Abstract

We theoretically study the cavity transmission spectra with three-level atoms coupled by a coherent external control field in the superstrong coupling regime (atoms-cavity coupling strength gN is near or larger than the cavity free-spectral range ∆FSR). When satisfying the superstrong coupling condition by increasing the number of the interaction atoms, more than one FSR cavity modes interact with atoms and each mode will split three peaks, which can be well explained by the linear dispersion enhancement of electromagnetically induced transparency medium due to the largely increased atomic density in the cavity.

© 2010 Optical Society of America

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  21. S. Slama, S. Bux, G. Krenz, C. Zimmermann, and Ph. W. Courteille, "Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity," Phys. Rev. Lett. 98, 053603 (2007).
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    [CrossRef]
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    [CrossRef]

2009

H. Wu, J. Gea-Banacloche, and M. Xiao, "Splitting of atom-cavity polariton peaks for three-level atoms in an optical cavity," Phys. Rev. A 80, 033806 (2009).
[CrossRef]

G. Gunter, A. A. Anappara, J. Hees, L. Sorba, G. Biasiol, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber "Sub-cycle switch-on of ultrastrong light-matter interaction," Nature 458, 178 (2009).
[CrossRef] [PubMed]

X. Yu, D. Xiong, H. Chen, P. Wang, M. Xiao, and J. Zhang, "Multi-normal-mode splitting of a cavity in the presence of atoms: A step towards the superstrong-coupling regime," Phys. Rev. A 79, 061803 (2009).
[CrossRef]

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, "Electromagnetically induced transparency controlled by a microwave field," Phys. Rev. A 80, 023820 (2009).
[CrossRef]

2008

H. Wu, J. Gea-Banacloche, and M. Xiao, "Observation of intracavity electromagnetically induced transparency and polariton resonances in a Doppler-broadened medium," Phys. Rev. Lett. 100, 173602 (2008).
[CrossRef] [PubMed]

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

J. Gea-Banacloche, H. Wu, and M. Xiao, "Transmission spectrum of Doppler-broadened two-level atoms in a cavity in the strong-coupling regime," Phys. Rev. A 78, 023828 (2008).
[CrossRef]

2007

G. Hernandez, J. Zhang, and Y. Zhu, "Vacuum Rabi splitting and intracavity dark state in a cavity-atom system," Phys. Rev. A 76, 053814 (2007).
[CrossRef]

S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, "Cavity nonlinear optics at low photon numbers from collective atomic motion," Phys. Rev. Lett. 99, 213601 (2007).
[CrossRef]

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

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Kohl, and T. Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268 (2007).
[CrossRef] [PubMed]

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P.W. H. Pinkse, and G. Rempe, "Trapping and observing single atoms in a blue-detuned intracavity dipole trap," Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and Ph. W. Courteille, "Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity," Phys. Rev. Lett. 98, 053603 (2007).
[CrossRef] [PubMed]

2006

D. Meiser and P. Meystre, "Superstrong coupling regime of cavity quantum electrodynamics," Phys. Rev. A 74, 065801 (2006).
[CrossRef]

J. Klinner, M. Lindholdt, B. Nagorny, and A. Hemmerich, "Normal mode splitting and mechanical effects of an optical lattice in a ring cavity," Phys. Rev. Lett. 96, 023002 (2006).
[CrossRef] [PubMed]

A. K. Tuchman, R. Long, G. Vrijsen, J. Boudet, J. Lee, and M. A. Kasevich, "Normal-mode splitting with large collective cooperativity," Phys. Rev. A 74, 053821 (2006).
[CrossRef]

2005

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, "Normal-mode spectroscopy of a single-bound-atom-cavity system," Phys. Rev. Lett. 94, 033002 (2005).
[CrossRef] [PubMed]

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

2004

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, "Observation of the vacuum Rabi spectrum for one trapped atom," Phys. Rev. Lett. 93, 233603 (2004).
[CrossRef] [PubMed]

2003

B. Nagorny, Th. Elsasser, and A. Hemmerich, "Collective atomic motion in an optical lattice formed inside a high finesse cavity," Phys. Rev. Lett. 91, 153003 (2003).
[CrossRef] [PubMed]

D. Kruse, C. von Cube, C. Zimmermann, and P. W. Courteille, "Observation of lasing mediated by collective atomic recoil," Phys. Rev. Lett. 91, 183601 (2003).
[CrossRef] [PubMed]

