2005 (1)

S. Zippilli and G. Morigi, “Mechanical effects of optical resonators on driven trapped atoms: Ground-state cooling in a high-finesse cavity,” Phys. Rev. A72, 053408 (2005).
[CrossRef]

2004 (2)

J. Evers and C. H. Keitel, “Double-EIT ground-state laser coupling without bue-sideband heating,” Europhys. Lett.68, 370–376 (2004).
[CrossRef]

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Cavity cooling of a single atom,” Nature428, 50–52 (2004).
[CrossRef] [PubMed]

2003 (2)

Y. Wu, J. Saldana, and Y. F. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A67, 013811 (2003).
[CrossRef]

P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B20, 1098–1130 (2003).
[CrossRef]

2002 (2)

S. Rebić, A. S. Parkins, and S. M. Tan, “Photon statistics of a single-atom intracavity system involving electromagnetically induced transparency,” Phys. Rev. A65, 063804 (2002).
[CrossRef]

C. Y. Ye, A. S. Zibrov, Yu. V. Rostovtsev, and M. O. Scully, “Unexpected Doppler-free resonance in generalized double dark states,” Phys. Rev. A65043805 (2002).
[CrossRef]

2001 (1)

F. Schmidt-Kaler, J. Eschner, G. Morigi, C. F. Roos, D. Leibfried, A. Mundt, and R. Blatt, “Laser cooling with electromagnetically induced transparency: Application to trapped samples of ions or neutral atoms,” Appl. Phys. B73, 807–814 (2001).
[CrossRef]

2000 (3)

V. Vuletić and S. Chu, “Laser Cooling of Atoms, Ions, or Molecules by Coherent Scattering,” Phys. Rev. Lett.84, 3787–3790 (2000).
[CrossRef]

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A62, 042305 (2000).
[CrossRef]

G. Morigi, J. Eschner, and C. H. Keitel, “Ground State Laser Cooling Using Electromagnetically Induced Transparency,” Phys. Rev. Lett.85, 4458–4461 (2000).
[CrossRef] [PubMed]

1999 (1)

M. D. Lukin, S. F. Yelin, M. Fleichhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A603225–3228 (1999).
[CrossRef]

1998 (2)

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl Inst. Stand. Technol.103259–328 (1998).
[CrossRef]

M. D. Lukin, M. Fleischhauer, M. O. Scully, and V. L. Velichansky, “Intracavity electromagnetically induced transparency,” Opt. Lett.23, 295–297 (1998).
[CrossRef]

1997 (1)

P. Horak, G. Hechenblaikner, K.M. Gheri, H. Stecher, and H. Ritsch, “Cavity-Induced Atom Cooling in the Strong Coupling Regime,” Phys. Rev. Lett.79, 4974–4977 (1997).
[CrossRef]

1995 (1)

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, “Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy,” Phys. Rev. Lett.75, 4011–4014 (1995).
[CrossRef] [PubMed]

1992 (1)

J. I. Cirac, R. Blatt, P. Zoller, and W. D. Phillips, “Laser cooling of trapped ions in a standing wave,” Phys. Rev. A46, 2668–2681 (1992).
[CrossRef] [PubMed]

1989 (1)

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Laser Cooling to the Zero-Point Energy of Motion,” Phys. Rev. Lett.62, 403–406 (1989).
[CrossRef] [PubMed]

1986 (1)

S. Stenholm, “The semiclassical theory of laser cooling,” Rev. Mod. Phys.58, 699–739 (1986).
[CrossRef]

1985 (1)

J. J. Bollinger, J. D. Prestage, W. M. Itano, and D. J. Wineland, “Laser-Cooled-Atomic Frequency Standard,” Phys. Rev. Lett.54, 1000–1003 (1985).
[CrossRef] [PubMed]

1984 (1)

Alt, W.

T. Kampschulte, W. Alt, S. Brakhane, M. Eckstein, R. Reimann, A. Widera, and D. Meschede, “Optical Control of the Refractive Index of a Single Atom,” Phys. Rev. Lett.105153603 (2010).
[CrossRef]

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “EIT-control of single-atom motion in an optical cavity,” arXiv:1212.3814v1 (2012).

Bergquist, J. C.

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Laser Cooling to the Zero-Point Energy of Motion,” Phys. Rev. Lett.62, 403–406 (1989).
[CrossRef] [PubMed]

Berman, P. R.

P. R. Berman, Cavity Quantum Electrodynamics (Academic Press, New York) (1994).

Bienert, M.

M. Bienert and G. Morigi, “Cavity cooling of a trapped atom using electromagnetically induced transparency,” New J. Phys.14, 023002 (2012).
[CrossRef]

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “EIT-control of single-atom motion in an optical cavity,” arXiv:1212.3814v1 (2012).

Blatt, R.

F. Schmidt-Kaler, J. Eschner, G. Morigi, C. F. Roos, D. Leibfried, A. Mundt, and R. Blatt, “Laser cooling with electromagnetically induced transparency: Application to trapped samples of ions or neutral atoms,” Appl. Phys. B73, 807–814 (2001).
[CrossRef]

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A62, 042305 (2000).
[CrossRef]

J. I. Cirac, R. Blatt, P. Zoller, and W. D. Phillips, “Laser cooling of trapped ions in a standing wave,” Phys. Rev. A46, 2668–2681 (1992).
[CrossRef] [PubMed]

Bochmann, J.

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature465, 755–758 (2010).
[CrossRef] [PubMed]

Bollinger, J. J.

J. J. Bollinger, J. D. Prestage, W. M. Itano, and D. J. Wineland, “Laser-Cooled-Atomic Frequency Standard,” Phys. Rev. Lett.54, 1000–1003 (1985).
[CrossRef] [PubMed]

Brakhane, S.

T. Kampschulte, W. Alt, S. Brakhane, M. Eckstein, R. Reimann, A. Widera, and D. Meschede, “Optical Control of the Refractive Index of a Single Atom,” Phys. Rev. Lett.105153603 (2010).
[CrossRef]

Buks, E.

E. Buks and B. Yurke, “Mass detection with a nonlinear nanomechanical resonator,” Phys. Rev. E74, 046619 (2006).
[CrossRef]

Cerrillo, J.

J. Cerrillo, A. Retzker, and M. B. Plenio, “Fast and Robust Laser Cooling of Trapped Systems,” Phys. Rev. Lett.104, 043003 (2010).
[CrossRef] [PubMed]

Chen, A.-X.

J.-H. Li, J.-B. Liu, A.-X. Chen, and Ch.-Ch. Qi, “Spontaneous emission spectra and simulating multiple spontaneous generation coherence in a five-level atomic medium,” Phys. Rev. A74033816 (2006).
[CrossRef]

Chen, P. X.

S. Zhang, C. W. Wu, and P. X. Chen, “Dark-state laser cooling of a trapped ion using standing waves,” Phys. Rev. A85, 053420 (2012).
[CrossRef]

Chu, S.

V. Vuletić and S. Chu, “Laser Cooling of Atoms, Ions, or Molecules by Coherent Scattering,” Phys. Rev. Lett.84, 3787–3790 (2000).
[CrossRef]

Chuang, I. L.

D. R. Leibrandt, J. Labaziewicz, V. Vuletić, and I. L. Chuang, “Cavity Sideband Cooling of a Single Trapped Ion,” Phys. Rev. Lett.103, 103001 (2009).
[CrossRef] [PubMed]

Cirac, J. I.

J. I. Cirac, R. Blatt, P. Zoller, and W. D. Phillips, “Laser cooling of trapped ions in a standing wave,” Phys. Rev. A46, 2668–2681 (1992).
[CrossRef] [PubMed]

de Vivie-Riedle, R.

