Abstract

By making use of the changes in optical properties such as absorption and dispersion around the resonance generated via electromagnetically induced transparency (EIT), we theoretically and experimentally investigate a “∞”-shape optical bistability (OB) versus frequency on the probe transmission with a Λ-shape EIT window in a rubidium atomic ensemble confined in a three-mirror optical ring cavity. Compared to the traditional OB reflected by a hysteresis loop versus power, such newly demonstrated optical bistable behavior (represented by a “∞”-shape non-overlapping region) by scanning probe and cavity detuning can experience dual bistabilities and be more sensitive to the change of experimental parameters. Further, we study the relationship between vacuum Rabi splitting and the “∞”-shape OB. Such study on frequency-induced OB could effectively improve the applications related to OB such as logic-gate devices and optical information processing.

© 2017 Optical Society of America

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  1. H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36(19), 1135–1138 (1976).
  2. A. Joshi and M. Xiao, “Atomic optical bistability in two- and three-level systems: perspectives and prospects,” J. Mod. Opt. 57(14–15), 1196–1220 (2001).
  3. H. Wang, D. J. Goorskey, and M. Xiao, “Bistability and instability of three-level atoms inside an optical cavity,” Phys. Rev. A 65(1), 011801 (2001).
  4. G. Hernandez, J. Zhang, and Y. Zhu, “Vacuum Rabi splitting and intracavity dark state in a cavity-atom system,” Phys. Rev. A 76(5), 053814 (2007).
  5. 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(21), 213601 (2007).
    [PubMed]
  6. H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
    [PubMed]
  7. A. Joshi and M. Xiao, “Optical bistability in a three-level semiconductor quantum-well system,” Appl. Phys. B 79(1), 65–69 (2004).
  8. A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67(4), 041801 (2003).
  9. X. Lü, J. Li, J. Liu, and J. Luo, “Optical bistability via quantum interference in a four-level atomic medium,” J. Phys. At. Mol. Opt. Phys. 39(24), 5161–5171 (2006).
  10. Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M. A. Miri, D. N. Christodoulides, B. He, Y. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117(12), 123601 (2016).
    [PubMed]
  11. J. Gea-Banacloche, Yq. Li, Sz. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A 51(1), 576–584 (1995).
    [PubMed]
  12. A. Brown, A. Joshi, and M. Xiao, “Controlled steady-state switching in optical bistability,” Appl. Phys. Lett. 83(7), 1301–1303 (2003).
  13. C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill, “Nonequilibrium phase transition in a dilute Rydberg ensemble,” Phys. Rev. Lett. 111(11), 113901 (2013).
    [PubMed]
  14. 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(21), 2499–2502 (1990).
    [PubMed]
  15. 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(3), 033806 (2009).
  16. 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(6), 061803 (2009).
  17. X. Yu and J. Zhang, “Multi-normal mode-splitting for an optical cavity with electromagnetically induced transparency medium,” Opt. Express 18(5), 4057–4065 (2010).
    [PubMed]
  18. Z. Zhang, H. Zheng, Y. Tian, H. Chen, S. Yang, and Y. Zhang, “Stable scanning of dressing fields on multiwave mixing in optical ring cavity,” IEEE J. Quantum Electron. 50(7), 575–580 (2014).
  19. 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(17), 173602 (2008).
    [PubMed]
  20. Z. Nie, H. Zheng, P. Li, Y. Yang, Y. Zhang, and M. Xiao, “Interacting multiwave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).
  21. H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333(6047), 1266–1269 (2011).
    [PubMed]
  22. J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).
  23. Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).
  24. H. Wang, D. Goorskey, and M. Xiao, “Dependence of enhanced Kerr nonlinearity on coupling power in a three-level atomic system,” Opt. Lett. 27(4), 258–260 (2002).
    [PubMed]

2016 (1)

Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M. A. Miri, D. N. Christodoulides, B. He, Y. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117(12), 123601 (2016).
[PubMed]

2014 (1)

Z. Zhang, H. Zheng, Y. Tian, H. Chen, S. Yang, and Y. Zhang, “Stable scanning of dressing fields on multiwave mixing in optical ring cavity,” IEEE J. Quantum Electron. 50(7), 575–580 (2014).