A. T. Black, H. W. Chan, and V. Vuletic, "Observation of collective friction forces due to spatial self-organization of atoms: From Rayleigh to Bragg scattering," Phys. Rev. Lett. 91, 203001 (2003).
[CrossRef] [PubMed]

M. D. Lukin, " Colloquium: Trapping and manipulating photon states in atomic ensembles," Rev. Mod. Phys. 75, 457 (2003).
[CrossRef]

2000

1998

J. P. Marangos, "Electromagnetically induced transparency," J. Mod. Opt. 45, 471 (1998).
[CrossRef]

1997

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50(7), 37 (1997).
[CrossRef]

1995

J. Gea-Banacloche, Y. Q. Li, S. Z. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment," Phys. Rev. A 51, 576 (1995).
[CrossRef] [PubMed]

1992

R. J. Thompson, G. Rempe, and H. J. Kimble, "Observation of normal-mode splitting for an atom in an optical cavity," Phys. Rev. Lett. 68, 1132 (1992).
[CrossRef] [PubMed]

1990

Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, "Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations," Phys. Rev. Lett. 64, 2499 (1990).
[CrossRef] [PubMed]

1984

G. S. Agarwal, "Vacuum-field Rabi splittings in microwave absorption by Rydberg atoms in a cavity," Phys. Rev. Lett. 53, 1732 (1984).
[CrossRef]

1968

M. Tavis, and F. W. Cummings, "Exact solution for an N-molecule-radiation-field Hamiltonian," Phys. Rev. 170, 379 (1968).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, "Vacuum-field Rabi splittings in microwave absorption by Rydberg atoms in a cavity," Phys. Rev. Lett. 53, 1732 (1984).
[CrossRef]

Anappara, A. A.

G. Gunter, A. A. Anappara, J. Hees, L. Sorba, G. Biasiol, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber "Sub-cycle switch-on of ultrastrong light-matter interaction," Nature 458, 178 (2009).
[CrossRef] [PubMed]

Biasiol, G.

G. Gunter, A. A. Anappara, J. Hees, L. Sorba, G. Biasiol, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber "Sub-cycle switch-on of ultrastrong light-matter interaction," Nature 458, 178 (2009).
[CrossRef] [PubMed]

Birnbaum, K. M.

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, "Observation of the vacuum Rabi spectrum for one trapped atom," Phys. Rev. Lett. 93, 233603 (2004).
[CrossRef] [PubMed]

Black, A. T.

A. T. Black, H. W. Chan, and V. Vuletic, "Observation of collective friction forces due to spatial self-organization of atoms: From Rayleigh to Bragg scattering," Phys. Rev. Lett. 91, 203001 (2003).
[CrossRef] [PubMed]

Boca, A.

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, "Observation of the vacuum Rabi spectrum for one trapped atom," Phys. Rev. Lett. 93, 233603 (2004).
[CrossRef] [PubMed]

Boozer, A. D.

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, "Observation of the vacuum Rabi spectrum for one trapped atom," Phys. Rev. Lett. 93, 233603 (2004).
[CrossRef] [PubMed]

Boudet, J.

A. K. Tuchman, R. Long, G. Vrijsen, J. Boudet, J. Lee, and M. A. Kasevich, "Normal-mode splitting with large collective cooperativity," Phys. Rev. A 74, 053821 (2006).
[CrossRef]

Bourdel, T.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Kohl, and T. Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268 (2007).
[CrossRef] [PubMed]

Brennecke, F.

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

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Kohl, and T. Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268 (2007).
[CrossRef] [PubMed]

Burkett, W. H.

Bux, S.

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and Ph. W. Courteille, "Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity," Phys. Rev. Lett. 98, 053603 (2007).
[CrossRef] [PubMed]

Carmichael, H. J.

Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, "Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations," Phys. Rev. Lett. 64, 2499 (1990).
[CrossRef] [PubMed]

Chan, H. W.

A. T. Black, H. W. Chan, and V. Vuletic, "Observation of collective friction forces due to spatial self-organization of atoms: From Rayleigh to Bragg scattering," Phys. Rev. Lett. 91, 203001 (2003).
[CrossRef] [PubMed]

Chen, H.