M. Kowalewski, G. Morigi, P. W. H. Pinkse, and R. de Vivie-Riedle, “Cavity cooling of translational and ro-vibrational motion of molecules: ab initio-based simulations for OH and NO,” Appl. Phys. B89, 459–467 (2007).
[CrossRef]

G. Morigi, P. W. H. Pinkse, M. Kowalewski, and R. de Vivie-Riedle, “Cavity Cooling of Internal Molecular Motion,” Phys. Rev. Lett.99, 073001 (2007).
[CrossRef] [PubMed]

Diedrich, F.

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Laser Cooling to the Zero-Point Energy of Motion,” Phys. Rev. Lett.62, 403–406 (1989).
[CrossRef] [PubMed]

Domokos, P.

Du, J. J.

P. F. Zhang, Y. Q. Guo, Zh. H. Li, Y. C. Zhang, Y. F. Zhang, J. J. Du, G. Li, J. M. Wang, and T. C. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A83, 031804(R) (2011).
[CrossRef]

Eckstein, M.

T. Kampschulte, W. Alt, S. Brakhane, M. Eckstein, R. Reimann, A. Widera, and D. Meschede, “Optical Control of the Refractive Index of a Single Atom,” Phys. Rev. Lett.105153603 (2010).
[CrossRef]

Eschner, J.

F. Schmidt-Kaler, J. Eschner, G. Morigi, C. F. Roos, D. Leibfried, A. Mundt, and R. Blatt, “Laser cooling with electromagnetically induced transparency: Application to trapped samples of ions or neutral atoms,” Appl. Phys. B73, 807–814 (2001).
[CrossRef]

G. Morigi, J. Eschner, and C. H. Keitel, “Ground State Laser Cooling Using Electromagnetically Induced Transparency,” Phys. Rev. Lett.85, 4458–4461 (2000).
[CrossRef] [PubMed]

Evers, J.

J. Evers and C. H. Keitel, “Double-EIT ground-state laser coupling without bue-sideband heating,” Europhys. Lett.68, 370–376 (2004).
[CrossRef]

Figueroa, E.

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature465, 755–758 (2010).
[CrossRef] [PubMed]

Fleichhauer, M.

M. D. Lukin, S. F. Yelin, M. Fleichhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A603225–3228 (1999).
[CrossRef]

Fleischhauer, M.

G. Nikoghosyan and M. Fleischhauer, “Photon-Number Selective Group Delay in Cavity Induced Transparency,” Phys. Rev. Lett.105, 013601 (2010).
[CrossRef] [PubMed]

M. D. Lukin, M. Fleischhauer, M. O. Scully, and V. L. Velichansky, “Intracavity electromagnetically induced transparency,” Opt. Lett.23, 295–297 (1998).
[CrossRef]

Gheri, K.M.

P. Horak, G. Hechenblaikner, K.M. Gheri, H. Stecher, and H. Ritsch, “Cavity-Induced Atom Cooling in the Strong Coupling Regime,” Phys. Rev. Lett.79, 4974–4977 (1997).
[CrossRef]

Gould, P.

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, “Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy,” Phys. Rev. Lett.75, 4011–4014 (1995).
[CrossRef] [PubMed]

Gu, W. J.

Z. Yi, W. J. Gu, and G. X. Li, “Sideband cooling of atoms with the help of an auxiliary transition,” Phys. Rev. A86, 055401 (2012).
[CrossRef]

Guo, Y. Q.

P. F. Zhang, Y. Q. Guo, Zh. H. Li, Y. C. Zhang, Y. F. Zhang, J. J. Du, G. Li, J. M. Wang, and T. C. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A83, 031804(R) (2011).
[CrossRef]

Hahn, C.

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature465, 755–758 (2010).
[CrossRef] [PubMed]

Hechenblaikner, G.

P. Horak, G. Hechenblaikner, K.M. Gheri, H. Stecher, and H. Ritsch, “Cavity-Induced Atom Cooling in the Strong Coupling Regime,” Phys. Rev. Lett.79, 4974–4977 (1997).
[CrossRef]

Horak, P.

P. Horak, G. Hechenblaikner, K.M. Gheri, H. Stecher, and H. Ritsch, “Cavity-Induced Atom Cooling in the Strong Coupling Regime,” Phys. Rev. Lett.79, 4974–4977 (1997).
[CrossRef]

Itano, W. M.

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl Inst. Stand. Technol.103259–328 (1998).
[CrossRef]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, “Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy,” Phys. Rev. Lett.75, 4011–4014 (1995).
[CrossRef] [PubMed]

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Laser Cooling to the Zero-Point Energy of Motion,” Phys. Rev. Lett.62, 403–406 (1989).
[CrossRef] [PubMed]

J. J. Bollinger, J. D. Prestage, W. M. Itano, and D. J. Wineland, “Laser-Cooled-Atomic Frequency Standard,” Phys. Rev. Lett.54, 1000–1003 (1985).
[CrossRef] [PubMed]

Javanainen, J.

Jefferts, S. R.

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, “Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy,” Phys. Rev. Lett.75, 4011–4014 (1995).
[CrossRef] [PubMed]

Kampschulte, T.

T. Kampschulte, W. Alt, S. Brakhane, M. Eckstein, R. Reimann, A. Widera, and D. Meschede, “Optical Control of the Refractive Index of a Single Atom,” Phys. Rev. Lett.105153603 (2010).
[CrossRef]

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “EIT-control of single-atom motion in an optical cavity,” arXiv:1212.3814v1 (2012).

Keitel, C. H.

J. Evers and C. H. Keitel, “Double-EIT ground-state laser coupling without bue-sideband heating,” Europhys. Lett.68, 370–376 (2004).
[CrossRef]

G. Morigi, J. Eschner, and C. H. Keitel, “Ground State Laser Cooling Using Electromagnetically Induced Transparency,” Phys. Rev. Lett.85, 4458–4461 (2000).
[CrossRef] [PubMed]

Kimble, H. J.

H. J. Kimble, in Cavity Quantum Electrodynamics, ed. P. R. Berman, (Academic Press, New York) (1994).

King, B. E.

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl Inst. Stand. Technol.103259–328 (1998).
[CrossRef]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, “Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy,” Phys. Rev. Lett.75, 4011–4014 (1995).
[CrossRef] [PubMed]

Kowalewski, M.

M. Kowalewski, G. Morigi, P. W. H. Pinkse, and R. de Vivie-Riedle, “Cavity cooling of translational and ro-vibrational motion of molecules: ab initio-based simulations for OH and NO,” Appl. Phys. B89, 459–467 (2007).
[CrossRef]

G. Morigi, P. W. H. Pinkse, M. Kowalewski, and R. de Vivie-Riedle, “Cavity Cooling of Internal Molecular Motion,” Phys. Rev. Lett.99, 073001 (2007).
[CrossRef] [PubMed]

Labaziewicz, J.

D. R. Leibrandt, J. Labaziewicz, V. Vuletić, and I. L. Chuang, “Cavity Sideband Cooling of a Single Trapped Ion,” Phys. Rev. Lett.103, 103001 (2009).
[CrossRef] [PubMed]

Leibfried, D.

F. Schmidt-Kaler, J. Eschner, G. Morigi, C. F. Roos, D. Leibfried, A. Mundt, and R. Blatt, “Laser cooling with electromagnetically induced transparency: Application to trapped samples of ions or neutral atoms,” Appl. Phys. B73, 807–814 (2001).
[CrossRef]

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A62, 042305 (2000).
[CrossRef]

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl Inst. Stand. Technol.103259–328 (1998).
[CrossRef]

Leibrandt, D. R.

