Abstract

Cavity-enhanced optical controlling is experimentally observed with a low-control laser power in a cavity-atom ensemble system. Here, the three-level atoms are coupled with two optical modes of a Fabry-Perot cavity, where a new theoretical model is developed to describe the effective three-wave mixing process between spin-wave and optical modes. By adjusting either temperature or cavity length, we demonstrate the precise frequency tuning of the hybrid optical-atomic resonances. When the doubly-resonant condition is satisfied, the probe laser can be easily modulated by a control laser. In addition, interesting non-Hermitian physics are predicted theoretically and demonstrated experimentally, and all-optical switching is also achieved. Such a doubly-resonant cavity-atom ensemble system without a specially designed cavity can be used for future applications, such as optical signal storage and microwave-to-optical frequency conversion.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

M.-A. Miri and A. Alù, “Exceptional points in optics and photonics,” Science 363, eaar7709 (2019).
[Crossref] [PubMed]

2018 (1)

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14, 11–19 (2018).
[Crossref]

2017 (3)

S. Dutta and S. A. Rangwala, “All-optical switching in a continuously operated and strongly coupled atom-cavity system,” Appl. Phys. Lett. 110, 121107 (2017).
[Crossref]

L. Wang, K. Di, Y. Zhu, and G. S. Agarwal, “Interference control of perfect photon absorption in cavity quantum electrodynamics,” Phys. Rev. A 95, 013841 (2017).
[Crossref]

L. Stern, B. Desiatov, N. Mazurski, and U. Levy, “Strong coupling and high-contrast all-optical modulation in atomic cladding waveguides,” Nat. Commun. 8, 14461 (2017).
[Crossref] [PubMed]

2016 (5)

R. Sawant and S. A. Rangwala, “Optical-bistability-enabled control of resonant light transmission for an atom-cavity system,” Phys. Rev. A 93, 023806 (2016).
[Crossref]

K. C. Balram, M. I. Davanço, J. D. Song, and K. Srinivasan, “Coherent coupling between radiofrequency, optical and acoustic waves in piezo-optomechanical circuits,” Nat. Photonics 10, 346–352 (2016).
[Crossref] [PubMed]

R. Ritter, N. Gruhler, W. H. P. Pernice, H. Kübler, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to an integrated ring resonator,” New J. Phys. 18, 103031 (2016).
[Crossref]

L. Stern, R. Zektzer, N. Mazurski, and U. Levy, “Enhanced light-vapor interactions and all optical switching in a chip scale micro-ring resonator coupled with atomic vapor,” Laser&Photon. Rev. 10, 1016–1022 (2016).

B. Hacker, S. Welte, G. Rempe, and S. Ritter, “A photon-photon quantum gate based on a single atom in an optical resonator,” Nature 536, 193–196 (2016).
[Crossref] [PubMed]

2015 (1)

L. Fan, K. Y. Fong, M. Poot, and H. X. Tang, “Cascaded optical transparency in multimode-cavity optomechanical systems,” Nat. Commun. 6, 5850 (2015).
[Crossref] [PubMed]

2014 (3)

J. Jing, Z. Zhou, C. Liu, Z. Qin, Y. Fang, J. Zhou, and W. Zhang, “Ultralow-light-level all-optical transistor in rubidium vapor,” Appl. Phys. Lett. 104, 151103 (2014).
[Crossref]

V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, and G. A. Steele, “Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity,” Nat. Nanotechnol. 9, 820–824 (2014).
[Crossref] [PubMed]

X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, “Strongly coupled magnons and cavity microwave photons,” Phys. Rev. Lett. 113, 156401 (2014).
[Crossref] [PubMed]

2013 (1)

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2013).
[Crossref]

2012 (1)

T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488, 57–60 (2012).
[Crossref] [PubMed]

2011 (3)

H. Tanji-Suzuki, I. D. Leroux, M. H. Schleier-Smith, M. Cetina, A. T. Grier, J. Simon, and V. Vuletić, “Interaction between atomic ensembles and optical resonators. classical description,” Adv. At. Mol. Opt. Phys. 60, 201–237 (2011).
[Crossref]

P. Zhang, Y. Guo, Z. Li, Y. Zhang, Y. Zhang, J. Du, G. Li, J. Wang, and T. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A 83, 031804 (2011).
[Crossref]

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

2010 (6)

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

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

K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
[Crossref]