2013 (1)

C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill, “Nonequilibrium phase transition in a dilute Rydberg ensemble,” Phys. Rev. Lett. 111(11), 113901 (2013).
[PubMed]

2012 (1)

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

2011 (1)

H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333(6047), 1266–1269 (2011).
[PubMed]

2010 (1)

2009 (3)

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(3), 033806 (2009).

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(6), 061803 (2009).

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).

2008 (2)

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(17), 173602 (2008).
[PubMed]

Z. Nie, H. Zheng, P. Li, Y. Yang, Y. Zhang, and M. Xiao, “Interacting multiwave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).

2007 (2)

G. Hernandez, J. Zhang, and Y. Zhu, “Vacuum Rabi splitting and intracavity dark state in a cavity-atom system,” Phys. Rev. A 76(5), 053814 (2007).

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(21), 213601 (2007).
[PubMed]

2006 (1)

X. Lü, J. Li, J. Liu, and J. Luo, “Optical bistability via quantum interference in a four-level atomic medium,” J. Phys. At. Mol. Opt. Phys. 39(24), 5161–5171 (2006).

2004 (1)

A. Joshi and M. Xiao, “Optical bistability in a three-level semiconductor quantum-well system,” Appl. Phys. B 79(1), 65–69 (2004).

2003 (2)

A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67(4), 041801 (2003).

A. Brown, A. Joshi, and M. Xiao, “Controlled steady-state switching in optical bistability,” Appl. Phys. Lett. 83(7), 1301–1303 (2003).

2002 (1)

2001 (3)

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
[PubMed]

A. Joshi and M. Xiao, “Atomic optical bistability in two- and three-level systems: perspectives and prospects,” J. Mod. Opt. 57(14–15), 1196–1220 (2001).

H. Wang, D. J. Goorskey, and M. Xiao, “Bistability and instability of three-level atoms inside an optical cavity,” Phys. Rev. A 65(1), 011801 (2001).

1995 (1)

J. Gea-Banacloche, Yq. Li, Sz. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A 51(1), 576–584 (1995).
[PubMed]

1990 (1)

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(21), 2499–2502 (1990).
[PubMed]

1976 (1)

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36(19), 1135–1138 (1976).

Adams, C. S.

C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill, “Nonequilibrium phase transition in a dilute Rydberg ensemble,” Phys. Rev. Lett. 111(11), 113901 (2013).
[PubMed]

Brown, A.

A. Brown, A. Joshi, and M. Xiao, “Controlled steady-state switching in optical bistability,” Appl. Phys. Lett. 83(7), 1301–1303 (2003).

A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67(4), 041801 (2003).

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(21), 2499–2502 (1990).
[PubMed]

Carr, C.

C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill, “Nonequilibrium phase transition in a dilute Rydberg ensemble,” Phys. Rev. Lett. 111(11), 113901 (2013).
[PubMed]

Chen, H.

Z. Zhang, H. Zheng, Y. Tian, H. Chen, S. Yang, and Y. Zhang, “Stable scanning of dressing fields on multiwave mixing in optical ring cavity,” IEEE J. Quantum Electron. 50(7), 575–580 (2014).

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(6), 061803 (2009).

Chen, W.

H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333(6047), 1266–1269 (2011).
[PubMed]

Christodoulides, D. N.

Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M. A. Miri, D. N. Christodoulides, B. He, Y. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117(12), 123601 (2016).
[PubMed]

Feng, W.

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

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(21), 2499–2502 (1990).
[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(3), 033806 (2009).

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(17), 173602 (2008).
[PubMed]

J. Gea-Banacloche, Yq. Li, Sz. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A 51(1), 576–584 (1995).
[PubMed]

Gibbs, H. M.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36(19), 1135–1138 (1976).

Goorskey, D.