X. Yu, D. Xiong, H. Chen, P. Wang, M. Xiao, and J. Zhang, "Multi-normal-mode splitting of a cavity in the presence of atoms: A step towards the superstrong-coupling regime," Phys. Rev. A 79, 061803 (2009).
[CrossRef]

Ciuti, C.

G. Gunter, A. A. Anappara, J. Hees, L. Sorba, G. Biasiol, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber "Sub-cycle switch-on of ultrastrong light-matter interaction," Nature 458, 178 (2009).
[CrossRef] [PubMed]

Colombe, Y.

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

Courteille, P. W.

D. Kruse, C. von Cube, C. Zimmermann, and P. W. Courteille, "Observation of lasing mediated by collective atomic recoil," Phys. Rev. Lett. 91, 183601 (2003).
[CrossRef] [PubMed]

Courteille, Ph. W.

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and Ph. W. Courteille, "Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity," Phys. Rev. Lett. 98, 053603 (2007).
[CrossRef] [PubMed]

Cummings, F. W.

M. Tavis, and F. W. Cummings, "Exact solution for an N-molecule-radiation-field Hamiltonian," Phys. Rev. 170, 379 (1968).
[CrossRef]

De Liberato, S.

G. Gunter, A. A. Anappara, J. Hees, L. Sorba, G. Biasiol, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber "Sub-cycle switch-on of ultrastrong light-matter interaction," Nature 458, 178 (2009).
[CrossRef] [PubMed]

Donner, T.

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

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Kohl, and T. Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268 (2007).
[CrossRef] [PubMed]

Dubois, G.

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

Elsasser, Th.

B. Nagorny, Th. Elsasser, and A. Hemmerich, "Collective atomic motion in an optical lattice formed inside a high finesse cavity," Phys. Rev. Lett. 91, 153003 (2003).
[CrossRef] [PubMed]

Esslinger, T.

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

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Kohl, and T. Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268 (2007).
[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]

Gauthier, D. J.

Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, "Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations," Phys. Rev. Lett. 64, 2499 (1990).
[CrossRef] [PubMed]

Gea-Banacloche, J.

H. Wu, J. Gea-Banacloche, and M. Xiao, "Splitting of atom-cavity polariton peaks for three-level atoms in an optical cavity," Phys. Rev. A 80, 033806 (2009).
[CrossRef]

H. Wu, J. Gea-Banacloche, and M. Xiao, "Observation of intracavity electromagnetically induced transparency and polariton resonances in a Doppler-broadened medium," Phys. Rev. Lett. 100, 173602 (2008).
[CrossRef] [PubMed]

J. Gea-Banacloche, H. Wu, and M. Xiao, "Transmission spectrum of Doppler-broadened two-level atoms in a cavity in the strong-coupling regime," Phys. Rev. A 78, 023828 (2008).
[CrossRef]

J. Gea-Banacloche, Y. Q. Li, S. Z. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment," Phys. Rev. A 51, 576 (1995).
[CrossRef] [PubMed]

Goorskey, D. J.

Grothe, A.

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P.W. H. Pinkse, and G. Rempe, "Trapping and observing single atoms in a blue-detuned intracavity dipole trap," Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

Gunter, G.

G. Gunter, A. A. Anappara, J. Hees, L. Sorba, G. Biasiol, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber "Sub-cycle switch-on of ultrastrong light-matter interaction," Nature 458, 178 (2009).
[CrossRef] [PubMed]

Gupta, S.

S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, "Cavity nonlinear optics at low photon numbers from collective atomic motion," Phys. Rev. Lett. 99, 213601 (2007).
[CrossRef]

Harris, S. E.

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50(7), 37 (1997).
[CrossRef]

Hees, J.

G. Gunter, A. A. Anappara, J. Hees, L. Sorba, G. Biasiol, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber "Sub-cycle switch-on of ultrastrong light-matter interaction," Nature 458, 178 (2009).
[CrossRef] [PubMed]

Hemmer, P. R.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, "Electromagnetically induced transparency controlled by a microwave field," Phys. Rev. A 80, 023820 (2009).
[CrossRef]

Hemmerich, A.

J. Klinner, M. Lindholdt, B. Nagorny, and A. Hemmerich, "Normal mode splitting and mechanical effects of an optical lattice in a ring cavity," Phys. Rev. Lett. 96, 023002 (2006).
[CrossRef] [PubMed]

B. Nagorny, Th. Elsasser, and A. Hemmerich, "Collective atomic motion in an optical lattice formed inside a high finesse cavity," Phys. Rev. Lett. 91, 153003 (2003).
[CrossRef] [PubMed]

Hernandez, G.