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).
[Crossref]

C. Guerlin, E. Brion, T. Esslinger, and K. Mølmer, “Cavity quantum electrodynamics with a Rydberg-blocked atomic ensemble,” Phys. Rev. A 82, 053832 (2010).
[Crossref]

X. Yu, M. Xiao, and J. Zhang, “Triply-resonant optical parametric oscillator by four-wave mixing with rubidium vapor inside an optical cavity,” Appl. Phys. Lett. 96, 041101 (2010).
[Crossref]

2009 (4)

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, “Collective coupling of atoms with cavity mode and free-space field,” Opt. Express 17, 4798 (2009).
[Crossref] [PubMed]

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient All-Optical Switching Using Slow Light within a Hollow Fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

A. J. Olson and S. K. Mayer, “Electromagnetically induced transparency in rubidium,” Am. J. Phys. 77, 116–121 (2009).
[Crossref]

2008 (2)

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B 41, 155004 (2008).
[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]

2007 (1)

J. Simon, H. Tanji, J. K. Thompson, and V. Vuletić, “Interfacing collective atomic excitations and single photons,” Phys. Rev. Lett. 98, 183601 (2007).
[Crossref] [PubMed]

2006 (1)

C. Fang-Yen, C. C. Yu, S. Ha, W. Choi, K. An, R. R. Dasari, and M. S. Feld, “Observation of multiple thresholds in the many-atom cavity QED microlaser,” Phys. Rev. A 73, 041802 (2006).
[Crossref]

2005 (2)

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
[Crossref] [PubMed]

A. M. C. Dawes, “All-Optical Switching in Rubidium Vapor,” Science 308, 672–674 (2005).
[Crossref] [PubMed]

2003 (3)

A. Joshi and M. Xiao, “Optical multistability in three-level atoms inside an optical ring cavity,” Phys. Rev. Lett. 91, 143904 (2003).
[Crossref] [PubMed]

M. Lukin, “Colloquium: Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75, 457–472 (2003).
[Crossref]

Min Xiao, “Novel linear and nonlinear optical properties of electromagnetically induced transparency systems,” IEEE J. Sel. Top. Quantum Electron. 9, 86–92 (2003).
[Crossref]

2002 (1)

1992 (1)

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, 1132–1135 (1992).
[Crossref] [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, 2499–2502 (1990).
[Crossref] [PubMed]

1989 (1)

M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H. J. Carmichael, “Normal-mode splitting and linewidth averaging for two-state atoms in an optical cavity,” Phys. Rev. Lett. 63, 240–243 (1989).
[Crossref] [PubMed]

Adams, C. S.

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B 41, 155004 (2008).
[Crossref]

Agarwal, G. S.

L. Wang, K. Di, Y. Zhu, and G. S. Agarwal, “Interference control of perfect photon absorption in cavity quantum electrodynamics,” Phys. Rev. A 95, 013841 (2017).
[Crossref]

Alù, A.

M.-A. Miri and A. Alù, “Exceptional points in optics and photonics,” Science 363, eaar7709 (2019).
[Crossref] [PubMed]

An, K.

C. Fang-Yen, C. C. Yu, S. Ha, W. Choi, K. An, R. R. Dasari, and M. S. Feld, “Observation of multiple thresholds in the many-atom cavity QED microlaser,” Phys. Rev. A 73, 041802 (2006).
[Crossref]

Arcizet, O.

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

Bajcsy, M.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient All-Optical Switching Using Slow Light within a Hollow Fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Balic, V.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient All-Optical Switching Using Slow Light within a Hollow Fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Balram, K. C.

K. C. Balram, M. I. Davanço, J. D. Song, and K. Srinivasan, “Coherent coupling between radiofrequency, optical and acoustic waves in piezo-optomechanical circuits,” Nat. Photonics 10, 346–352 (2016).
[Crossref] [PubMed]

Birnbaum, K. M.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
[Crossref] [PubMed]

Blanter, Y. M.

V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, and G. A. Steele, “Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity,” Nat. Nanotechnol. 9, 820–824 (2014).
[Crossref] [PubMed]

Boca, A.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
[Crossref] [PubMed]

Boozer, A. D.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
[Crossref] [PubMed]

Bosman, S. J.

V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, and G. A. Steele, “Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity,” Nat. Nanotechnol. 9, 820–824 (2014).
[Crossref] [PubMed]

Brecha, R. J.