H. Wang, D. Goorskey, and M. Xiao, “Dependence of enhanced Kerr nonlinearity on coupling power in a three-level atomic system,” Opt. Lett. 27(4), 258–260 (2002).
[PubMed]

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
[PubMed]

Goorskey, D. J.

H. Wang, D. J. Goorskey, and M. Xiao, “Bistability and instability of three-level atoms inside an optical cavity,” Phys. Rev. A 65(1), 011801 (2001).

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(21), 213601 (2007).
[PubMed]

He, B.

Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M. A. Miri, D. N. Christodoulides, B. He, Y. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117(12), 123601 (2016).
[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(5), 053814 (2007).

Jin, Sz.

J. Gea-Banacloche, Yq. Li, Sz. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A 51(1), 576–584 (1995).
[PubMed]

Joshi, A.

A. Joshi and M. Xiao, “Optical bistability in a three-level semiconductor quantum-well system,” Appl. Phys. B 79(1), 65–69 (2004).

A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67(4), 041801 (2003).

A. Brown, A. Joshi, and M. Xiao, “Controlled steady-state switching in optical bistability,” Appl. Phys. Lett. 83(7), 1301–1303 (2003).

A. Joshi and M. Xiao, “Atomic optical bistability in two- and three-level systems: perspectives and prospects,” J. Mod. Opt. 57(14–15), 1196–1220 (2001).

Landig, R.

H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333(6047), 1266–1269 (2011).
[PubMed]

Li, C.

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).

Li, J.

X. Lü, J. Li, J. Liu, and J. Luo, “Optical bistability via quantum interference in a four-level atomic medium,” J. Phys. At. Mol. Opt. Phys. 39(24), 5161–5171 (2006).

Li, P.

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

Z. Nie, H. Zheng, P. Li, Y. Yang, Y. Zhang, and M. Xiao, “Interacting multiwave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).

Li, Yq.

J. Gea-Banacloche, Yq. Li, Sz. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A 51(1), 576–584 (1995).
[PubMed]

Liu, J.

X. Lü, J. Li, J. Liu, and J. Luo, “Optical bistability via quantum interference in a four-level atomic medium,” J. Phys. At. Mol. Opt. Phys. 39(24), 5161–5171 (2006).

Lü, X.

X. Lü, J. Li, J. Liu, and J. Luo, “Optical bistability via quantum interference in a four-level atomic medium,” J. Phys. At. Mol. Opt. Phys. 39(24), 5161–5171 (2006).

Luo, J.

X. Lü, J. Li, J. Liu, and J. Luo, “Optical bistability via quantum interference in a four-level atomic medium,” J. Phys. At. Mol. Opt. Phys. 39(24), 5161–5171 (2006).

McCall, S. L.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36(19), 1135–1138 (1976).

Miri, M. A.

Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M. A. Miri, D. N. Christodoulides, B. He, Y. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117(12), 123601 (2016).
[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(21), 213601 (2007).
[PubMed]

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(21), 2499–2502 (1990).
[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(21), 2499–2502 (1990).
[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(21), 213601 (2007).
[PubMed]

Nie, Z.

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).

Z. Nie, H. Zheng, P. Li, Y. Yang, Y. Zhang, and M. Xiao, “Interacting multiwave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).

Ritter, R.

C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill, “Nonequilibrium phase transition in a dilute Rydberg ensemble,” Phys. Rev. Lett. 111(11), 113901 (2013).
[PubMed]

Sheng, J.

Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M. A. Miri, D. N. Christodoulides, B. He, Y. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117(12), 123601 (2016).
[PubMed]

Simon, J.

H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333(6047), 1266–1269 (2011).
[PubMed]

Song, J.

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).

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(21), 213601 (2007).
[PubMed]

Tanji-Suzuki, H.

H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333(6047), 1266–1269 (2011).
[PubMed]

Tian, Y.

Z. Zhang, H. Zheng, Y. Tian, H. Chen, S. Yang, and Y. Zhang, “Stable scanning of dressing fields on multiwave mixing in optical ring cavity,” IEEE J. Quantum Electron. 50(7), 575–580 (2014).