G. Hernandez, J. Zhang, and Y. Zhu, "Vacuum Rabi splitting and intracavity dark state in a cavity-atom system," Phys. Rev. A 76, 053814 (2007).
[CrossRef]

Huber, R.

G. Gunter, A. A. Anappara, J. Hees, L. Sorba, G. Biasiol, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber "Sub-cycle switch-on of ultrastrong light-matter interaction," Nature 458, 178 (2009).
[CrossRef] [PubMed]

Hunger, D.

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

Imamoglu, A.

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

Jin, S. Z.

J. Gea-Banacloche, Y. Q. Li, S. Z. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment," Phys. Rev. A 51, 576 (1995).
[CrossRef] [PubMed]

Kasevich, M. A.

A. K. Tuchman, R. Long, G. Vrijsen, J. Boudet, J. Lee, and M. A. Kasevich, "Normal-mode splitting with large collective cooperativity," Phys. Rev. A 74, 053821 (2006).
[CrossRef]

Kimble, H. J.

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, "Observation of the vacuum Rabi spectrum for one trapped atom," Phys. Rev. Lett. 93, 233603 (2004).
[CrossRef] [PubMed]

R. J. Thompson, G. Rempe, and H. J. Kimble, "Observation of normal-mode splitting for an atom in an optical cavity," Phys. Rev. Lett. 68, 1132 (1992).
[CrossRef] [PubMed]

Klinner, J.

J. Klinner, M. Lindholdt, B. Nagorny, and A. Hemmerich, "Normal mode splitting and mechanical effects of an optical lattice in a ring cavity," Phys. Rev. Lett. 96, 023002 (2006).
[CrossRef] [PubMed]

Kohl, M.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Kohl, and T. Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268 (2007).
[CrossRef] [PubMed]

Krenz, G.

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and Ph. W. Courteille, "Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity," Phys. Rev. Lett. 98, 053603 (2007).
[CrossRef] [PubMed]

Kruse, D.

D. Kruse, C. von Cube, C. Zimmermann, and P. W. Courteille, "Observation of lasing mediated by collective atomic recoil," Phys. Rev. Lett. 91, 183601 (2003).
[CrossRef] [PubMed]

Kubanek, A.

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P.W. H. Pinkse, and G. Rempe, "Trapping and observing single atoms in a blue-detuned intracavity dipole trap," Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

Lee, J.

A. K. Tuchman, R. Long, G. Vrijsen, J. Boudet, J. Lee, and M. A. Kasevich, "Normal-mode splitting with large collective cooperativity," Phys. Rev. A 74, 053821 (2006).
[CrossRef]

Leitenstorfer, A.

G. Gunter, A. A. Anappara, J. Hees, L. Sorba, G. Biasiol, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber "Sub-cycle switch-on of ultrastrong light-matter interaction," Nature 458, 178 (2009).
[CrossRef] [PubMed]

Li, H.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, "Electromagnetically induced transparency controlled by a microwave field," Phys. Rev. A 80, 023820 (2009).
[CrossRef]

Li, Y. Q.

J. Gea-Banacloche, Y. Q. Li, S. Z. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment," Phys. Rev. A 51, 576 (1995).
[CrossRef] [PubMed]

Lindholdt, M.

J. Klinner, M. Lindholdt, B. Nagorny, and A. Hemmerich, "Normal mode splitting and mechanical effects of an optical lattice in a ring cavity," Phys. Rev. Lett. 96, 023002 (2006).
[CrossRef] [PubMed]

Linke, F.

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

Long, R.

A. K. Tuchman, R. Long, G. Vrijsen, J. Boudet, J. Lee, and M. A. Kasevich, "Normal-mode splitting with large collective cooperativity," Phys. Rev. A 74, 053821 (2006).
[CrossRef]

Lukin, M. D.

M. D. Lukin, " Colloquium: Trapping and manipulating photon states in atomic ensembles," Rev. Mod. Phys. 75, 457 (2003).
[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]

J. P. Marangos, "Electromagnetically induced transparency," J. Mod. Opt. 45, 471 (1998).
[CrossRef]

Maunz, P.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, "Normal-mode spectroscopy of a single-bound-atom-cavity system," Phys. Rev. Lett. 94, 033002 (2005).
[CrossRef] [PubMed]

McKeever, J.