M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H. J. Carmichael, “Normal-mode splitting and linewidth averaging for two-state atoms in an optical cavity,” Phys. Rev. Lett. 63, 240–243 (1989).
[Crossref] [PubMed]

Brion, E.

C. Guerlin, E. Brion, T. Esslinger, and K. Mølmer, “Cavity quantum electrodynamics with a Rydberg-blocked atomic ensemble,” Phys. Rev. A 82, 053832 (2010).
[Crossref]

Buchler, B. C.

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

Campbell, G.

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[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, 2499–2502 (1990).
[Crossref] [PubMed]

M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H. J. Carmichael, “Normal-mode splitting and linewidth averaging for two-state atoms in an optical cavity,” Phys. Rev. Lett. 63, 240–243 (1989).
[Crossref] [PubMed]

Castellanos-Gomez, A.

V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, and G. A. Steele, “Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity,” Nat. Nanotechnol. 9, 820–824 (2014).
[Crossref] [PubMed]

Cetina, M.

H. Tanji-Suzuki, I. D. Leroux, M. H. Schleier-Smith, M. Cetina, A. T. Grier, J. Simon, and V. Vuletić, “Interaction between atomic ensembles and optical resonators. classical description,” Adv. At. Mol. Opt. Phys. 60, 201–237 (2011).
[Crossref]

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]

Chen, J. F.

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L. Stern, B. Desiatov, N. Mazurski, and U. Levy, “Strong coupling and high-contrast all-optical modulation in atomic cladding waveguides,” Nat. Commun. 8, 14461 (2017).
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K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
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K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
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R. Wen, C.-L. Zou, X. Zhu, P. Chen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Non-Hermitian magnon-photon interference in an atomic ensemble,” arXiv p. 1811.00307 (2018).

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R. Ritter, N. Gruhler, W. H. P. Pernice, H. Kübler, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to an integrated ring resonator,” New J. Phys. 18, 103031 (2016).
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T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488, 57–60 (2012).
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M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient All-Optical Switching Using Slow Light within a Hollow Fiber,” Phys. Rev. Lett. 102, 203902 (2009).
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R. Ritter, N. Gruhler, W. H. P. Pernice, H. Kübler, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to an integrated ring resonator,” New J. Phys. 18, 103031 (2016).
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T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488, 57–60 (2012).
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K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
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L. Fan, K. Y. Fong, M. Poot, and H. X. Tang, “Cascaded optical transparency in multimode-cavity optomechanical systems,” Nat. Commun. 6, 5850 (2015).
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J. Jing, Z. Zhou, C. Liu, Z. Qin, Y. Fang, J. Zhou, and W. Zhang, “Ultralow-light-level all-optical transistor in rubidium vapor,” Appl. Phys. Lett. 104, 151103 (2014).
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M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H. J. Carmichael, “Normal-mode splitting and linewidth averaging for two-state atoms in an optical cavity,” Phys. Rev. Lett. 63, 240–243 (1989).
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B. Hacker, S. Welte, G. Rempe, and S. Ritter, “A photon-photon quantum gate based on a single atom in an optical resonator,” Nature 536, 193–196 (2016).
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R. Ritter, N. Gruhler, W. H. P. Pernice, H. Kübler, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to an integrated ring resonator,” New J. Phys. 18, 103031 (2016).
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B. Hacker, S. Welte, G. Rempe, and S. Ritter, “A photon-photon quantum gate based on a single atom in an optical resonator,” Nature 536, 193–196 (2016).
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S. Weis, R. Riviere, S. Deleglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
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R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14, 11–19 (2018).
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V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2013).
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R. Sawant and S. A. Rangwala, “Optical-bistability-enabled control of resonant light transmission for an atom-cavity system,” Phys. Rev. A 93, 023806 (2016).
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S. Weis, R. Riviere, S. Deleglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
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B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).
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V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, and G. A. Steele, “Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity,” Nat. Nanotechnol. 9, 820–824 (2014).
[Crossref] [PubMed]

Song, J. D.

K. C. Balram, M. I. Davanço, J. D. Song, and K. Srinivasan, “Coherent coupling between radiofrequency, optical and acoustic waves in piezo-optomechanical circuits,” Nat. Photonics 10, 346–352 (2016).
[Crossref] [PubMed]

Sørensen, A. S.