D. R. Leibrandt, J. Labaziewicz, V. Vuletić, and I. L. Chuang, “Cavity Sideband Cooling of a Single Trapped Ion,” Phys. Rev. Lett.103, 103001 (2009).
[CrossRef] [PubMed]

Li, G.

P. F. Zhang, Y. Q. Guo, Zh. H. Li, Y. C. Zhang, Y. F. Zhang, J. J. Du, G. Li, J. M. Wang, and T. C. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A83, 031804(R) (2011).
[CrossRef]

Li, G. X.

Z. Yi, W. J. Gu, and G. X. Li, “Sideband cooling of atoms with the help of an auxiliary transition,” Phys. Rev. A86, 055401 (2012).
[CrossRef]

J. S. Peng and G. X. Li, Introduction to Modern Quantum Optics (Singapore: World Scientific) (1998).

Li, J.-H.

J.-H. Li, J.-B. Liu, A.-X. Chen, and Ch.-Ch. Qi, “Spontaneous emission spectra and simulating multiple spontaneous generation coherence in a five-level atomic medium,” Phys. Rev. A74033816 (2006).
[CrossRef]

Li, Zh. H.

P. F. Zhang, Y. Q. Guo, Zh. H. Li, Y. C. Zhang, Y. F. Zhang, J. J. Du, G. Li, J. M. Wang, and T. C. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A83, 031804(R) (2011).
[CrossRef]

Lindberg, M.

Liu, J.-B.

J.-H. Li, J.-B. Liu, A.-X. Chen, and Ch.-Ch. Qi, “Spontaneous emission spectra and simulating multiple spontaneous generation coherence in a five-level atomic medium,” Phys. Rev. A74033816 (2006).
[CrossRef]

Lukin, M. D.

M. D. Lukin, S. F. Yelin, M. Fleichhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A603225–3228 (1999).
[CrossRef]

M. D. Lukin, M. Fleischhauer, M. O. Scully, and V. L. Velichansky, “Intracavity electromagnetically induced transparency,” Opt. Lett.23, 295–297 (1998).
[CrossRef]

Manz, S.

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “EIT-control of single-atom motion in an optical cavity,” arXiv:1212.3814v1 (2012).

Martinez-Dorantes, M.

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “EIT-control of single-atom motion in an optical cavity,” arXiv:1212.3814v1 (2012).

Maunz, P.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Cavity cooling of a single atom,” Nature428, 50–52 (2004).
[CrossRef] [PubMed]

Meekhof, D. M.

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl Inst. Stand. Technol.103259–328 (1998).
[CrossRef]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, “Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy,” Phys. Rev. Lett.75, 4011–4014 (1995).
[CrossRef] [PubMed]

Meschede, D.

T. Kampschulte, W. Alt, S. Brakhane, M. Eckstein, R. Reimann, A. Widera, and D. Meschede, “Optical Control of the Refractive Index of a Single Atom,” Phys. Rev. Lett.105153603 (2010).
[CrossRef]

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “EIT-control of single-atom motion in an optical cavity,” arXiv:1212.3814v1 (2012).

Monroe, C.

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl Inst. Stand. Technol.103259–328 (1998).
[CrossRef]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, “Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy,” Phys. Rev. Lett.75, 4011–4014 (1995).
[CrossRef] [PubMed]

Morigi, G.

M. Bienert and G. Morigi, “Cavity cooling of a trapped atom using electromagnetically induced transparency,” New J. Phys.14, 023002 (2012).
[CrossRef]

M. Kowalewski, G. Morigi, P. W. H. Pinkse, and R. de Vivie-Riedle, “Cavity cooling of translational and ro-vibrational motion of molecules: ab initio-based simulations for OH and NO,” Appl. Phys. B89, 459–467 (2007).
[CrossRef]

G. Morigi, P. W. H. Pinkse, M. Kowalewski, and R. de Vivie-Riedle, “Cavity Cooling of Internal Molecular Motion,” Phys. Rev. Lett.99, 073001 (2007).
[CrossRef] [PubMed]

S. Zippilli and G. Morigi, “Mechanical effects of optical resonators on driven trapped atoms: Ground-state cooling in a high-finesse cavity,” Phys. Rev. A72, 053408 (2005).
[CrossRef]

F. Schmidt-Kaler, J. Eschner, G. Morigi, C. F. Roos, D. Leibfried, A. Mundt, and R. Blatt, “Laser cooling with electromagnetically induced transparency: Application to trapped samples of ions or neutral atoms,” Appl. Phys. B73, 807–814 (2001).
[CrossRef]

G. Morigi, J. Eschner, and C. H. Keitel, “Ground State Laser Cooling Using Electromagnetically Induced Transparency,” Phys. Rev. Lett.85, 4458–4461 (2000).
[CrossRef] [PubMed]

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “EIT-control of single-atom motion in an optical cavity,” arXiv:1212.3814v1 (2012).

Mücke, M.

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature465, 755–758 (2010).
[CrossRef] [PubMed]

Mundt, A.

F. Schmidt-Kaler, J. Eschner, G. Morigi, C. F. Roos, D. Leibfried, A. Mundt, and R. Blatt, “Laser cooling with electromagnetically induced transparency: Application to trapped samples of ions or neutral atoms,” Appl. Phys. B73, 807–814 (2001).
[CrossRef]

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A62, 042305 (2000).
[CrossRef]

Murr, K.

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature465, 755–758 (2010).
[CrossRef] [PubMed]

Nikoghosyan, G.

G. Nikoghosyan and M. Fleischhauer, “Photon-Number Selective Group Delay in Cavity Induced Transparency,” Phys. Rev. Lett.105, 013601 (2010).
[CrossRef] [PubMed]

Nölleke, C.

A. Reiserer, C. Nölleke, S. Ritter, and G. Rempe, “Ground-state cooling of a single atom at the center of an optical cavity,” arXiv:1212.5295v1 (2012).

Parkins, A. S.

S. Rebić, A. S. Parkins, and S. M. Tan, “Photon statistics of a single-atom intracavity system involving electromagnetically induced transparency,” Phys. Rev. A65, 063804 (2002).
[CrossRef]

Peng, J. S.

J. S. Peng and G. X. Li, Introduction to Modern Quantum Optics (Singapore: World Scientific) (1998).

Phillips, W. D.

J. I. Cirac, R. Blatt, P. Zoller, and W. D. Phillips, “Laser cooling of trapped ions in a standing wave,” Phys. Rev. A46, 2668–2681 (1992).
[CrossRef] [PubMed]

Pinkse, P. W. H.

M. Kowalewski, G. Morigi, P. W. H. Pinkse, and R. de Vivie-Riedle, “Cavity cooling of translational and ro-vibrational motion of molecules: ab initio-based simulations for OH and NO,” Appl. Phys. B89, 459–467 (2007).
[CrossRef]

G. Morigi, P. W. H. Pinkse, M. Kowalewski, and R. de Vivie-Riedle, “Cavity Cooling of Internal Molecular Motion,” Phys. Rev. Lett.99, 073001 (2007).
[CrossRef] [PubMed]

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Cavity cooling of a single atom,” Nature428, 50–52 (2004).
[CrossRef] [PubMed]

Plenio, M. B.

J. Cerrillo, A. Retzker, and M. B. Plenio, “Fast and Robust Laser Cooling of Trapped Systems,” Phys. Rev. Lett.104, 043003 (2010).
[CrossRef] [PubMed]

Prestage, J. D.