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, "Observation of the vacuum Rabi spectrum for one trapped atom," Phys. Rev. Lett. 93, 233603 (2004).
[CrossRef] [PubMed]

Meiser, D.

D. Meiser and P. Meystre, "Superstrong coupling regime of cavity quantum electrodynamics," Phys. Rev. A 74, 065801 (2006).
[CrossRef]

Meystre, P.

D. Meiser and P. Meystre, "Superstrong coupling regime of cavity quantum electrodynamics," Phys. Rev. A 74, 065801 (2006).
[CrossRef]

Miller, R.

A. Boca, R. Miller, K. M. Birnbaum, A. D. Boozer, J. McKeever, and H. J. Kimble, "Observation of the vacuum Rabi spectrum for one trapped atom," Phys. Rev. Lett. 93, 233603 (2004).
[CrossRef] [PubMed]

Moore, K. L.

S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, "Cavity nonlinear optics at low photon numbers from collective atomic motion," Phys. Rev. Lett. 99, 213601 (2007).
[CrossRef]

Morin, S. E.

Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, "Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations," Phys. Rev. Lett. 64, 2499 (1990).
[CrossRef] [PubMed]

Mossberg, T. W.

Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, "Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations," Phys. Rev. Lett. 64, 2499 (1990).
[CrossRef] [PubMed]

Murch, K. W.

S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, "Cavity nonlinear optics at low photon numbers from collective atomic motion," Phys. Rev. Lett. 99, 213601 (2007).
[CrossRef]

Murr, K.

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P.W. H. Pinkse, and G. Rempe, "Trapping and observing single atoms in a blue-detuned intracavity dipole trap," Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

Nagorny, B.

J. Klinner, M. Lindholdt, B. Nagorny, and A. Hemmerich, "Normal mode splitting and mechanical effects of an optical lattice in a ring cavity," Phys. Rev. Lett. 96, 023002 (2006).
[CrossRef] [PubMed]

B. Nagorny, Th. Elsasser, and A. Hemmerich, "Collective atomic motion in an optical lattice formed inside a high finesse cavity," Phys. Rev. Lett. 91, 153003 (2003).
[CrossRef] [PubMed]

Pinkse, P. W. H.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, "Normal-mode spectroscopy of a single-bound-atom-cavity system," Phys. Rev. Lett. 94, 033002 (2005).
[CrossRef] [PubMed]

Pinkse, P.W. H.

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P.W. H. Pinkse, and G. Rempe, "Trapping and observing single atoms in a blue-detuned intracavity dipole trap," Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

Puppe, T.

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P.W. H. Pinkse, and G. Rempe, "Trapping and observing single atoms in a blue-detuned intracavity dipole trap," Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, "Normal-mode spectroscopy of a single-bound-atom-cavity system," Phys. Rev. Lett. 94, 033002 (2005).
[CrossRef] [PubMed]

Reichel, J.

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

Rempe, G.

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P.W. H. Pinkse, and G. Rempe, "Trapping and observing single atoms in a blue-detuned intracavity dipole trap," Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, "Normal-mode spectroscopy of a single-bound-atom-cavity system," Phys. Rev. Lett. 94, 033002 (2005).
[CrossRef] [PubMed]

R. J. Thompson, G. Rempe, and H. J. Kimble, "Observation of normal-mode splitting for an atom in an optical cavity," Phys. Rev. Lett. 68, 1132 (1992).
[CrossRef] [PubMed]

Ritter, S.

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

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Kohl, and T. Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268 (2007).
[CrossRef] [PubMed]

Rostovtsev, Y. V.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, "Electromagnetically induced transparency controlled by a microwave field," Phys. Rev. A 80, 023820 (2009).
[CrossRef]

Sautenkov, V. A.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, "Electromagnetically induced transparency controlled by a microwave field," Phys. Rev. A 80, 023820 (2009).
[CrossRef]

Schuster, I.

T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P.W. H. Pinkse, and G. Rempe, "Trapping and observing single atoms in a blue-detuned intracavity dipole trap," Phys. Rev. Lett. 99, 013002 (2007).
[CrossRef] [PubMed]

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, "Normal-mode spectroscopy of a single-bound-atom-cavity system," Phys. Rev. Lett. 94, 033002 (2005).
[CrossRef] [PubMed]

Scully, M. O.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, "Electromagnetically induced transparency controlled by a microwave field," Phys. Rev. A 80, 023820 (2009).
[CrossRef]

Slama, S.