K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
[Crossref]

Sparkes, B. M.

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

Srinivasan, K.

K. C. Balram, M. I. Davanço, J. D. Song, and K. Srinivasan, “Coherent coupling between radiofrequency, optical and acoustic waves in piezo-optomechanical circuits,” Nat. Photonics 10, 346–352 (2016).
[Crossref] [PubMed]

Steele, G. A.

V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, and G. A. Steele, “Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity,” Nat. Nanotechnol. 9, 820–824 (2014).
[Crossref] [PubMed]

Stern, L.

L. Stern, B. Desiatov, N. Mazurski, and U. Levy, “Strong coupling and high-contrast all-optical modulation in atomic cladding waveguides,” Nat. Commun. 8, 14461 (2017).
[Crossref] [PubMed]

L. Stern, R. Zektzer, N. Mazurski, and U. Levy, “Enhanced light-vapor interactions and all optical switching in a chip scale micro-ring resonator coupled with atomic vapor,” Laser&Photon. Rev. 10, 1016–1022 (2016).

Tang, H. X.

L. Fan, K. Y. Fong, M. Poot, and H. X. Tang, “Cascaded optical transparency in multimode-cavity optomechanical systems,” Nat. Commun. 6, 5850 (2015).
[Crossref] [PubMed]

X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, “Strongly coupled magnons and cavity microwave photons,” Phys. Rev. Lett. 113, 156401 (2014).
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Tanji, H.

J. Simon, H. Tanji, J. K. Thompson, and V. Vuletić, “Interfacing collective atomic excitations and single photons,” Phys. Rev. Lett. 98, 183601 (2007).
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Tanji-Suzuki, H.

H. Tanji-Suzuki, I. D. Leroux, M. H. Schleier-Smith, M. Cetina, A. T. Grier, J. Simon, and V. Vuletić, “Interaction between atomic ensembles and optical resonators. classical description,” Adv. At. Mol. Opt. Phys. 60, 201–237 (2011).
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Thompson, J. K.

J. Simon, H. Tanji, J. K. Thompson, and V. Vuletić, “Interfacing collective atomic excitations and single photons,” Phys. Rev. Lett. 98, 183601 (2007).
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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, 1132–1135 (1992).
[Crossref] [PubMed]

M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H. J. Carmichael, “Normal-mode splitting and linewidth averaging for two-state atoms in an optical cavity,” Phys. Rev. Lett. 63, 240–243 (1989).
[Crossref] [PubMed]

Venkataraman, V.

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2013).
[Crossref]

Vuletic, V.

T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488, 57–60 (2012).
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H. Tanji-Suzuki, I. D. Leroux, M. H. Schleier-Smith, M. Cetina, A. T. Grier, J. Simon, and V. Vuletić, “Interaction between atomic ensembles and optical resonators. classical description,” Adv. At. Mol. Opt. Phys. 60, 201–237 (2011).
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M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient All-Optical Switching Using Slow Light within a Hollow Fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

J. Simon, H. Tanji, J. K. Thompson, and V. Vuletić, “Interfacing collective atomic excitations and single photons,” Phys. Rev. Lett. 98, 183601 (2007).
[Crossref] [PubMed]

Wang, H.

Wang, J.

P. Zhang, Y. Guo, Z. Li, Y. Zhang, Y. Zhang, J. Du, G. Li, J. Wang, and T. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A 83, 031804 (2011).
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Wang, L.

L. Wang, K. Di, Y. Zhu, and G. S. Agarwal, “Interference control of perfect photon absorption in cavity quantum electrodynamics,” Phys. Rev. A 95, 013841 (2017).
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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).
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Wei, X.

X. Wei, J. Zhang, and Y. Zhu, “All-optical switching in a coupled cavity-atom system,” Phys. Rev. A 82, 033808 (2010).
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S. Weis, R. Riviere, S. Deleglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
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Welte, S.

B. Hacker, S. Welte, G. Rempe, and S. Ritter, “A photon-photon quantum gate based on a single atom in an optical resonator,” Nature 536, 193–196 (2016).
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Wen, R.

R. Wen, C.-L. Zou, X. Zhu, P. Chen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Non-Hermitian magnon-photon interference in an atomic ensemble,” arXiv p. 1811.00307 (2018).

Wu, B.

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).
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Wu, H.

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]

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, 2499–2502 (1990).
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Xiao, M.

