Abstract

We investigate the nonreciprocity “∞”-shape optical bistability (OB) induced by the feedback dressing effect of six-wave mixing parametrically amplified process in a four-level atomic system. Compared to the traditional OB by scanning power, the “∞”-shape OB is scanning probe frequency and demonstrated by “∞”-shape non-overlapping region. More, this non-overlapping region in the x direction (frequency difference) and in the y direction (intensity difference) could demonstrate the degree of this OB phenomenon of dressed probe and conjugate signals, which can be changed by the intensity of feedback dressing. Further, we find the feedback intensity can be controlled by experimental parameters include powers of external-dressing, frequency detuning, incident phase and the nonlinear phase shift of internal-dressing beam. As a result, the nonreciprocity “∞”-shape OB is more sensitive and multiple than traditional OB. These outcomes have potential applications in logic-gate devices and quantum information processing.

© 2017 Optical Society of America

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References

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  1. M. D. Lukin, A. B. Matsko, M. Fleischhauer, and M. O. Scully, “Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence,” Phys. Rev. Lett. 82(9), 1847–1850 (1999).
    [Crossref]
  2. L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maitre, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100(1), 013604 (2008).
    [Crossref] [PubMed]
  3. L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
    [Crossref] [PubMed]
  4. R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55(22), 2409–2412 (1985).
    [Crossref] [PubMed]
  5. H. Chen, Y. Zhang, X. Yao, Z. Wu, X. Zhang, Y. Zhang, and M. Xiao, “Parametrically amplified bright-state polariton of four- and six-wave mixing in an optical ring cavity,” Sci. Rep. 4(1), 3619 (2014).
    [Crossref] [PubMed]
  6. H. Zheng, X. Zhang, Z. Zhang, Y. Tian, H. Chen, C. Li, and Y. Zhang, “Parametric amplification and cascaded-nonlinearity processes in common atomic system,” Sci. Rep. 3(1), 1885 (2013).
    [Crossref] [PubMed]
  7. C. F. Mccormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
    [Crossref]
  8. J. B. Clark, Z. Zhou, Q. Glorieux, A. M. Marino, and P. D. Letter, “Imaging using quantum noise properties of light,” Opt. Express 20(15), 17050 (2012).
    [Crossref]
  9. M. W. Holtfrerich, M. Dowran, R. Davidson, B. J. Lawrie, R. C. Pooser, and A. M. Mareno, “Toward quantum plasmonic networks,” Optica 3(9), 985 (2016).
    [Crossref]
  10. C. Liu, J. Jing, Z. Zhou, R. C. Pooser, F. Hudelist, L. Zhou, and W. Zhang, “Realization of low frequency and controllable bandwidth squeezing based on a four-wave-mixing amplifier in rubidium vapor,” Opt. Lett. 36(15), 2979–2981 (2011).
    [Crossref] [PubMed]
  11. Y. M. Fang and J. T. Jing, “Quantum squeezing and entanglement from a two-mode phase-sensitive amplifier via four-wave mixing in rubidium vapor,” New J. Phys. 17(2), 023027 (2015).
    [Crossref]
  12. R. C. Pooser and B. Lawrie, “Ultrasensitive measurement of microcantilever displacement below the shot-noise limit,” Optica 2(5), 393 (2015).
    [Crossref]
  13. R. C. Pooser and B. Lawrie, “Plasmonic trace sensing below the photon shot noise limit,” ACS Photonics 3(1), 8–13 (2016).
    [Crossref]
  14. A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch, “Radiation trapping in coherent media,” Phys. Rev. Lett. 87(13), 133601 (2001).
    [Crossref] [PubMed]
  15. G. Ankerhold, M. Schiffer, D. Mutschall, T. Scholz, and W. Lange, “Nonlinear effects of radiation trapping in ground-state oriented sodium vapor,” Phys. Rev. A 48(6), 4031–4034 (1993).
    [Crossref] [PubMed]
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    [Crossref]
  17. A. Yariv and D. M. Pepper, “Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing,” Opt. Lett. 1(1), 16 (1977).
    [Crossref] [PubMed]
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    [Crossref]
  19. 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).
    [Crossref]
  20. 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).
    [Crossref]
  21. J. M. Yuan, W. K. Feng, P. Y. Li, X. Zhang, Y. Q. Zhang, H. B. Zheng, and Y. P. Zhang, “Controllable vacuum Rabi splitting and optical bistability of multi-wave-mixing signal inside a ring cavity,” Phys. Rev. A 86(6), 063820 (2012).
    [Crossref]
  22. D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64(15), 1721–1724 (1990).
    [Crossref] [PubMed]
  23. M. Soljacić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
    [Crossref] [PubMed]
  24. Z. Zhang, D. Ma, J. Liu, Y. Sun, L. Cheng, G. A. Khan, and Y. Zhang, “Comparison between optical bistabilities versus power and frequency in a composite cavity-atom system,” Opt. Express 25(8), 8916–8925 (2017).
    [Crossref] [PubMed]