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and Ph. W. Courteille, "Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity," Phys. Rev. Lett. 98, 053603 (2007).
[CrossRef] [PubMed]

Sorba, L.

G. Gunter, A. A. Anappara, J. Hees, L. Sorba, G. Biasiol, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber "Sub-cycle switch-on of ultrastrong light-matter interaction," Nature 458, 178 (2009).
[CrossRef] [PubMed]

Stamper-Kurn, D. M.

S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, "Cavity nonlinear optics at low photon numbers from collective atomic motion," Phys. Rev. Lett. 99, 213601 (2007).
[CrossRef]

Steinmetz, T.

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

Syassen, N.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, "Normal-mode spectroscopy of a single-bound-atom-cavity system," Phys. Rev. Lett. 94, 033002 (2005).
[CrossRef] [PubMed]

Tavis, M.

M. Tavis, and F. W. Cummings, "Exact solution for an N-molecule-radiation-field Hamiltonian," Phys. Rev. 170, 379 (1968).
[CrossRef]

Thompson, R. J.

R. J. Thompson, G. Rempe, and H. J. Kimble, "Observation of normal-mode splitting for an atom in an optical cavity," Phys. Rev. Lett. 68, 1132 (1992).
[CrossRef] [PubMed]

Tredicucci, A.

G. Gunter, A. A. Anappara, J. Hees, L. Sorba, G. Biasiol, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber "Sub-cycle switch-on of ultrastrong light-matter interaction," Nature 458, 178 (2009).
[CrossRef] [PubMed]

Tuchman, A. K.

A. K. Tuchman, R. Long, G. Vrijsen, J. Boudet, J. Lee, and M. A. Kasevich, "Normal-mode splitting with large collective cooperativity," Phys. Rev. A 74, 053821 (2006).
[CrossRef]

von Cube, C.

D. Kruse, C. von Cube, C. Zimmermann, and P. W. Courteille, "Observation of lasing mediated by collective atomic recoil," Phys. Rev. Lett. 91, 183601 (2003).
[CrossRef] [PubMed]

Vrijsen, G.

A. K. Tuchman, R. Long, G. Vrijsen, J. Boudet, J. Lee, and M. A. Kasevich, "Normal-mode splitting with large collective cooperativity," Phys. Rev. A 74, 053821 (2006).
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Vuletic, V.

A. T. Black, H. W. Chan, and V. Vuletic, "Observation of collective friction forces due to spatial self-organization of atoms: From Rayleigh to Bragg scattering," Phys. Rev. Lett. 91, 203001 (2003).
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Wang, H.

Wang, P.

X. Yu, D. Xiong, H. Chen, P. Wang, M. Xiao, and J. Zhang, "Multi-normal-mode splitting of a cavity in the presence of atoms: A step towards the superstrong-coupling regime," Phys. Rev. A 79, 061803 (2009).
[CrossRef]

Welch, G. R.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, "Electromagnetically induced transparency controlled by a microwave field," Phys. Rev. A 80, 023820 (2009).
[CrossRef]

Wu, H.

H. Wu, J. Gea-Banacloche, and M. Xiao, "Splitting of atom-cavity polariton peaks for three-level atoms in an optical cavity," Phys. Rev. A 80, 033806 (2009).
[CrossRef]

H. Wu, J. Gea-Banacloche, and M. Xiao, "Observation of intracavity electromagnetically induced transparency and polariton resonances in a Doppler-broadened medium," Phys. Rev. Lett. 100, 173602 (2008).
[CrossRef] [PubMed]

J. Gea-Banacloche, H. Wu, and M. Xiao, "Transmission spectrum of Doppler-broadened two-level atoms in a cavity in the strong-coupling regime," Phys. Rev. A 78, 023828 (2008).
[CrossRef]

Wu, Q.

Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, "Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations," Phys. Rev. Lett. 64, 2499 (1990).
[CrossRef] [PubMed]

Xiao, M.