J. J. Bollinger, J. D. Prestage, W. M. Itano, and D. J. Wineland, “Laser-Cooled-Atomic Frequency Standard,” Phys. Rev. Lett.54, 1000–1003 (1985).
[CrossRef] [PubMed]

Puppe, T.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Cavity cooling of a single atom,” Nature428, 50–52 (2004).
[CrossRef] [PubMed]

Qi, Ch.-Ch.

J.-H. Li, J.-B. Liu, A.-X. Chen, and Ch.-Ch. Qi, “Spontaneous emission spectra and simulating multiple spontaneous generation coherence in a five-level atomic medium,” Phys. Rev. A74033816 (2006).
[CrossRef]

Rabl, P.

P. Rabl, “Cooling of mechanical motion with a two-level system: The high-temperature regime,” Phys. Rev. B82, 165320 (2010).
[CrossRef]

Rebic, S.

S. Rebić, A. S. Parkins, and S. M. Tan, “Photon statistics of a single-atom intracavity system involving electromagnetically induced transparency,” Phys. Rev. A65, 063804 (2002).
[CrossRef]

Reimann, R.

T. Kampschulte, W. Alt, S. Brakhane, M. Eckstein, R. Reimann, A. Widera, and D. Meschede, “Optical Control of the Refractive Index of a Single Atom,” Phys. Rev. Lett.105153603 (2010).
[CrossRef]

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “EIT-control of single-atom motion in an optical cavity,” arXiv:1212.3814v1 (2012).

Reiserer, A.

A. Reiserer, C. Nölleke, S. Ritter, and G. Rempe, “Ground-state cooling of a single atom at the center of an optical cavity,” arXiv:1212.5295v1 (2012).

Rempe, G.

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature465, 755–758 (2010).
[CrossRef] [PubMed]

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Cavity cooling of a single atom,” Nature428, 50–52 (2004).
[CrossRef] [PubMed]

A. Reiserer, C. Nölleke, S. Ritter, and G. Rempe, “Ground-state cooling of a single atom at the center of an optical cavity,” arXiv:1212.5295v1 (2012).

Retzker, A.

J. Cerrillo, A. Retzker, and M. B. Plenio, “Fast and Robust Laser Cooling of Trapped Systems,” Phys. Rev. Lett.104, 043003 (2010).
[CrossRef] [PubMed]

Ritsch, H.

P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B20, 1098–1130 (2003).
[CrossRef]

P. Horak, G. Hechenblaikner, K.M. Gheri, H. Stecher, and H. Ritsch, “Cavity-Induced Atom Cooling in the Strong Coupling Regime,” Phys. Rev. Lett.79, 4974–4977 (1997).
[CrossRef]

Ritter, S.

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature465, 755–758 (2010).
[CrossRef] [PubMed]

A. Reiserer, C. Nölleke, S. Ritter, and G. Rempe, “Ground-state cooling of a single atom at the center of an optical cavity,” arXiv:1212.5295v1 (2012).

Roos, C. F.

F. Schmidt-Kaler, J. Eschner, G. Morigi, C. F. Roos, D. Leibfried, A. Mundt, and R. Blatt, “Laser cooling with electromagnetically induced transparency: Application to trapped samples of ions or neutral atoms,” Appl. Phys. B73, 807–814 (2001).
[CrossRef]

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A62, 042305 (2000).
[CrossRef]

Rostovtsev, Yu. V.

C. Y. Ye, A. S. Zibrov, Yu. V. Rostovtsev, and M. O. Scully, “Unexpected Doppler-free resonance in generalized double dark states,” Phys. Rev. A65043805 (2002).
[CrossRef]

Saldana, J.

Y. Wu, J. Saldana, and Y. F. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A67, 013811 (2003).
[CrossRef]

Schmidt-Kaler, F.

F. Schmidt-Kaler, J. Eschner, G. Morigi, C. F. Roos, D. Leibfried, A. Mundt, and R. Blatt, “Laser cooling with electromagnetically induced transparency: Application to trapped samples of ions or neutral atoms,” Appl. Phys. B73, 807–814 (2001).
[CrossRef]

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A62, 042305 (2000).
[CrossRef]

Schuster, I.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Cavity cooling of a single atom,” Nature428, 50–52 (2004).
[CrossRef] [PubMed]

Scully, M. O.

C. Y. Ye, A. S. Zibrov, Yu. V. Rostovtsev, and M. O. Scully, “Unexpected Doppler-free resonance in generalized double dark states,” Phys. Rev. A65043805 (2002).
[CrossRef]

M. D. Lukin, S. F. Yelin, M. Fleichhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A603225–3228 (1999).
[CrossRef]

M. D. Lukin, M. Fleischhauer, M. O. Scully, and V. L. Velichansky, “Intracavity electromagnetically induced transparency,” Opt. Lett.23, 295–297 (1998).
[CrossRef]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge1997).

Steane, A.

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A62, 042305 (2000).
[CrossRef]

Stecher, H.

P. Horak, G. Hechenblaikner, K.M. Gheri, H. Stecher, and H. Ritsch, “Cavity-Induced Atom Cooling in the Strong Coupling Regime,” Phys. Rev. Lett.79, 4974–4977 (1997).
[CrossRef]

Stenholm, S.

Stevens, D.

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A62, 042305 (2000).
[CrossRef]

Syassen, N.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Cavity cooling of a single atom,” Nature428, 50–52 (2004).
[CrossRef] [PubMed]

Tan, S. M.

S. Rebić, A. S. Parkins, and S. M. Tan, “Photon statistics of a single-atom intracavity system involving electromagnetically induced transparency,” Phys. Rev. A65, 063804 (2002).
[CrossRef]

Velichansky, V. L.

Villas-Boas, C. J.

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature465, 755–758 (2010).
[CrossRef] [PubMed]

Vuletic, V.

D. R. Leibrandt, J. Labaziewicz, V. Vuletić, and I. L. Chuang, “Cavity Sideband Cooling of a Single Trapped Ion,” Phys. Rev. Lett.103, 103001 (2009).
[CrossRef] [PubMed]

V. Vuletić and S. Chu, “Laser Cooling of Atoms, Ions, or Molecules by Coherent Scattering,” Phys. Rev. Lett.84, 3787–3790 (2000).
[CrossRef]

Wang, J. M.

P. F. Zhang, Y. Q. Guo, Zh. H. Li, Y. C. Zhang, Y. F. Zhang, J. J. Du, G. Li, J. M. Wang, and T. C. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A83, 031804(R) (2011).
[CrossRef]

Widera, A.

T. Kampschulte, W. Alt, S. Brakhane, M. Eckstein, R. Reimann, A. Widera, and D. Meschede, “Optical Control of the Refractive Index of a Single Atom,” Phys. Rev. Lett.105153603 (2010).
[CrossRef]

Wineland, D. J.

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl Inst. Stand. Technol.103259–328 (1998).
[CrossRef]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, “Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy,” Phys. Rev. Lett.75, 4011–4014 (1995).
[CrossRef] [PubMed]

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Laser Cooling to the Zero-Point Energy of Motion,” Phys. Rev. Lett.62, 403–406 (1989).
[CrossRef] [PubMed]

J. J. Bollinger, J. D. Prestage, W. M. Itano, and D. J. Wineland, “Laser-Cooled-Atomic Frequency Standard,” Phys. Rev. Lett.54, 1000–1003 (1985).
[CrossRef] [PubMed]

Wu, C. W.

S. Zhang, C. W. Wu, and P. X. Chen, “Dark-state laser cooling of a trapped ion using standing waves,” Phys. Rev. A85, 053420 (2012).
[CrossRef]

Wu, Y.