2017 (1)

2016 (2)

M. W. Holtfrerich, M. Dowran, R. Davidson, B. J. Lawrie, R. C. Pooser, and A. M. Mareno, “Toward quantum plasmonic networks,” Optica 3(9), 985 (2016).
[Crossref]

R. C. Pooser and B. Lawrie, “Plasmonic trace sensing below the photon shot noise limit,” ACS Photonics 3(1), 8–13 (2016).
[Crossref]

2015 (2)

Y. M. Fang and J. T. Jing, “Quantum squeezing and entanglement from a two-mode phase-sensitive amplifier via four-wave mixing in rubidium vapor,” New J. Phys. 17(2), 023027 (2015).
[Crossref]

R. C. Pooser and B. Lawrie, “Ultrasensitive measurement of microcantilever displacement below the shot-noise limit,” Optica 2(5), 393 (2015).
[Crossref]

2014 (1)

H. Chen, Y. Zhang, X. Yao, Z. Wu, X. Zhang, Y. Zhang, and M. Xiao, “Parametrically amplified bright-state polariton of four- and six-wave mixing in an optical ring cavity,” Sci. Rep. 4(1), 3619 (2014).
[Crossref] [PubMed]

2013 (1)

H. Zheng, X. Zhang, Z. Zhang, Y. Tian, H. Chen, C. Li, and Y. Zhang, “Parametric amplification and cascaded-nonlinearity processes in common atomic system,” Sci. Rep. 3(1), 1885 (2013).
[Crossref] [PubMed]

2012 (2)

J. B. Clark, Z. Zhou, Q. Glorieux, A. M. Marino, and P. D. Letter, “Imaging using quantum noise properties of light,” Opt. Express 20(15), 17050 (2012).
[Crossref]

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

2011 (1)

2008 (2)

C. F. Mccormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maitre, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100(1), 013604 (2008).
[Crossref] [PubMed]

2003 (1)

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).
[Crossref]

2002 (1)

M. Soljacić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
[Crossref] [PubMed]

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).
[Crossref]

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch, “Radiation trapping in coherent media,” Phys. Rev. Lett. 87(13), 133601 (2001).
[Crossref] [PubMed]

1999 (1)

M. D. Lukin, A. B. Matsko, M. Fleischhauer, and M. O. Scully, “Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence,” Phys. Rev. Lett. 82(9), 1847–1850 (1999).
[Crossref]

1993 (1)

G. Ankerhold, M. Schiffer, D. Mutschall, T. Scholz, and W. Lange, “Nonlinear effects of radiation trapping in ground-state oriented sodium vapor,” Phys. Rev. A 48(6), 4031–4034 (1993).
[Crossref] [PubMed]

1990 (1)

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64(15), 1721–1724 (1990).
[Crossref] [PubMed]

1985 (1)

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55(22), 2409–2412 (1985).
[Crossref] [PubMed]

1980 (1)

H. G. Winful and J. H. Marburger, “Hysteresis and optical bistability in degenerate fourwave mixing,” Appl. Phys. Lett. 36(8), 613–614 (1980).
[Crossref]

1977 (1)

1972 (1)

W. Happer, “Optical Pumping,” Rev. Mod. Phys. 44(2), 169–249 (1972).
[Crossref]

Ankerhold, G.

G. Ankerhold, M. Schiffer, D. Mutschall, T. Scholz, and W. Lange, “Nonlinear effects of radiation trapping in ground-state oriented sodium vapor,” Phys. Rev. A 48(6), 4031–4034 (1993).
[Crossref] [PubMed]

Boyd, R. W.