Venkatesan, T. N. C.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36(19), 1135–1138 (1976).

Vuletic, V.

H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333(6047), 1266–1269 (2011).
[PubMed]

Wade, C. G.

C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill, “Nonequilibrium phase transition in a dilute Rydberg ensemble,” Phys. Rev. Lett. 111(11), 113901 (2013).
[PubMed]

Wang, H.

A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67(4), 041801 (2003).

H. Wang, D. Goorskey, and M. Xiao, “Dependence of enhanced Kerr nonlinearity on coupling power in a three-level atomic system,” Opt. Lett. 27(4), 258–260 (2002).
[PubMed]

H. Wang, D. J. Goorskey, and M. Xiao, “Bistability and instability of three-level atoms inside an optical cavity,” Phys. Rev. A 65(1), 011801 (2001).

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
[PubMed]

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(6), 061803 (2009).

Weatherill, K. J.

C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill, “Nonequilibrium phase transition in a dilute Rydberg ensemble,” Phys. Rev. Lett. 111(11), 113901 (2013).
[PubMed]

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(3), 033806 (2009).

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(17), 173602 (2008).
[PubMed]

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(21), 2499–2502 (1990).
[PubMed]

Xiao, M.

Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M. A. Miri, D. N. Christodoulides, B. He, Y. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117(12), 123601 (2016).
[PubMed]

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(3), 033806 (2009).

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(6), 061803 (2009).

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).

Z. Nie, H. Zheng, P. Li, Y. Yang, Y. Zhang, and M. Xiao, “Interacting multiwave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (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(17), 173602 (2008).
[PubMed]

A. Joshi and M. Xiao, “Optical bistability in a three-level semiconductor quantum-well system,” Appl. Phys. B 79(1), 65–69 (2004).

A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67(4), 041801 (2003).

A. Brown, A. Joshi, and M. Xiao, “Controlled steady-state switching in optical bistability,” Appl. Phys. Lett. 83(7), 1301–1303 (2003).

H. Wang, D. Goorskey, and M. Xiao, “Dependence of enhanced Kerr nonlinearity on coupling power in a three-level atomic system,” Opt. Lett. 27(4), 258–260 (2002).
[PubMed]

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
[PubMed]

A. Joshi and M. Xiao, “Atomic optical bistability in two- and three-level systems: perspectives and prospects,” J. Mod. Opt. 57(14–15), 1196–1220 (2001).

H. Wang, D. J. Goorskey, and M. Xiao, “Bistability and instability of three-level atoms inside an optical cavity,” Phys. Rev. A 65(1), 011801 (2001).

J. Gea-Banacloche, Yq. Li, Sz. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A 51(1), 576–584 (1995).
[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(6), 061803 (2009).

Yang, L.

Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M. A. Miri, D. N. Christodoulides, B. He, Y. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117(12), 123601 (2016).
[PubMed]

Yang, S.

Z. Zhang, H. Zheng, Y. Tian, H. Chen, S. Yang, and Y. Zhang, “Stable scanning of dressing fields on multiwave mixing in optical ring cavity,” IEEE J. Quantum Electron. 50(7), 575–580 (2014).

Yang, Y.

Z. Nie, H. Zheng, P. Li, Y. Yang, Y. Zhang, and M. Xiao, “Interacting multiwave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).

Yu, X.

X. Yu and J. Zhang, “Multi-normal mode-splitting for an optical cavity with electromagnetically induced transparency medium,” Opt. Express 18(5), 4057–4065 (2010).
[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(6), 061803 (2009).

Yuan, J.

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

Zhang, J.

X. Yu and J. Zhang, “Multi-normal mode-splitting for an optical cavity with electromagnetically induced transparency medium,” Opt. Express 18(5), 4057–4065 (2010).
[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(6), 061803 (2009).

G. Hernandez, J. Zhang, and Y. Zhu, “Vacuum Rabi splitting and intracavity dark state in a cavity-atom system,” Phys. Rev. A 76(5), 053814 (2007).

