Abstract

We conducted a theoretical investigation of the optical steady-state behavior in N four-level Y-type atoms driven coherently by a probe laser and a single elliptically polarized field (EPF) by means of a unidirectional ring cavity. It was found that the optical bistability can be observed for a wide regime of frequency detuning of the probe field, intensity of the EPF, and the atomic cooperation parameter. Interestingly, in principle the optical steady-state behavior can be switched from optical bistability to multistability or vice versa by adjusting the phase difference between two components of the polarized electric field of the EPF if the perfect spontaneously generated coherence of atoms is included. Our results illustrate the potential to utilize EPF for all-optical switching in atomic systems through the phase control, as well as provide guidance in the design for possible experimental implementations.

© 2014 Optical Society of America

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    [CrossRef]
  48. H. B. 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]
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    [CrossRef]

2013

S. H. Asadpour, M. Jaberi, and H. R. Soleimani, “Phase control of optical bistability and multistability via spin coherence in a quantum well waveguide,” J. Opt. Soc. Am. B 30, 1815–1820 (2013).
[CrossRef]

Z. P. Wang and B. Yu, “Optical bistability via dual electromagnetically induced transparency in a coupled quantum-well nanostructure,” J. Appl. Phys. 113, 113101 (2013).
[CrossRef]

2012

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, 063820 (2012).
[CrossRef]

Z. Wang, A. X. Chen, Y. Bai, W. X. Yang, and R. K. Lee, “Coherent control of optical bistability in an open Λ-type three-level atomic system,” J. Opt. Soc. Am. B 29, 2891–2896 (2012).
[CrossRef]

2011

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
[CrossRef]

W. X. Yang, A. X. Chen, R. K. Lee, and Y. Wu, “Matched slow optical soliton pairs via biexciton coherence in quantum dots,” Phys. Rev. A 84, 013835 (2011).
[CrossRef]

M. Sahrai, S. H. Asadpour, H. Mahrami, and R. Sadighi-Bonabi, “Controlling the optical bistability via quantum interference in a four-level N-type atomic system,” J. Lumin. 131, 1682–1686 (2011).
[CrossRef]

2010

U. Khadka, Y. P. Zhang, and M. Xiao, “Control of multitransparency windows via dark-state phase manipulation,” Phys. Rev. A 81, 023830 (2010).
[CrossRef]

Z. P. Wang and H. Fan, “Phase-dependent optical bistability and multistability in a semiconductor quantum well system,” J. Lumin. 130, 2084–2088 (2010).
[CrossRef]

2009

W. X. Yang, J. M. Hou, Y. Y. Lin, and R. K. Lee, “Detuning management of optical solitons in coupled quantum wells,” Phys. Rev. A 79, 033825 (2009).
[CrossRef]

2008

W. X. Yang, J. M. Hou, and R. K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838 (2008).
[CrossRef]

H. B. 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]

2006

J.-H. Li, X.-Y. Lü, J.-M. Luo, and Q.-J. Huang, “Optical bistability and multistability via atomic coherence in an N-type atomic medium,” Phys. Rev. A 74, 035801 (2006).
[CrossRef]

X.-Y. Lü, J.-H. Li, J.-B. Liu, and J.-M. Luo, “Optical bistability via quantum interference in a four-level atomic medium,” J. Phys. B 39, 5161–5171 (2006).

J. F. Dynes and E. Paspalakis, “Phase control of electron population, absorption, and dispersion properties of a semiconductor quantum well,” Phys. Rev. B 73, 233305 (2006).
[CrossRef]

2004

A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on the dynamics of multi-level atomic systems,” Phys. Lett. A 325, 30–36 (2004).
[CrossRef]

Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Preparation of multiparty entangled states using pairwise perfectly efficient single-probe photon four-wave mixing,” Phys. Rev. A 69, 063803 (2004).
[CrossRef]

Y. Wu and X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70, 053818 (2004).
[CrossRef]

Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Efficient multiwave mixing in the ultraslow propagation regime and the role of multiphoton quantum destructive interference,” Opt. Lett. 29, 2294–2296 (2004).
[CrossRef]

Y. Wu and L. Deng, “Achieving multifrequency mode entanglement with ultraslow multiwave mixing,” Opt. Lett. 29, 1144–1146 (2004).
[CrossRef]

C. Liu, S. Gong, X. Fan, and Z. Xu, “Phase control of spontaneously generated coherence induced bistability,” Opt. Commun. 239, 383–388 (2004).
[CrossRef]

Y. Bai, H. Guo, H. Sun, D. Han, C. Liu, and X. Chen, “Effects of spontaneously generated coherence on the conditions for exhibiting lasing without inversion in a V system,” Phys. Rev. A 69, 043814 (2004).
[CrossRef]

D. Cheng, C. Liu, and S. Gong, “Optical bistability and multistability via the effect of spontaneously generated coherence in a three-level ladder-type atomic system,” Phys. Lett. A 332, 244–249 (2004).
[CrossRef]

2003

A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on optical bistability in three-level Λ-type atomic system,” Phys. Lett. A 315, 203–207 (2003).
[CrossRef]

M. Shapiro and P. Brumer, “Coherent control of molecular dynamics,” Rep. Prog. Phys. 66, 859 (2003).
[CrossRef]

A. Joshi, W. Yang, and M. Xiao, “Effect of quantum interference on optical bistability in the three-level V-type atomic system,” Phys. Rev. A 68, 015806 (2003).
[CrossRef]

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

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

2002

J. H. Wu and J. Y. Gao, “Phase control of light amplification without inversion in a Λ system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
[CrossRef]