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64(15), 1721–1724 (1990).
[Crossref] [PubMed]

Boyer, V.

C. F. Mccormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

Brown, A.

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).
[Crossref]

Chalopin, B.

L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maitre, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100(1), 013604 (2008).
[Crossref] [PubMed]

Chen, H.

H. Chen, Y. Zhang, X. Yao, Z. Wu, X. Zhang, Y. Zhang, and M. Xiao, “Parametrically amplified bright-state polariton of four- and six-wave mixing in an optical ring cavity,” Sci. Rep. 4(1), 3619 (2014).
[Crossref] [PubMed]

H. Zheng, X. Zhang, Z. Zhang, Y. Tian, H. Chen, C. Li, and Y. Zhang, “Parametric amplification and cascaded-nonlinearity processes in common atomic system,” Sci. Rep. 3(1), 1885 (2013).
[Crossref] [PubMed]

Cheng, L.

Cirac, J. I.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

Clark, J. B.

Davidson, R.

Dowran, M.

Duan, L. M.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

Fabre, C.

L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maitre, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100(1), 013604 (2008).
[Crossref] [PubMed]

Fang, Y. M.

Y. M. Fang and J. T. Jing, “Quantum squeezing and entanglement from a two-mode phase-sensitive amplifier via four-wave mixing in rubidium vapor,” New J. Phys. 17(2), 023027 (2015).
[Crossref]

Feng, W. K.

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

Fink, Y.

M. Soljacić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
[Crossref] [PubMed]

Fleischhauer, M.

M. D. Lukin, A. B. Matsko, M. Fleischhauer, and M. O. Scully, “Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence,” Phys. Rev. Lett. 82(9), 1847–1850 (1999).
[Crossref]

Gaeta, A. L.

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64(15), 1721–1724 (1990).
[Crossref] [PubMed]

Gauthier, D. J.

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64(15), 1721–1724 (1990).
[Crossref] [PubMed]

Glorieux, Q.

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).
[Crossref]

Happer, W.

W. Happer, “Optical Pumping,” Rev. Mod. Phys. 44(2), 169–249 (1972).
[Crossref]

Hollberg, L. W.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55(22), 2409–2412 (1985).
[Crossref] [PubMed]

Holtfrerich, M. W.

Hudelist, F.

Ibanescu, M.

M. Soljacić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
[Crossref] [PubMed]

Jing, J.

Jing, J. T.

Y. M. Fang and J. T. Jing, “Quantum squeezing and entanglement from a two-mode phase-sensitive amplifier via four-wave mixing in rubidium vapor,” New J. Phys. 17(2), 023027 (2015).
[Crossref]

Joannopoulos, J. D.

M. Soljacić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
[Crossref] [PubMed]

Johnson, S. G.

M. Soljacić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
[Crossref] [PubMed]

Joshi, A.

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).
[Crossref]

Khan, G. A.

Lange, W.

G. Ankerhold, M. Schiffer, D. Mutschall, T. Scholz, and W. Lange, “Nonlinear effects of radiation trapping in ground-state oriented sodium vapor,” Phys. Rev. A 48(6), 4031–4034 (1993).
[Crossref] [PubMed]

Lawrie, B.

R. C. Pooser and B. Lawrie, “Plasmonic trace sensing below the photon shot noise limit,” ACS Photonics 3(1), 8–13 (2016).
[Crossref]

R. C. Pooser and B. Lawrie, “Ultrasensitive measurement of microcantilever displacement below the shot-noise limit,” Optica 2(5), 393 (2015).
[Crossref]

Lawrie, B. J.

Lett, P. D.

C. F. Mccormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

Letter, P. D.

Li, C.

H. Zheng, X. Zhang, Z. Zhang, Y. Tian, H. Chen, C. Li, and Y. Zhang, “Parametric amplification and cascaded-nonlinearity processes in common atomic system,” Sci. Rep. 3(1), 1885 (2013).
[Crossref] [PubMed]

Li, P. Y.

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

Liu, C.

Liu, J.

Lopez, L.