Zhang, X.

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

Zhang, Y.

Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M. A. Miri, D. N. Christodoulides, B. He, Y. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117(12), 123601 (2016).
[PubMed]

Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M. A. Miri, D. N. Christodoulides, B. He, Y. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117(12), 123601 (2016).
[PubMed]

Z. Zhang, H. Zheng, Y. Tian, H. Chen, S. Yang, and Y. Zhang, “Stable scanning of dressing fields on multiwave mixing in optical ring cavity,” IEEE J. Quantum Electron. 50(7), 575–580 (2014).

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).

Z. Nie, H. Zheng, P. Li, Y. Yang, Y. Zhang, and M. Xiao, “Interacting multiwave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).

Zhang, Z.

Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M. A. Miri, D. N. Christodoulides, B. He, Y. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117(12), 123601 (2016).
[PubMed]

Z. Zhang, H. Zheng, Y. Tian, H. Chen, S. Yang, and Y. Zhang, “Stable scanning of dressing fields on multiwave mixing in optical ring cavity,” IEEE J. Quantum Electron. 50(7), 575–580 (2014).

Zheng, H.

Z. Zhang, H. Zheng, Y. Tian, H. Chen, S. Yang, and Y. Zhang, “Stable scanning of dressing fields on multiwave mixing in optical ring cavity,” IEEE J. Quantum Electron. 50(7), 575–580 (2014).

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).

Z. Nie, H. Zheng, P. Li, Y. Yang, Y. Zhang, and M. Xiao, “Interacting multiwave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).

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(5), 053814 (2007).

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(21), 2499–2502 (1990).
[PubMed]

Appl. Phys. B (1)

A. Joshi and M. Xiao, “Optical bistability in a three-level semiconductor quantum-well system,” Appl. Phys. B 79(1), 65–69 (2004).

Appl. Phys. Lett. (1)

A. Brown, A. Joshi, and M. Xiao, “Controlled steady-state switching in optical bistability,” Appl. Phys. Lett. 83(7), 1301–1303 (2003).

IEEE J. Quantum Electron. (1)

Z. Zhang, H. Zheng, Y. Tian, H. Chen, S. Yang, and Y. Zhang, “Stable scanning of dressing fields on multiwave mixing in optical ring cavity,” IEEE J. Quantum Electron. 50(7), 575–580 (2014).

J. Mod. Opt. (1)

A. Joshi and M. Xiao, “Atomic optical bistability in two- and three-level systems: perspectives and prospects,” J. Mod. Opt. 57(14–15), 1196–1220 (2001).

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

X. Lü, J. Li, J. Liu, and J. Luo, “Optical bistability via quantum interference in a four-level atomic medium,” J. Phys. At. Mol. Opt. Phys. 39(24), 5161–5171 (2006).

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (9)

Z. Nie, H. Zheng, P. Li, Y. Yang, Y. Zhang, and M. Xiao, “Interacting multiwave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).

J. Yuan, W. Feng, P. Li, X. Zhang, Y. Zhang, H. Zheng, and Y. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).

A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67(4), 041801 (2003).

H. Wang, D. J. Goorskey, and M. Xiao, “Bistability and instability of three-level atoms inside an optical cavity,” Phys. Rev. A 65(1), 011801 (2001).

G. Hernandez, J. Zhang, and Y. Zhu, “Vacuum Rabi splitting and intracavity dark state in a cavity-atom system,” Phys. Rev. A 76(5), 053814 (2007).

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(3), 033806 (2009).

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(6), 061803 (2009).

J. Gea-Banacloche, Yq. Li, Sz. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A 51(1), 576–584 (1995).
[PubMed]

Phys. Rev. Lett. (7)

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36(19), 1135–1138 (1976).