H. Wu, J. Gea-Banacloche, and M. Xiao, "Splitting of atom-cavity polariton peaks for three-level atoms in an optical cavity," Phys. Rev. A 80, 033806 (2009).
[CrossRef]

X. Yu, D. Xiong, H. Chen, P. Wang, M. Xiao, and J. Zhang, "Multi-normal-mode splitting of a cavity in the presence of atoms: A step towards the superstrong-coupling regime," Phys. Rev. A 79, 061803 (2009).
[CrossRef]

H. Wu, J. Gea-Banacloche, and M. Xiao, "Observation of intracavity electromagnetically induced transparency and polariton resonances in a Doppler-broadened medium," Phys. Rev. Lett. 100, 173602 (2008).
[CrossRef] [PubMed]

J. Gea-Banacloche, H. Wu, and M. Xiao, "Transmission spectrum of Doppler-broadened two-level atoms in a cavity in the strong-coupling regime," Phys. Rev. A 78, 023828 (2008).
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H. Wang, D. J. Goorskey, W. H. Burkett, and M. Xiao, "Cavity-linewidth narrowing by means of electromagnetically induced transparency," Opt. Lett. 25, 1732 (2000).
[CrossRef]

J. Gea-Banacloche, Y. Q. Li, S. Z. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment," Phys. Rev. A 51, 576 (1995).
[CrossRef] [PubMed]

Xiong, D.

X. Yu, D. Xiong, H. Chen, P. Wang, M. Xiao, and J. Zhang, "Multi-normal-mode splitting of a cavity in the presence of atoms: A step towards the superstrong-coupling regime," Phys. Rev. A 79, 061803 (2009).
[CrossRef]

Yu, X.

X. Yu, D. Xiong, H. Chen, P. Wang, M. Xiao, and J. Zhang, "Multi-normal-mode splitting of a cavity in the presence of atoms: A step towards the superstrong-coupling regime," Phys. Rev. A 79, 061803 (2009).
[CrossRef]

Zhang, J.

X. Yu, D. Xiong, H. Chen, P. Wang, M. Xiao, and J. Zhang, "Multi-normal-mode splitting of a cavity in the presence of atoms: A step towards the superstrong-coupling regime," Phys. Rev. A 79, 061803 (2009).
[CrossRef]

G. Hernandez, J. Zhang, and Y. Zhu, "Vacuum Rabi splitting and intracavity dark state in a cavity-atom system," Phys. Rev. A 76, 053814 (2007).
[CrossRef]

Zhu, Y.

G. Hernandez, J. Zhang, and Y. Zhu, "Vacuum Rabi splitting and intracavity dark state in a cavity-atom system," Phys. Rev. A 76, 053814 (2007).
[CrossRef]

Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, "Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations," Phys. Rev. Lett. 64, 2499 (1990).
[CrossRef] [PubMed]

Zimmermann, C.

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and Ph. W. Courteille, "Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity," Phys. Rev. Lett. 98, 053603 (2007).
[CrossRef] [PubMed]

D. Kruse, C. von Cube, C. Zimmermann, and P. W. Courteille, "Observation of lasing mediated by collective atomic recoil," Phys. Rev. Lett. 91, 183601 (2003).
[CrossRef] [PubMed]

J. Mod. Opt.

J. P. Marangos, "Electromagnetically induced transparency," J. Mod. Opt. 45, 471 (1998).
[CrossRef]

Nature

G. Gunter, A. A. Anappara, J. Hees, L. Sorba, G. Biasiol, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Huber "Sub-cycle switch-on of ultrastrong light-matter interaction," Nature 458, 178 (2009).
[CrossRef] [PubMed]

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

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Kohl, and T. Esslinger, "Cavity QED with a Bose-Einstein condensate," Nature 450, 268 (2007).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev.

M. Tavis, and F. W. Cummings, "Exact solution for an N-molecule-radiation-field Hamiltonian," Phys. Rev. 170, 379 (1968).
[CrossRef]

Phys. Rev. A

A. K. Tuchman, R. Long, G. Vrijsen, J. Boudet, J. Lee, and M. A. Kasevich, "Normal-mode splitting with large collective cooperativity," Phys. Rev. A 74, 053821 (2006).
[CrossRef]

J. Gea-Banacloche, H. Wu, and M. Xiao, "Transmission spectrum of Doppler-broadened two-level atoms in a cavity in the strong-coupling regime," Phys. Rev. A 78, 023828 (2008).
[CrossRef]