L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maitre, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100(1), 013604 (2008).
[Crossref] [PubMed]

Lukin, M. D.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

M. D. Lukin, A. B. Matsko, M. Fleischhauer, and M. O. Scully, “Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence,” Phys. Rev. Lett. 82(9), 1847–1850 (1999).
[Crossref]

Ma, D.

Maitre, A.

L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maitre, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100(1), 013604 (2008).
[Crossref] [PubMed]

Malcuit, M. S.

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64(15), 1721–1724 (1990).
[Crossref] [PubMed]

Marburger, J. H.

H. G. Winful and J. H. Marburger, “Hysteresis and optical bistability in degenerate fourwave mixing,” Appl. Phys. Lett. 36(8), 613–614 (1980).
[Crossref]

Mareno, A. M.

Marino, A. M.

J. B. Clark, Z. Zhou, Q. Glorieux, A. M. Marino, and P. D. Letter, “Imaging using quantum noise properties of light,” Opt. Express 20(15), 17050 (2012).
[Crossref]

C. F. Mccormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

Matsko, A. B.

A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch, “Radiation trapping in coherent media,” Phys. Rev. Lett. 87(13), 133601 (2001).
[Crossref] [PubMed]

M. D. Lukin, A. B. Matsko, M. Fleischhauer, and M. O. Scully, “Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence,” Phys. Rev. Lett. 82(9), 1847–1850 (1999).
[Crossref]

Mccormick, C. F.

C. F. Mccormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

Mertz, J. C.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55(22), 2409–2412 (1985).
[Crossref] [PubMed]

Mutschall, D.

G. Ankerhold, M. Schiffer, D. Mutschall, T. Scholz, and W. Lange, “Nonlinear effects of radiation trapping in ground-state oriented sodium vapor,” Phys. Rev. A 48(6), 4031–4034 (1993).
[Crossref] [PubMed]

Novikova, I.

A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch, “Radiation trapping in coherent media,” Phys. Rev. Lett. 87(13), 133601 (2001).
[Crossref] [PubMed]

Pepper, D. M.

Pooser, R. C.

Schiffer, M.

G. Ankerhold, M. Schiffer, D. Mutschall, T. Scholz, and W. Lange, “Nonlinear effects of radiation trapping in ground-state oriented sodium vapor,” Phys. Rev. A 48(6), 4031–4034 (1993).
[Crossref] [PubMed]

Scholz, T.

G. Ankerhold, M. Schiffer, D. Mutschall, T. Scholz, and W. Lange, “Nonlinear effects of radiation trapping in ground-state oriented sodium vapor,” Phys. Rev. A 48(6), 4031–4034 (1993).
[Crossref] [PubMed]

Scully, M. O.

A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch, “Radiation trapping in coherent media,” Phys. Rev. Lett. 87(13), 133601 (2001).
[Crossref] [PubMed]

M. D. Lukin, A. B. Matsko, M. Fleischhauer, and M. O. Scully, “Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence,” Phys. Rev. Lett. 82(9), 1847–1850 (1999).
[Crossref]

Slusher, R. E.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55(22), 2409–2412 (1985).
[Crossref] [PubMed]

Soljacic, M.

M. Soljacić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
[Crossref] [PubMed]

Sun, Y.

Tian, Y.

H. Zheng, X. Zhang, Z. Zhang, Y. Tian, H. Chen, C. Li, and Y. Zhang, “Parametric amplification and cascaded-nonlinearity processes in common atomic system,” Sci. Rep. 3(1), 1885 (2013).
[Crossref] [PubMed]

Treps, N.

L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maitre, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100(1), 013604 (2008).
[Crossref] [PubMed]

Valley, J. F.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55(22), 2409–2412 (1985).
[Crossref] [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).
[Crossref]

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).
[Crossref]

Welch, G. R.

A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch, “Radiation trapping in coherent media,” Phys. Rev. Lett. 87(13), 133601 (2001).
[Crossref] [PubMed]

Winful, H. G.