C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill, “Nonequilibrium phase transition in a dilute Rydberg ensemble,” Phys. Rev. Lett. 111(11), 113901 (2013).
[PubMed]

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(21), 2499–2502 (1990).
[PubMed]

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(17), 173602 (2008).
[PubMed]

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(21), 213601 (2007).
[PubMed]

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
[PubMed]

Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M. A. Miri, D. N. Christodoulides, B. He, Y. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117(12), 123601 (2016).
[PubMed]

Science (1)

H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333(6047), 1266–1269 (2011).
[PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) Experimental setup. PBS: polarization beam splitter; L: lens; M1~M3: cavity mirrors; M4: high-reflectivity mirror; PZT: piezoelectric transducer. APD: avalanche photodiode detector; EOM: Electro-optic modulator. (b) Energy-level diagram for the three-level 85Rb atomic system. (c) The experimentally observed cavity modes (lower curve) by scanning the frequency detuning Δac of the cavity. The upper ramp curve with four periods (arm ramps) represents scanning triangular wave added on the PZT mounted on M1, which is used for controlling the length of the cavity.

Fig. 2
Fig. 2

(a1)-(a4) Evolutions of the cavity output of by scanning the power P1 of E1 at different power P2 of E2. (a5) The measured (squares) and simulated (solid curve) power difference δP1 between the thresholds of the left and right curves according to (a1)-(a4). (b1)-(b4) The cavity modes versus ∆ac at different P2. (b5) The measured (triangles) and simulated (solid curve) frequency difference δΔac between the pair of partially overlapped cavity modes at ∆ac<0. The shape of the two peaks at ∆ac<0 can be viewed as a “∞”.

Fig. 3
Fig. 3

(a1)-(a4) Observed cavity modes by scanning ∆ac at different P1. (a5) Dependence of the frequency difference δΔac on the probe-field power P1. (b1)-(b4) Observed cavity modes by scanning the probe detuning ∆1 at different P1. (b5) Dependence of the frequency difference δΔ1 on the probe-field power P1 at Δ1<0. For the two dependency curves, the squares and curve represent the observations and simulation, respectively.

Fig. 4
Fig. 4

(a1)-(a3) Evolution of the cavity output by scanning power P1 at different ∆ac. (a4) Dependency of the difference between the thresholds on ∆ac according to (a1)-(a3). (b1)-(b3) Signal evolutions by scanning detuning ∆1 at different ∆ac. (b4) Dependency of frequency difference between the left and right peaks on ∆ac according to (b1)-(b3). The squares and solid curves in (a4) and (b4) represent the experimental observations and simulation, respectively. (c) The signals in (b1)-(b3) are rearranged from top down.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

ρ 10 (1) =i G 1 / d 1 .
ρ 10 (1) =i G 1 /[ d 1 +| G 1 | 2 /( Γ 11 +| G 2 | 2 / d 2 )],
a ˙ =[ i( Δ 1 Δ ac )+γ ]a+ig N ρ 10 ,
ρ ˙ 00 = Γ 00 ρ 00 +i G T * ρ 10 +g N ρ 10 ,
ρ ˙ 10 =[ i Δ 1 + Γ 10 ] ρ 10 i G 1 ρ 11 +i G T ρ 00 +ig N a ρ 00 ,
ρ ˙ 11 = Γ 11 ρ 11 i G 1 * ρ 10 +i G 2 * ρ 21 ,
ρ ˙ 21 =( Γ 21 +i Δ 2 ) ρ 21 +i G 2 ρ 11 ,
a=g N G 1 /{ d c [ d 1 + g 2 N/ d c +| G 1 | 2 /( Γ 11 +| G 2 | 2 / d 2 )+ | G T | 2 / Γ 00 ]}.
I o I i | ig N [ d c ( d 1 + g 2 N/ d c +| G 1 | 2 /[( Γ 11 +| G 2 | 2 / d 2 ]+ | G T | 2 / Γ 00 ) ] 1 | 2 .
Δ n =N( n 2up I up n 2down I down )=Δσc/ ω p l.
χ (3) = N μ 10 4 ρ ˜ 10 (3) / ( 3 ε 0 G T G 1 2 ) ,
λ + λ = Δ ac 2 +4 | g N | 2