G. Hernandez, J. Zhang, and Y. Zhu, "Vacuum Rabi splitting and intracavity dark state in a cavity-atom system," Phys. Rev. A 76, 053814 (2007).
[CrossRef]

H. Wu, J. Gea-Banacloche, and M. Xiao, "Splitting of atom-cavity polariton peaks for three-level atoms in an optical cavity," Phys. Rev. A 80, 033806 (2009).
[CrossRef]

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, "Electromagnetically induced transparency controlled by a microwave field," Phys. Rev. A 80, 023820 (2009).
[CrossRef]

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[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

A schematic diagram of a ring cavity containing the three-level atoms coupled by a coherent external control field. The optical cavity length, which is fixed on atomic transition frequency, is adjusted by piezoelectric transducer (PZT) mounted on the mirror M3. The frequency of the input laser (as probe light) is scanned to measure the transmission spectra.

Fig. 2.
Fig. 2.

(Color online). Theoretical calculations of the transmission spectra of the coupled atoms-cavity system with the two-level atoms with different atomic density. For comparison, the cavity transmission spectrum for the empty cavity (blue dashed) is plotted in (a)-(d). m = {…;-2;-1;0;+1;+2;…} label the FSR empty cavity modes and m′ = {…,{-21;-22};{-11;-12};{01;02};{+11;+12};{+21;2+2};…} the multi-normal-mode splitting peaks. (a) NDLa = 3.15×1015 m -2; (b)NDLa = 3.15×1016m-2); (c)NDLa = 7.85×1016 m -2; (d)NDLa = 1.77×1017m-2; (e), (f), (g) and (h) are the re-plots of the multi-normal-mode splitting peaks of (a),(b) (c) and (d) with blue elliptical points, respectively. The function ϕ(∆)/2π = ∆/∆ FSR +Re[χ(∆)]La /2λL is also plotted in (e), (f), (g) and (h) with pink dot line.

Fig. 3.
Fig. 3.

(Color online). Theoretical calculations of the transmission spectra of the coupled atoms-cavity system with the three-level atoms with different atomic density. The cavity transmission spectrum for the empty cavity (blue dashed) is plotted in (a)-(d). m = {…;-2;-1;0;+1;+2;…} label the FSR empty cavity modes and m′ = {…;{-21;-22;-23};{-11;-12;-13};{01;02;03};{+11; +12;+13};{+21;+22;+23};…} the multi-normal-mode splitting peaks. The Rabi frequency of the coupling laser is Ω c = 2π × 60 MHz. The other parameters are same as the Fig.2. (e), (f), (g) and (h) are the re-plots of the multi-normal-mode splitting peaks of (a),(b) (c) and (d) with blue elliptical points, respectively. The function ϕ(∆)/2π = ∆/∆ FSR +Re[χ(∆)]La /2λL is also plotted in (e),(f),(g) and (h)with pink dot line.

Equations (13)

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T c ( ω L ) = t c ( Δ ) 2
= t 1 2 t 2 2 e α L a ( 1 r 1 r 2 e α L a / 2 ) 2 + 4 r 1 r 2 e α L a / 2 sin 2 ( ϕ / 2 ) ,
ϕ ( ω L ) = 2 π ( Δ Δ ac ) / Δ FSR + ( n 1 ) L a ω L / c
α = 2 ω a c Im [ ( 1 + χ ) 1 2 ]
n = Re [ ( 1 + χ ) 1 2 ] ,
ρ ˙ be = ( γ be i Δ c ) ρ be + i μ be E c * 2 ( ρ bb ρ ee ) + i μ ea E p * 2 ρ ba
ρ ˙ ea = ( γ ea i Δ p ) ρ ea + i μ ea E p 2 ( ρ ee ρ aa ) + i μ be E c 2 ρ ba
ρ ˙ ba = [ γ ba i ( Δ p + Δ c ) ] ρ ba i μ be E c * 2 ρ ea + i μ ea E p 2 ρ be
ρ ea i μ ea E p γ ea i Δ p + Ω c 2 / 4 γ ba i Δ p ,
χ = i μ ea 2 N D h ̄ ε 0 1 γ ea i Δ p + Ω c 2 / 4 γ ba i Δ p
= i 3 π c 3 N D ω a 3 γ ea γ ea i Δ p + Ω c 2 / 4 γ ba i Δ p ,
α = ω a c Im [ χ ]
n = 1 + Re [ χ ] / 2 .

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