Y. Wu, J. Saldana, and Y. F. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A67, 013811 (2003).
[CrossRef]

Ye, C. Y.

C. Y. Ye, A. S. Zibrov, Yu. V. Rostovtsev, and M. O. Scully, “Unexpected Doppler-free resonance in generalized double dark states,” Phys. Rev. A65043805 (2002).
[CrossRef]

Yelin, S. F.

M. D. Lukin, S. F. Yelin, M. Fleichhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A603225–3228 (1999).
[CrossRef]

Yi, Z.

Z. Yi, W. J. Gu, and G. X. Li, “Sideband cooling of atoms with the help of an auxiliary transition,” Phys. Rev. A86, 055401 (2012).
[CrossRef]

Yoon, S.

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “EIT-control of single-atom motion in an optical cavity,” arXiv:1212.3814v1 (2012).

Yurke, B.

E. Buks and B. Yurke, “Mass detection with a nonlinear nanomechanical resonator,” Phys. Rev. E74, 046619 (2006).
[CrossRef]

Zhang, P. F.

P. F. Zhang, Y. Q. Guo, Zh. H. Li, Y. C. Zhang, Y. F. Zhang, J. J. Du, G. Li, J. M. Wang, and T. C. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A83, 031804(R) (2011).
[CrossRef]

Zhang, S.

S. Zhang, C. W. Wu, and P. X. Chen, “Dark-state laser cooling of a trapped ion using standing waves,” Phys. Rev. A85, 053420 (2012).
[CrossRef]

Zhang, T. C.

P. F. Zhang, Y. Q. Guo, Zh. H. Li, Y. C. Zhang, Y. F. Zhang, J. J. Du, G. Li, J. M. Wang, and T. C. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A83, 031804(R) (2011).
[CrossRef]

Zhang, Y. C.

P. F. Zhang, Y. Q. Guo, Zh. H. Li, Y. C. Zhang, Y. F. Zhang, J. J. Du, G. Li, J. M. Wang, and T. C. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A83, 031804(R) (2011).
[CrossRef]

Zhang, Y. F.

P. F. Zhang, Y. Q. Guo, Zh. H. Li, Y. C. Zhang, Y. F. Zhang, J. J. Du, G. Li, J. M. Wang, and T. C. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A83, 031804(R) (2011).
[CrossRef]

Zhu, Y. F.

Y. Wu, J. Saldana, and Y. F. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A67, 013811 (2003).
[CrossRef]

Zibrov, A. S.

C. Y. Ye, A. S. Zibrov, Yu. V. Rostovtsev, and M. O. Scully, “Unexpected Doppler-free resonance in generalized double dark states,” Phys. Rev. A65043805 (2002).
[CrossRef]

Zippilli, S.

S. Zippilli and G. Morigi, “Mechanical effects of optical resonators on driven trapped atoms: Ground-state cooling in a high-finesse cavity,” Phys. Rev. A72, 053408 (2005).
[CrossRef]

Zoller, P.

J. I. Cirac, R. Blatt, P. Zoller, and W. D. Phillips, “Laser cooling of trapped ions in a standing wave,” Phys. Rev. A46, 2668–2681 (1992).
[CrossRef] [PubMed]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge1997).

Appl. Phys. B (2)

M. Kowalewski, G. Morigi, P. W. H. Pinkse, and R. de Vivie-Riedle, “Cavity cooling of translational and ro-vibrational motion of molecules: ab initio-based simulations for OH and NO,” Appl. Phys. B89, 459–467 (2007).
[CrossRef]

F. Schmidt-Kaler, J. Eschner, G. Morigi, C. F. Roos, D. Leibfried, A. Mundt, and R. Blatt, “Laser cooling with electromagnetically induced transparency: Application to trapped samples of ions or neutral atoms,” Appl. Phys. B73, 807–814 (2001).
[CrossRef]

Europhys. Lett. (1)

J. Evers and C. H. Keitel, “Double-EIT ground-state laser coupling without bue-sideband heating,” Europhys. Lett.68, 370–376 (2004).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Res. Natl Inst. Stand. Technol. (1)

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl Inst. Stand. Technol.103259–328 (1998).
[CrossRef]

Nature (2)

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, “Cavity cooling of a single atom,” Nature428, 50–52 (2004).
[CrossRef] [PubMed]

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature465, 755–758 (2010).
[CrossRef] [PubMed]

New J. Phys. (1)

M. Bienert and G. Morigi, “Cavity cooling of a trapped atom using electromagnetically induced transparency,” New J. Phys.14, 023002 (2012).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (11)

Z. Yi, W. J. Gu, and G. X. Li, “Sideband cooling of atoms with the help of an auxiliary transition,” Phys. Rev. A86, 055401 (2012).
[CrossRef]

J. I. Cirac, R. Blatt, P. Zoller, and W. D. Phillips, “Laser cooling of trapped ions in a standing wave,” Phys. Rev. A46, 2668–2681 (1992).
[CrossRef] [PubMed]

S. Zhang, C. W. Wu, and P. X. Chen, “Dark-state laser cooling of a trapped ion using standing waves,” Phys. Rev. A85, 053420 (2012).
[CrossRef]

S. Zippilli and G. Morigi, “Mechanical effects of optical resonators on driven trapped atoms: Ground-state cooling in a high-finesse cavity,” Phys. Rev. A72, 053408 (2005).
[CrossRef]

M. D. Lukin, S. F. Yelin, M. Fleichhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A603225–3228 (1999).
[CrossRef]

C. Y. Ye, A. S. Zibrov, Yu. V. Rostovtsev, and M. O. Scully, “Unexpected Doppler-free resonance in generalized double dark states,” Phys. Rev. A65043805 (2002).
[CrossRef]

J.-H. Li, J.-B. Liu, A.-X. Chen, and Ch.-Ch. Qi, “Spontaneous emission spectra and simulating multiple spontaneous generation coherence in a five-level atomic medium,” Phys. Rev. A74033816 (2006).
[CrossRef]

Y. Wu, J. Saldana, and Y. F. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A67, 013811 (2003).
[CrossRef]

S. Rebić, A. S. Parkins, and S. M. Tan, “Photon statistics of a single-atom intracavity system involving electromagnetically induced transparency,” Phys. Rev. A65, 063804 (2002).
[CrossRef]

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A62, 042305 (2000).
[CrossRef]

P. F. Zhang, Y. Q. Guo, Zh. H. Li, Y. C. Zhang, Y. F. Zhang, J. J. Du, G. Li, J. M. Wang, and T. C. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A83, 031804(R) (2011).
[CrossRef]

Phys. Rev. B (1)

P. Rabl, “Cooling of mechanical motion with a two-level system: The high-temperature regime,” Phys. Rev. B82, 165320 (2010).
[CrossRef]

Phys. Rev. E (1)

E. Buks and B. Yurke, “Mass detection with a nonlinear nanomechanical resonator,” Phys. Rev. E74, 046619 (2006).
[CrossRef]

Phys. Rev. Lett. (11)

J. J. Bollinger, J. D. Prestage, W. M. Itano, and D. J. Wineland, “Laser-Cooled-Atomic Frequency Standard,” Phys. Rev. Lett.54, 1000–1003 (1985).
[CrossRef] [PubMed]

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Laser Cooling to the Zero-Point Energy of Motion,” Phys. Rev. Lett.62, 403–406 (1989).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, “Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy,” Phys. Rev. Lett.75, 4011–4014 (1995).
[CrossRef] [PubMed]