X. Yu, M. Xiao, and J. Zhang, “Triply-resonant optical parametric oscillator by four-wave mixing with rubidium vapor inside an optical cavity,” Appl. Phys. Lett. 96, 041101 (2010).
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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).
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A. Joshi and M. Xiao, “Optical multistability in three-level atoms inside an optical ring cavity,” Phys. Rev. Lett. 91, 143904 (2003).
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H. Wang, D. Goorskey, and M. Xiao, “Controlling light by light with three-level atoms inside an optical cavity,” Opt. Lett. 27, 1354 (2002).
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Xiao, Min

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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).
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Yu, C. C.

C. Fang-Yen, C. C. Yu, S. Ha, W. Choi, K. An, R. R. Dasari, and M. S. Feld, “Observation of multiple thresholds in the many-atom cavity QED microlaser,” Phys. Rev. A 73, 041802 (2006).
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Yu, X.

X. Yu, M. Xiao, and J. Zhang, “Triply-resonant optical parametric oscillator by four-wave mixing with rubidium vapor inside an optical cavity,” Appl. Phys. Lett. 96, 041101 (2010).
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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]

Zektzer, R.

L. Stern, R. Zektzer, N. Mazurski, and U. Levy, “Enhanced light-vapor interactions and all optical switching in a chip scale micro-ring resonator coupled with atomic vapor,” Laser&Photon. Rev. 10, 1016–1022 (2016).

Zhang, J.

X. Yu, M. Xiao, and J. Zhang, “Triply-resonant optical parametric oscillator by four-wave mixing with rubidium vapor inside an optical cavity,” Appl. Phys. Lett. 96, 041101 (2010).
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X. Wei, J. Zhang, and Y. Zhu, “All-optical switching in a coupled cavity-atom system,” Phys. Rev. A 82, 033808 (2010).
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G. Hernandez, J. Zhang, and Y. Zhu, “Collective coupling of atoms with cavity mode and free-space field,” Opt. Express 17, 4798 (2009).
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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, P.

P. Zhang, Y. Guo, Z. Li, Y. Zhang, Y. Zhang, J. Du, G. Li, J. Wang, and T. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A 83, 031804 (2011).
[Crossref]

Zhang, T.

P. Zhang, Y. Guo, Z. Li, Y. Zhang, Y. Zhang, J. Du, G. Li, J. Wang, and T. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A 83, 031804 (2011).
[Crossref]

Zhang, W.

J. Jing, Z. Zhou, C. Liu, Z. Qin, Y. Fang, J. Zhou, and W. Zhang, “Ultralow-light-level all-optical transistor in rubidium vapor,” Appl. Phys. Lett. 104, 151103 (2014).
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R. Wen, C.-L. Zou, X. Zhu, P. Chen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Non-Hermitian magnon-photon interference in an atomic ensemble,” arXiv p. 1811.00307 (2018).

Zhang, X.

X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, “Strongly coupled magnons and cavity microwave photons,” Phys. Rev. Lett. 113, 156401 (2014).
[Crossref] [PubMed]

Zhang, Y.

P. Zhang, Y. Guo, Z. Li, Y. Zhang, Y. Zhang, J. Du, G. Li, J. Wang, and T. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A 83, 031804 (2011).
[Crossref]

P. Zhang, Y. Guo, Z. Li, Y. Zhang, Y. Zhang, J. Du, G. Li, J. Wang, and T. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A 83, 031804 (2011).
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Zhou, J.

J. Jing, Z. Zhou, C. Liu, Z. Qin, Y. Fang, J. Zhou, and W. Zhang, “Ultralow-light-level all-optical transistor in rubidium vapor,” Appl. Phys. Lett. 104, 151103 (2014).
[Crossref]

Zhou, Z.

J. Jing, Z. Zhou, C. Liu, Z. Qin, Y. Fang, J. Zhou, and W. Zhang, “Ultralow-light-level all-optical transistor in rubidium vapor,” Appl. Phys. Lett. 104, 151103 (2014).
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Zhu, X.

R. Wen, C.-L. Zou, X. Zhu, P. Chen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Non-Hermitian magnon-photon interference in an atomic ensemble,” arXiv p. 1811.00307 (2018).

Zhu, Y.