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Figures (4)

Fig. 1
Fig. 1 (a1) Spatial beams alignment of the PA-FWM and PA-SWM process. (a2) Phase-matching geometrical diagram of the SP-FWM process. (b) Energy-level diagram for the inverted-Y configuration in 85Rb vapor. (c) The signal of 85Rb, F = 2 (probe) that external-dressing field E3 is blocked (c1) and got through (c2), respectively. (d) Measured probe signal versus probe frequency. (e) Measured conjugate signal versus probe frequency. (f) Energy-level diagram for multi-peaks.
Fig. 2
Fig. 2 Measured (a) probe and (b) conjugate fields with external-dressing field E3 at different power of E3. From bottom to top, the power of E3 is changed from 8mw to 18mw. The signals in (c,d) and (e,f) are enlarged views from dressed probe signal in (a) and dressed conjugate signal in (b), respectively. And the signals in (c,e) and (d,f) are 85Rb, F = 3 and 85Rb, F = 2, respectively. In (c-f), the left (right) peaks belong to the signals of rising (falling) edge.
Fig. 3
Fig. 3 Same as Fig. 2, but with external-dressing field E3 at different pump detuning ∆1. From bottom to top, the wavelength of E1 is changed from 795.9741 nm to 795.9720 nm.
Fig. 4
Fig. 4 Same as Fig. 2, but with external-dressing field E3 at different diameter of pump beam E1. From bottom to top, the diameter of E1 is changed from large to small. Besides, the signals in (c,e) and (d,f) are 85Rb, F = 2 and 85Rb, F = 3, respectively. In (c-f), the left (right) peaks belong to the signals of falling (rising) edge.

Equations (12)

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ρ 21(S) ( 3 ) =i G 1 2 G aS / d 21 d 01D d 21 .
ρ 20(aS) ( 3 ) =i G 1 2 G S / d 20 d 10D d 20 .
ρ 21(S) ( 3 ) = ρ 21(S) ( 3 ) +( G 3 2 / d 01 d 31 ) ρ 21(S) ( 3 ) = ρ 21(S) ( 3 ) + ρ 21(S) ( 5 ) .
ρ 20(aS) ( 3 ) = ρ 20(aS) ( 3 ) +( G 3 2 / d 10 d 13 ) ρ 20(aS) ( 3 ) = ρ 20(aS) ( 3 ) + ρ 20(aS) ( 5 ) .
a ^ out + a ^ out =g a ^ in + a ^ in +(g1).
b ^ out + b ^ out =(g1) a ^ in + a ^ in +g.
ρ 21(S) (3) = ρ 21(S) (3) + ρ 21(S) (5) .
ρ 20(aS) (3) = ρ 20(aS) (3) + ρ 20(aS) (5) .
ρ 21(S) (5) = i G c G 1 2 G 3 2 [ Γ 21 +i Δ 1 +G 3 2 /(Γ23+i Δ 1 Δ 3 )+ G p 2 / Γ 22 ][ Γ 01 +G 1 2 e i(Δα+Δϕ) /( Γ 21 +i Δ 1 )] × 1 [ G 1 2 e i(Δα+Δϕ) /[ Γ 01 +i( Δ 1 ' Δ 1 )]+ G p 2 /[ Γ 11 i( Δ 1 ' Δ 1 )]+ G 1 2 e i(Δα+Δϕ) / Γ 22 +G 3 2 /(Γ23+i Δ 1 Δ 3 )+i Δ 1 '+ Γ 21 ]( Γ 31 +i Δ 3 ) Γ 11 .
ρ 20(aS) (5) = i G p G 1 2 G 3 2 [ Γ 10 +G 3 2 /( Γ 30 + Δ 3 )+G 1 2 e i(Δα+Δϕ) /( Γ 20 +i Δ 1 )+G 1 2 e i(Δα+Δϕ) /( Γ 12 i Δ 1 )] × 1 [ Γ 20 +i Δ 1 +G 1 2 e i(Δα+Δϕ) / Γ 22 + G 1 2 e i(Δα+Δϕ) /( Γ 10 +i( Δ 1 Δ 1 ))] . × 1 [ Γ 20 +i Δ 1 + G c 2 / Γ 00 ][ Γ 30 + Δ 3 ][ Γ 10 ]
ρ 20 (1) =i G p /[ d 21 + | G p | 2 / Γ 11 + | G p | 2 / Γ 22 + | G 1 | 2 / d 10 + | G 1 | 2 /[ Γ 22 +i( Δ p Δ 1 ) ] ].
Δφ=N( n 2up I up n 2down I down ) ω p l/c= n 1 δl/c.

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