G. Morigi, J. Eschner, and C. H. Keitel, “Ground State Laser Cooling Using Electromagnetically Induced Transparency,” Phys. Rev. Lett.85, 4458–4461 (2000).
[CrossRef] [PubMed]

P. Horak, G. Hechenblaikner, K.M. Gheri, H. Stecher, and H. Ritsch, “Cavity-Induced Atom Cooling in the Strong Coupling Regime,” Phys. Rev. Lett.79, 4974–4977 (1997).
[CrossRef]

V. Vuletić and S. Chu, “Laser Cooling of Atoms, Ions, or Molecules by Coherent Scattering,” Phys. Rev. Lett.84, 3787–3790 (2000).
[CrossRef]

G. Nikoghosyan and M. Fleischhauer, “Photon-Number Selective Group Delay in Cavity Induced Transparency,” Phys. Rev. Lett.105, 013601 (2010).
[CrossRef] [PubMed]

G. Morigi, P. W. H. Pinkse, M. Kowalewski, and R. de Vivie-Riedle, “Cavity Cooling of Internal Molecular Motion,” Phys. Rev. Lett.99, 073001 (2007).
[CrossRef] [PubMed]

D. R. Leibrandt, J. Labaziewicz, V. Vuletić, and I. L. Chuang, “Cavity Sideband Cooling of a Single Trapped Ion,” Phys. Rev. Lett.103, 103001 (2009).
[CrossRef] [PubMed]

T. Kampschulte, W. Alt, S. Brakhane, M. Eckstein, R. Reimann, A. Widera, and D. Meschede, “Optical Control of the Refractive Index of a Single Atom,” Phys. Rev. Lett.105153603 (2010).
[CrossRef]

J. Cerrillo, A. Retzker, and M. B. Plenio, “Fast and Robust Laser Cooling of Trapped Systems,” Phys. Rev. Lett.104, 043003 (2010).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

S. Stenholm, “The semiclassical theory of laser cooling,” Rev. Mod. Phys.58, 699–739 (1986).
[CrossRef]

Other (6)

T. Kampschulte, W. Alt, S. Manz, M. Martinez-Dorantes, R. Reimann, S. Yoon, D. Meschede, M. Bienert, and G. Morigi, “EIT-control of single-atom motion in an optical cavity,” arXiv:1212.3814v1 (2012).

H. J. Kimble, in Cavity Quantum Electrodynamics, ed. P. R. Berman, (Academic Press, New York) (1994).

J. S. Peng and G. X. Li, Introduction to Modern Quantum Optics (Singapore: World Scientific) (1998).

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge1997).

A. Reiserer, C. Nölleke, S. Ritter, and G. Rempe, “Ground-state cooling of a single atom at the center of an optical cavity,” arXiv:1212.5295v1 (2012).

P. R. Berman, Cavity Quantum Electrodynamics (Academic Press, New York) (1994).

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Figures (6)

Fig. 1
Fig. 1

(a) The setup of the cooling system. An atom confined inside a high-finesse optical resonator by a harmonic trap with frequency ν is transversally driven by two laser fields with Rabi frequencies Ω1 and Ω2 and couples to the cavity mode with strength g(x). The cavity field is weakly pumped by a laser with coupling strength Ωp and decays at the rate κ. θlj (θc) denotes the angle between the axis of the motion and the j-th laser (cavity) wave vector. (b)The relevant electronic level transitions. The two transverse laser fields drive transitions |gj〉 → |e〉, respectively, while the cavity field couples to the transition |g3〉 → |e〉. δj and δc3 are the detunings between the photon fields and the corresponding transitions and Δ is the detuning between the cavity field and the probe laser.

Fig. 2
Fig. 2

Sketch of the level configuration described by the states in Eq. (7). The ground state |g2〉 is the additional level with respect to transition paths |g3〉 ↔ |1〉 ↔ |e〉 ↔ |g1〉 presented in the cavity-induced single EIT system, which is designed to cancel the carrier transition.

Fig. 3
Fig. 3

The numerical calculations of heating and cooling coefficients A±/η2 as functions of δ2 and Ω2 with the parameters in units of ν: γ = 10ν, κ = 0.2ν, g = 10ν, Ω1 = 12ν, Ωp/2 = 0.1ν, δ1 = 60ν, δc3 = 59ν, Δ = ν, θc = θli = 0, φ = π/3, α = 2/5. The dash line in A+ shows the zero heating coefficient.

Fig. 4
Fig. 4

The analytical plots of heating and cooling coefficients A±/η2 as functions of δ2 and Ω2 with the parameters in units of ν: γ = 10ν, κ = 0.2ν, g = 10ν, Ω1 = 12ν, Ωp/2 = 0.1ν, δ1 = 60ν, δc3 = 59ν, Δ = ν, θc = θli = 0, φ = π/3. The dot line shows the zero heating coefficient.

Fig. 5
Fig. 5

The sketch of heating processes. The states are at phonon state |n〉 in (a) and |n + 1〉 in (b). By using cavity-induced double EIT, i.e. the quantum destructive interferences between excitation paths |g3, n〉 → |1, n〉 → |e, n〉 and |g1, n〉 → |e, n〉, and between excitation paths |g3, n〉 → |1, n〉 → |e, n + 1〉 and |g2, n + 1〉 → |e, n + 1〉 respectively, carrier- and blue-sideband transitions are eliminated.

Fig. 6
Fig. 6

The cooling coefficient A/η2 as a function of Ω2 with the parameters in units of ν: γ = 10ν, κ = 0.2ν, g = 10ν, Ω1 = 12ν, Ωp/2 = 0.1ν, δ1 = 60ν, δ2 = 59ν, δc3 = 59ν, Δ = ν, θc = θli = 0, φ = π/3.

Equations (64)