L. Wang, K. Di, Y. Zhu, and G. S. Agarwal, “Interference control of perfect photon absorption in cavity quantum electrodynamics,” Phys. Rev. A 95, 013841 (2017).
[Crossref]

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

G. Hernandez, J. Zhang, and Y. Zhu, “Collective coupling of atoms with cavity mode and free-space field,” Opt. Express 17, 4798 (2009).
[Crossref] [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, 2499–2502 (1990).
[Crossref] [PubMed]

Zibrov, A. S.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient All-Optical Switching Using Slow Light within a Hollow Fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Zou, C.-L.

X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, “Strongly coupled magnons and cavity microwave photons,” Phys. Rev. Lett. 113, 156401 (2014).
[Crossref] [PubMed]

R. Wen, C.-L. Zou, X. Zhu, P. Chen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Non-Hermitian magnon-photon interference in an atomic ensemble,” arXiv p. 1811.00307 (2018).

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

H. Tanji-Suzuki, I. D. Leroux, M. H. Schleier-Smith, M. Cetina, A. T. Grier, J. Simon, and V. Vuletić, “Interaction between atomic ensembles and optical resonators. classical description,” Adv. At. Mol. Opt. Phys. 60, 201–237 (2011).
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Am. J. Phys. (1)

A. J. Olson and S. K. Mayer, “Electromagnetically induced transparency in rubidium,” Am. J. Phys. 77, 116–121 (2009).
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Appl. Phys. Lett. (3)

J. Jing, Z. Zhou, C. Liu, Z. Qin, Y. Fang, J. Zhou, and W. Zhang, “Ultralow-light-level all-optical transistor in rubidium vapor,” Appl. Phys. Lett. 104, 151103 (2014).
[Crossref]

X. Yu, M. Xiao, and J. Zhang, “Triply-resonant optical parametric oscillator by four-wave mixing with rubidium vapor inside an optical cavity,” Appl. Phys. Lett. 96, 041101 (2010).
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S. Dutta and S. A. Rangwala, “All-optical switching in a continuously operated and strongly coupled atom-cavity system,” Appl. Phys. Lett. 110, 121107 (2017).
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IEEE J. Sel. Top. Quantum Electron. (1)

Min Xiao, “Novel linear and nonlinear optical properties of electromagnetically induced transparency systems,” IEEE J. Sel. Top. Quantum Electron. 9, 86–92 (2003).
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J. Phys. B (1)

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B 41, 155004 (2008).
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Laser&Photon. Rev. (1)

L. Stern, R. Zektzer, N. Mazurski, and U. Levy, “Enhanced light-vapor interactions and all optical switching in a chip scale micro-ring resonator coupled with atomic vapor,” Laser&Photon. Rev. 10, 1016–1022 (2016).

Nat. Commun. (3)

L. Stern, B. Desiatov, N. Mazurski, and U. Levy, “Strong coupling and high-contrast all-optical modulation in atomic cladding waveguides,” Nat. Commun. 8, 14461 (2017).
[Crossref] [PubMed]

L. Fan, K. Y. Fong, M. Poot, and H. X. Tang, “Cascaded optical transparency in multimode-cavity optomechanical systems,” Nat. Commun. 6, 5850 (2015).
[Crossref] [PubMed]

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, and G. A. Steele, “Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity,” Nat. Nanotechnol. 9, 820–824 (2014).
[Crossref] [PubMed]

Nat. Photonics (3)

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).
[Crossref]

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2013).
[Crossref]

K. C. Balram, M. I. Davanço, J. D. Song, and K. Srinivasan, “Coherent coupling between radiofrequency, optical and acoustic waves in piezo-optomechanical circuits,” Nat. Photonics 10, 346–352 (2016).
[Crossref] [PubMed]

Nat. Phys. (1)

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14, 11–19 (2018).
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Nature (3)

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
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T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488, 57–60 (2012).
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B. Hacker, S. Welte, G. Rempe, and S. Ritter, “A photon-photon quantum gate based on a single atom in an optical resonator,” Nature 536, 193–196 (2016).
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New J. Phys. (1)

R. Ritter, N. Gruhler, W. H. P. Pernice, H. Kübler, T. Pfau, and R. Löw, “Coupling thermal atomic vapor to an integrated ring resonator,” New J. Phys. 18, 103031 (2016).
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Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (7)