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H = H at + H cav + H ext + H L-cav + H at-cav + H L-at ,
H at = δ c 3 | e e | + j ( δ j δ c 3 ) | g j g j | + Δ | g 3 g 3 | , H cav = Δ a a , H ext = ν ( b b + 1 2 ) ,
H L-cav = Ω p 2 ( a + a ) , H at-cav = g ( x ) ( | e g 3 | a + | g 3 e | a ) , H L-at = j Ω j 2 ( | e g j | exp ( i k j cos θ L j x ) + h . c . ) .
d d t ρ = i [ H , ρ ] + at ρ + 𝒦 ρ ,
at ρ = i γ i 2 ( 2 | g i e | ρ ˜ | e g i | | e e | ρ ρ | e e | ) , 𝒦 ρ = κ 2 ( 2 a ρ a a a ρ ρ a a ) ,
ρ ˜ = 1 1 𝒩 i ( θ ) exp ( i k i x cos θ ) ρ exp ( i k i x cos θ ) d cos θ
| e , 0 , | g 1 , 0 , | g 2 , 0 , | g 3 , 0 , | g 3 , 1 .
H L-cav = Ω p 2 ( | g 3 1 | + | 1 g 3 | ) , H at-cav = g ( x ) ( | e 1 | + | 1 e | ) ,
𝒦 ρ = κ 2 ( 2 | g 3 1 | ρ | 1 | g 3 | 1 1 | ρ ρ | 1 1 | ) ,
V 1 = j i Ω j η l j 2 | e g j | η c g sin φ | e 1 | + h . c . ,
H 0 = H at + H cav + H L-cav + H 0 L-at + H 0 at-cav ,
d d t ρ = 0 ρ + 0 E ρ + 1 ρ ,
0 ρ = i [ H 0 , ρ ] + 𝒦 ρ + 0 at ρ ,
0 at ρ = i γ i 2 ( 2 | g i e | ρ | e g i | | e e | ρ ρ | e e | )
0 E ρ = i [ H ext , ρ ]
1 ρ = i [ H 1 , ρ ] .
d d t μ = [ S ( ν ) + D ] ( b μ b b b μ ) + [ S ( ν ) + D ] ( b μ b b b μ ) + h . c . ,
S ( ν ) = 0 d τ e i ν τ V 1 ( τ ) V 1 ( 0 ) s , D = i α i γ i 2 η i 2 Tr { σ e g i σ g i e ρ s } ,
α i = 1 1 d cos θ cos 2 θ 𝒩 i ( θ )
n ˙ = ( A A + ) n + A + ,
A ± = 2 Re { S ( ± ν ) + D }
n s t = A + A A + , W = A A + .
ρ n m ( i ) ( s ) = 0 e s τ ρ n m ( i ) ( τ ) d τ .
ρ ˙ g 3 g 3 ( 0 ) = γ ρ e e ( 0 )
ρ ( 0 ) ( ) = | g 3 g 3 | .
ρ ˙ e g 3 ( 1 ) = [ i ( δ c 3 + Δ ) γ 2 ] ρ e g 3 ( 1 ) i j Ω j 2 ρ g j g 3 ( 1 ) i g cos φ ρ 1 g 3 ( 1 ) ,
ρ ˙ g 1 g 3 ( 1 ) = i [ Δ ( δ 1 δ c 3 ) ] ρ g 1 g 3 ( 1 ) i Ω 1 2 ρ e g 3 ( 1 ) ,
ρ ˙ g 2 g 3 ( 1 ) = i [ Δ ( δ 2 δ c 3 ) ] ρ g 2 g 3 ( 1 ) i Ω 2 2 ρ e g 3 ( 1 ) ,
ρ ˙ 1 g 3 ( 1 ) = ( i Δ κ 2 ) ρ 1 g 3 ( 1 ) i g cos φ ρ e g 3 ( 1 ) i Ω p 2 ρ g 3 g 3 ( 0 ) ,
ρ e g 3 ( 1 ) ( ) = Ω p / 2 f ( Δ ) g cos φ ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ δ 2 ) ,
ρ g 1 g 3 ( 1 ) ( ) = Ω p / 2 f ( Δ ) g cos φ Ω 1 2 ( δ c 3 + Δ δ 2 ) ,
ρ g 2 g 3 ( 1 ) ( ) = Ω p / 2 f ( Δ ) g cos φ Ω 2 2 ( δ c 3 + Δ δ 1 ) ,
ρ 1 g 3 ( 1 ) ( ) = Ω p / 2 f ( Δ ) [ ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ + i γ 2 ) ( δ c 3 + Δ δ 2 ) ( δ c 3 + Δ δ 2 ) Ω 1 2 / 4 ( δ c 3 + Δ δ 1 ) Ω 2 2 / 4 ] ,
f ( Δ ) = ( i κ 2 + Δ ) [ ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ + i γ 2 ) ( δ c 3 + Δ δ 2 ) ( δ c 3 + Δ δ 2 ) Ω 1 2 / 4 ( δ c 3 + Δ δ 1 ) Ω 2 2 / 4 ] g 2 cos 2 φ ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ δ 2 ) .
S κ | ρ 1 g 3 ( 1 ) ( ) | 2 ,
S γ | ρ e g 3 ( 1 ) ( ) | 2 .
δ c 3 + Δ δ 1 = 0 ,
δ c 3 + Δ δ 2 = 0 .
ρ ( 1 ) ( s ) = 1 s ( 1 ) ρ ( 1 ) ( ) ,
ρ ˙ g j g j ( 2 ) = γ j δ j 3 ρ e e ( 2 ) i Ω j 2 ( ρ e g j ( 2 ) ρ g j e ( 2 ) ) ,
ρ ˙ 11 ( 2 ) = κ ρ 11 ( 2 ) + i ( Ω p 2 ρ 1 g 3 ( 1 ) g cos φ ρ e 1 ( 2 ) ) + c . c ,
ρ ˙ e e ( 2 ) = γ ρ e e ( 2 ) + i ( Ω 1 2 ρ e g 1 ( 2 ) + Ω 2 2 ρ e g 2 ( 2 ) + g cos φ ρ e 1 ( 2 ) ) + c . c ,
ρ ˙ g 1 g 2 ( 2 ) = i ( δ 2 δ 1 ) ρ g 1 g 2 ( 2 ) i Ω 1 2 ρ e g 2 ( 2 ) + i Ω 2 2 ρ g 1 e ( 2 ) ,
ρ ˙ e g 1 ( 2 ) = ( i δ 1 γ 2 ) ρ e g 1 ( 2 ) + i Ω 1 2 ( ρ e e ( 2 ) ρ g 1 g 1 ( 2 ) ) i Ω 2 2 ρ g 2 g 1 ( 2 ) i g cos φ ρ 1 g 1 ( 2 ) ,
ρ ˙ e g 2 ( 2 ) = ( i δ 2 γ 2 ) ρ e g 2 ( 2 ) + i Ω 2 2 ( ρ e e ( 2 ) ρ g 2 g 2 ( 2 ) ) i Ω 1 2 ρ g 1 g 2 ( 2 ) i g cos φ ρ 1 g 2 ( 2 ) ,
ρ ˙ e 1 ( 2 ) = ( i δ c 3 γ + κ 2 ) ρ e 1 ( 2 ) + i g cos φ ( ρ e e ( 2 ) ρ 11 ( 2 ) ) i j Ω j 2 ρ g j 1 ( 2 ) + i Ω p 2 ρ e g 3 ( 1 ) ,
ρ ˙ g 1 1 ( 2 ) = [ i ( δ c 3 δ 1 ) κ 2 ] ρ g 1 1 ( 2 ) i Ω 1 2 ρ e 1 ( 2 ) + i g cos φ ρ g 1 e ( 2 ) + i Ω p 2 ρ g 1 g 3 ( 1 ) ,
ρ ˙ g 2 1 ( 2 ) = [ i ( δ c 3 δ 2 ) κ 2 ] ρ g 2 1 ( 2 ) i Ω 2 2 ρ e 1 ( 2 ) + i g cos φ ρ g 2 e ( 2 ) + i Ω p 2 ρ g 2 g 3 ( 1 ) .
ρ ( 2 ) ( s ) = 1 s ( 2 ) [ ρ ( 2 ) ( ) + 1 s ( 1 ) ρ ( 1 ) ( ) ] ,
D = γ 2 η 3 2 α σ e e ( 2 ) ( ) .