R. Sawant and S. A. Rangwala, “Optical-bistability-enabled control of resonant light transmission for an atom-cavity system,” Phys. Rev. A 93, 023806 (2016).
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C. Fang-Yen, C. C. Yu, S. Ha, W. Choi, K. An, R. R. Dasari, and M. S. Feld, “Observation of multiple thresholds in the many-atom cavity QED microlaser,” Phys. Rev. A 73, 041802 (2006).
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C. Guerlin, E. Brion, T. Esslinger, and K. Mølmer, “Cavity quantum electrodynamics with a Rydberg-blocked atomic ensemble,” Phys. Rev. A 82, 053832 (2010).
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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]

L. Wang, K. Di, Y. Zhu, and G. S. Agarwal, “Interference control of perfect photon absorption in cavity quantum electrodynamics,” Phys. Rev. A 95, 013841 (2017).
[Crossref]

P. Zhang, Y. Guo, Z. Li, Y. Zhang, Y. Zhang, J. Du, G. Li, J. Wang, and T. Zhang, “Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM10 cavity mode,” Phys. Rev. A 83, 031804 (2011).
[Crossref]

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

Phys. Rev. Lett. (8)

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, 1132–1135 (1992).
[Crossref] [PubMed]

M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H. J. Carmichael, “Normal-mode splitting and linewidth averaging for two-state atoms in an optical cavity,” Phys. Rev. Lett. 63, 240–243 (1989).
[Crossref] [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, 2499–2502 (1990).
[Crossref] [PubMed]

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient All-Optical Switching Using Slow Light within a Hollow Fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

J. Simon, H. Tanji, J. K. Thompson, and V. Vuletić, “Interfacing collective atomic excitations and single photons,” Phys. Rev. Lett. 98, 183601 (2007).
[Crossref] [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, 173602 (2008).
[Crossref] [PubMed]

X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, “Strongly coupled magnons and cavity microwave photons,” Phys. Rev. Lett. 113, 156401 (2014).
[Crossref] [PubMed]

A. Joshi and M. Xiao, “Optical multistability in three-level atoms inside an optical ring cavity,” Phys. Rev. Lett. 91, 143904 (2003).
[Crossref] [PubMed]

Rev. Mod. Phys. (2)

M. Lukin, “Colloquium: Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75, 457–472 (2003).
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K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
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Science (3)

A. M. C. Dawes, “All-Optical Switching in Rubidium Vapor,” Science 308, 672–674 (2005).
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S. Weis, R. Riviere, S. Deleglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
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M.-A. Miri and A. Alù, “Exceptional points in optics and photonics,” Science 363, eaar7709 (2019).
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Other (1)

R. Wen, C.-L. Zou, X. Zhu, P. Chen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Non-Hermitian magnon-photon interference in an atomic ensemble,” arXiv p. 1811.00307 (2018).

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic illustration of the experimental system, consisting of an ensemble of   87 Rb with Λ-type that couples with two optical modes in a Fabry-Perot cavity. (b) The effective three-wave mixing model. Here, the atom ensemble is regarded as χ ( 2 ) medium, which leads to the interaction between probe and control lasers. (c) The energy diagram of the   87 Rb  D 2 line.
Fig. 2
Fig. 2 (a) is the dependence of δ a eff on the δa for given temperatures and (c) is the dependence on the temperature for a given δ a / 2 π = 250 MHz. δa is the detuning of probe laser. (b) and (d) are the real and imaginary parts of G. The non-negligible imaginary part in (d) indicates the non-Hermitian interaction between the three modes.
Fig. 3
Fig. 3 The experimental setup. Two external cavity diode lasers provide the probe and control lasers, which can be locked by saturated absorption spectrum (SAS) and coupled into polarization-maintaining (PM) fibers. The FP cavity with the length of 18 cm composes of two concave mirrors with the same curvature radius of 100 mm and reflectivity of 97% at 780 nm. The cavity length is stabilized by the piezoelectric transducer and PID feedback loop. A glass vapor cell filled with pure   87 Rb is placed inside the cavity and covered with a soft heater which is not shown in the figure. The inset figure is the energy diagram for the system with the effective three-wave coupling, where the control laser ( ω c ) causes the change of the excitations of both cavity and spin-wave modes, and the probe laser (ωp) probes cavity transmittance.
Fig. 4
Fig. 4 (a) The saturated absorption spectrum (SAS) of   87 Rb  D 2 line (red solid line) and the transmission spectrum of the cavity while the probe laser scanning across the   87 Rb  D 2 lines (black line). (b) The transmission of the cavity for different temperature ( 22 C , 35 C, 43 C and 48 C, respectively) with the control cavity lasers are locked to the transition 5 S 1 / 2 , F = 1 5 P 3 / 2 , F   ' = 1, as shown in (a) with a yellow arrow B. The probe laser scan across the transition 5 S 1 / 2 , F = 2 5 P 3 / 2 , F   ' = 1 at around 240 MHz. (c) The transmission of the cavity for different cavity length in a fixed temperature 40 C, with the assistance of nonlinear dispersion by the cavity-atom ensemble hybridization. For an appropriate cavity length, there are two modes with a frequency difference matching 6.835 GHz and satisfying the doubly-resonant condition. The cavity modes is locked around the transition 5 S 1 / 2 , F = 1 5 P 3 / 2 , F   ' = 1 with the detuning at 100 MHz, as shown in (a) with a blue arrow (C). The peak shape observed in the blue shade at (b) and (c) is the modulation induced by three-wave coupling between cavity modes and atom ensemble.
Fig. 5
Fig. 5 The transmissions of the probe laser with different control laser powers for the second approach. (a) Enlarged spectrum under doubly-resonant condition. The spectra are obviously deviated from the Lorentzian lineshape (grey solid line), while they can be perfectly fitted by Eq. (9) (black solid line). (b) The real (black) and imaginary (red) part of the fitted parameter n c G 2 / P c against the control power, which effectively changes the intrinsic loss and frequency of hybrid optical mode. (c) The fitted effective incoherent transition of spin-wave mode κm (blue line) and cavity mode κa (green line) against the control power.
Fig. 6
Fig. 6 All-optical switching based on the doubly-resonant cavity EIT. (a) (b) The temporal response of cavity signal transmission for a square-wave control power modulation, with the modulation rate of 1 kHz and 10 kHz, respectively. (c) The contrast of the signal transmittance for different switching rate. Here, the control laser power is fixed at 1.4 mW.

Equations (15)

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H 0 = ω a a a + ω c c c + j [ ( ω 3 + k v j ) σ 33 , j + ω 2 σ 22 , j ] + j [ g a , j a σ 32 , j + g c , j c σ 31 , j + h . c . ] .
j Im [ g a , j 2 σ 22 , j i ( ω 3 , j ω 2 ) γ 23 + i ω a eff ] = ω a ω a eff ,
j Im [ g c , j 2 σ 11 , j i ω 3 , j γ 13 + i ω c eff ] = ω c ω c eff .
F ( ξ ) = d v z P M B ( v z ) i k v z + ξ = 1 k π 2 σ v e ξ 2 2 k 2 σ v ( 1 erf ( ξ 2 σ v k ) ) ,
δ a eff δ a + σ 22 G a Im [ F ( i δ a eff γ 23 ) ] = 0 ,
δ c eff δ c + σ 11 G c Im [ F ( i δ c eff γ 13 ) ] = 0 ,
m = ρ g a ( x ) g c ( x ) σ 12 ( x ) d 3 x g a 2 ( x ) g c 2 ( x ) d 3 x ,
H eff = ω a eff a a + ω c eff c c + ω 2 m m + G ( a c m + a c m ) ,
G = ρ g a 2 ( x ) g c 2 ( x ) d 3 x × F ( i δ a eff γ 23 ) .
H = ( δ a eff δ p ) a a + ( δ c δ l ) c c + ( ω 2 + δ p δ l ) m m + G ( a c m + a c m ) + i ( 2 κ a , 1 a i n a + 2 κ c , 1 c i n c h . c . ) ,
d a d t = [ κ a + i ( δ a eff δ p ) ] a i G n c m + 2 κ a , 1 a i n ,
d m d t = [ κ m i ( ω 2 + δ p δ l ) ] m + i G n c a ,
a = 2 κ a , 1 a i n i ( δ a eff δ p ) + κ a + n c G 2 i ( ω 2 + δ p δ l ) + κ m .
T = | a o u t a i n | 2 = | 2 κ a , 1 κ a , 2 i ( δ a eff δ p ) + κ a + n c G 2 i ( ω 2 + δ p δ l ) + κ m | 2 .
η = | 1 1 + C | 2 = | 1 1 + n c G 2 κ m κ a | 2 .

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