A ± = | ε | 2 η ˜ 2 g 2 ν 2 | f ˜ ( Δ ν ) | 2 { γ | Δ ν + i κ / 2 | 2 + κ g 2 cos 2 φ } ,
η ˜ 2 = η l 1 2 cos 2 φ + η c 2 sin 2 φ
f ˜ ( Δ ν ) = ± ν g 2 cos 2 φ + ( Δ ν + i κ / 2 ) [ ν ( δ 1 ν + i γ / 2 ) ( Ω 1 / 2 ) 2 + ε ± ] ,
ε ± = ± ν ( Ω 2 / 2 ) 2 δ 1 ν δ 2 .
A ± = | ε | 2 η ˜ 2 g 2 γ ( 1 + C ± ) ( δ 1 ν δ 2 ) 2 γ 2 4 ( 1 + C ± ) 2 ( δ 1 ν δ 2 ) 2 + { Ω 2 2 4 + [ γ κ C ± ( Δ ν ) ± ν δ 1 Ω 1 2 4 ν ] ( δ 1 ν δ 2 ) } 2 = | ε | 2 η ˜ 2 g 2 γ ( 1 + C ± ) γ 2 4 ( 1 + C ± ) 2 + [ 1 ν ( Ω 1 2 4 ε ± ) ± ν δ 1 + γ κ C ± ( Δ ν ) ] 2 ,
C ± = C ( κ / 2 ) 2 ( Δ ν ) 2 + ( κ / 2 ) 2
ρ dark = | Ψ Ψ | ,
| Ψ = | g 3 , 0 + Ω p / 2 Δ + i κ / 2 | 1 , 0 Ω p Ω 1 g cos φ Δ + i κ / 2 | g 1 , 0 + Ω p g / Ω 2 Δ + i κ / 2 ( i η ˜ l 1 cos φ η ˜ c sin φ ) | g 2 , 1 ,
( 0 + 0 E + 1 ) ρ dark = 0 .
A = | ε | 2 η ˜ 2 g 2 γ ( 1 + C ) γ 2 4 ( 1 + C ) 2 + [ 1 ν ( Ω 1 2 4 + Ω 2 2 8 ) ν δ 1 + γ κ C ( Δ + ν ) ] 2 .
Ω 2 2 8 ν = δ 1 Ω 1 2 4 ν + ν ( Δ + ν ) g 2 cos 2 φ ( Δ + ν ) 2 + ( κ / 2 ) 2 .
A = | ε | 2 η ˜ 2 g 2 γ 4 ( 1 + C ) ,
ρ ˙ e e = γ ρ e e + i ( Ω 1 2 ρ e g 1 + Ω 2 2 ρ e g 2 + g cos φ ρ e 1 ) + c . c . , ρ ˙ g j g j = γ j ρ e e i Ω j 2 ( ρ e g j ρ g j e ) , ρ ˙ 11 = κ ρ 11 + i ( Ω p 2 ρ 1 g 3 g cos φ ρ e 1 ) + c . c . , ρ ˙ e g 1 = ( i δ 1 γ 2 ) ρ e g 1 + i Ω 1 2 ( ρ e e ρ g 1 g 1 ) i Ω 2 2 ρ g 2 g 1 i g cos φ ρ 1 g 1 , ρ ˙ e g 2 = ( i δ 2 γ 2 ) ρ e g 2 + i Ω 2 2 ( ρ e e ρ g 2 g 2 ) i Ω 1 2 ρ g 1 g 2 i g cos φ ρ 1 g 2 , ρ ˙ e 1 = ( i δ c 3 γ + κ 2 ) ρ e 1 + i g cos φ ( ρ e e ρ 11 i j Ω j 2 ρ g j 1 + i Ω p 2 ρ e g 3 ) , ρ ˙ g 1 g 2 = i ( δ 2 δ 1 ) ρ g 1 g 2 i Ω 1 2 ρ e g 2 + i Ω 2 2 ρ g 1 e , ρ ˙ g 1 1 = [ i ( δ c 3 δ 1 ) κ 2 ] ρ g 1 1 i Ω 1 2 ρ e 1 + i g cos φ ρ g 1 e + i Ω p 2 ρ g 1 g 3 , ρ ˙ g 2 1 = [ i ( δ c 3 δ 2 ) κ 2 ] ρ g 2 1 i Ω 2 2 ρ e 1 + i g cos φ ρ g 2 e + i Ω p 2 ρ g 2 g 3 , ρ ˙ e g 3 = [ i ( δ c 3 + Δ ) γ 2 ] ρ e g 3 i j Ω j 2 ρ g j g 3 i g cos φ ρ 1 g 3 + i Ω p 2 ρ e 1 , ρ ˙ g 1 g 3 = i [ Δ ( δ 1 δ c 3 ) ] ρ g 1 g 3 i Ω 1 2 ρ e g 3 + i Ω p 2 ρ g 1 1 , ρ ˙ g 2 g 3 = i [ Δ ( δ 2 δ c 3 ) ] ρ g 2 g 3 i Ω 2 2 ρ e g 3 + i Ω p 2 ρ g 2 1 , ρ ˙ 1 g 3 = ( i Δ κ 2 ) ρ 1 g 3 i g cos φ ρ e g 3 i Ω p 2 ( ρ g 3 g 3 ρ 11 ) .
ρ e e ( 2 ) ( ) = ( Ω p / 2 ) 2 | f ( Δ ) | 2 g 2 cos 2 φ ( δ c 3 + Δ δ 1 ) 2 ( δ c 3 + Δ δ 2 ) 2 , ρ g 1 g 1 ( 2 ) ( ) = ( Ω p / 2 ) 2 | f ( Δ ) | 2 g 2 cos 2 φ ( Ω 1 / 2 ) 2 ( δ c 3 + Δ δ 2 ) 2 , ρ g 2 g 2 ( 2 ) ( ) = ( Ω p / 2 ) 2 | f ( Δ ) | 2 g 2 cos 2 φ ( Ω 2 / 2 ) 2 ( δ c 3 + Δ δ 1 ) 2 , ρ 11 ( 2 ) ( ) = ( Ω p / 2 ) 2 | f ( Δ ) | 2 { ( γ / 2 ) 2 ( δ c 3 + Δ δ 1 ) 2 ( δ c 3 + Δ δ 2 ) 2 + [ ( δ c 3 + Δ ) ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ δ 2 ) ( Ω 1 / 2 ) 2 ( δ c 3 + Δ δ 2 ) ( δ c 3 + Δ δ 1 ) ( Ω 2 / 2 ) 2 ] 2 } , ρ e g 1 ( 2 ) ( ) = ( Ω p / 2 ) 2 | f ( Δ ) | 2 g 2 cos 2 φ ( Ω 1 / 2 ) ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ δ 2 ) 2 , ρ e g 2 ( 2 ) ( ) = ( Ω p / 2 ) 2 | f ( Δ ) | 2 g 2 cos 2 φ ( Ω 2 / 2 ) ( δ c 3 + Δ δ 1 ) 2 ( δ c 3 + Δ δ 2 ) , ρ e 1 ( 2 ) ( ) = ( Ω p / 2 ) 2 | f ( Δ ) | 2 g cos φ ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ δ 2 ) { ( δ c 3 + Δ i γ 2 ) ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ δ 2 ) ( Ω 1 / 2 ) 2 ( δ c 3 + Δ δ 2 ) ( δ c 3 + Δ δ 1 ) ( Ω 2 / 2 ) 2 } , ρ g 1 g 2 ( 2 ) ( ) = ( Ω p / 2 ) 2 | f ( Δ ) | 2 g 2 cos 2 φ ( Ω 1 / 2 ) ( Ω 2 / 2 ) ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ δ 2 ) , ρ g 1 1 ( 2 ) ( ) = ( Ω p / 2 ) 2 | f ( Δ ) | 2 g cos φ ( Ω 1 / 2 ) ( δ c 3 + Δ δ 2 ) { ( δ c 3 + Δ i γ 2 ) ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ δ 2 ) ( Ω 1 / 2 ) 2 ( δ c 3 + Δ δ 2 ) ( δ c 3 + Δ δ 1 ) ( Ω 2 / 2 ) 2 } , ρ g 2 1 ( 2 ) ( ) = ( Ω p / 2 ) 2 | f ( Δ ) | 2 g cos φ ( Ω 2 / 2 ) ( δ c 3 + Δ δ 1 ) { ( δ c 3 + Δ i γ 2 ) ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ δ 2 ) ( Ω 1 / 2 ) 2 ( δ c 3 + Δ δ 2 ) ( δ c 3 + Δ δ 1 ) ( Ω 2 / 2 ) 2 } ,

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