J. Evers, D. Bullock, and C. H. Keitel, “Dark state suppression and narrow fluorescent feature in a laser-driven Λ atom,” Opt. Commun. 209, 173–179 (2002).
[CrossRef]

2001

X. M. Hu and Z. Z. Xu, “Phase control of amplitude-fluctuation-induced bistability,” J. Opt. B Quant. Semiclass. Opt. 3, 35–38 (2001).
[CrossRef]

2000

X.-M. Hu and J.-S. Peng, “Quantum interference from spontaneous decay in Lamba systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
[CrossRef]

F. Ghafoor, S. Y. Zhu, and M. S. Zubairy, “Amplitude and phase control of spontaneous emission,” Phys. Rev. A 62, 013811 (2000).
[CrossRef]

1999

P. Zhou and S. Swain, “Phase-dependent spectra in a driven two-level atom,” Phys. Rev. Lett. 82, 2500 (1999).
[CrossRef]

1998

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296 (1998).
[CrossRef]

S. Menon and G. S. Agarwal, “Effects of spontaneously generated coherence on the pump-probe response of a Λ system,” Phys. Rev. A 57, 4014 (1998).
[CrossRef]

1997

S. Y. Zhu, H. Chen, and H. Huang, “Quantum interference effects in spontaneous emission from an atom embedded in a photonic band gap structure,” Phys. Rev. Lett. 79, 205 (1997).
[CrossRef]

M. A. G. Martinez, P. R. Herezfeld, C. Samuels, L. M. Narducci, and C. H. Keitel, “Quantum interference effects in spontaneous atomic emission: dependence of the resonance fluorescence spectrum on the phase of the driving field,” Phys. Rev. A 55, 4483 (1997).
[CrossRef]

Y. Wu and X. Yang, “Effective two-level model for a three-level atom in the Ξ configuration,” Phys. Rev. A 56, 2443–2446 (1997).
[CrossRef]

1996

S. Gong, S. Du, Z. Xu, and S. Pan, “Optical bistability via a phase fluctuation effect of the control field,” Phys. Lett. A 222, 237–240 (1996).
[CrossRef]

Y. Wu, “Simple algebraic method to solve a coupled-channel cavity QED model,” Phys. Rev. A 54, 4534–4543 (1996).
[CrossRef]

1994

S. E. Harris, “Normal modes for electromagnetically induced transparency,” Phys. Rev. Lett. 72, 52 (1994).
[CrossRef]

1992

J. Javanainen, “Effect of state superpositions created by spontaneous emission on laser-driven transitions,” Europhys. Lett. 17, 407 (1992).
[CrossRef]

M. O. Scully and M. Fleischhauer, “High-sensitivity magnetometer based on index-enhanced media,” Phys. Rev. Lett. 69, 1360 (1992).
[CrossRef]

1991

K. Hakuta, L. Marmet, and B. P. Stoicheff, “Electric-field-induced second-harmonic generation with reduced absorption in atomic hydrogen,” Phys. Rev. Lett. 66, 596 (1991).
[CrossRef]

1990

N. A. Ansari, J. Gea-Banacloche, and M. S. Zubairy, “Phase-sensitive amplification in a three-level atomic system,” Phys. Rev. A 41, 5179 (1990).
[CrossRef]

1984

L. A. Lugiato, “II theory of optical bistability,” Prog. Opt. 21, 69–216 (1984).
[CrossRef]

Agarwal, G. S.

S. Menon and G. S. Agarwal, “Effects of spontaneously generated coherence on the pump-probe response of a Λ system,” Phys. Rev. A 57, 4014 (1998).
[CrossRef]

Ansari, N. A.

N. A. Ansari, J. Gea-Banacloche, and M. S. Zubairy, “Phase-sensitive amplification in a three-level atomic system,” Phys. Rev. A 41, 5179 (1990).
[CrossRef]

Asadpour, S. H.

S. H. Asadpour, M. Jaberi, and H. R. Soleimani, “Phase control of optical bistability and multistability via spin coherence in a quantum well waveguide,” J. Opt. Soc. Am. B 30, 1815–1820 (2013).
[CrossRef]

M. Sahrai, S. H. Asadpour, H. Mahrami, and R. Sadighi-Bonabi, “Controlling the optical bistability via quantum interference in a four-level N-type atomic system,” J. Lumin. 131, 1682–1686 (2011).
[CrossRef]

Bai, Y.

Z. Wang, A. X. Chen, Y. Bai, W. X. Yang, and R. K. Lee, “Coherent control of optical bistability in an open Λ-type three-level atomic system,” J. Opt. Soc. Am. B 29, 2891–2896 (2012).
[CrossRef]

Y. Bai, H. Guo, H. Sun, D. Han, C. Liu, and X. Chen, “Effects of spontaneously generated coherence on the conditions for exhibiting lasing without inversion in a V system,” Phys. Rev. A 69, 043814 (2004).
[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, 041801(R) (2003).
[CrossRef]

Brumer, P.

M. Shapiro and P. Brumer, “Coherent control of molecular dynamics,” Rep. Prog. Phys. 66, 859 (2003).
[CrossRef]

Bullock, D.

J. Evers, D. Bullock, and C. H. Keitel, “Dark state suppression and narrow fluorescent feature in a laser-driven Λ atom,” Opt. Commun. 209, 173–179 (2002).
[CrossRef]

Chen, A. X.

Z. Wang, A. X. Chen, Y. Bai, W. X. Yang, and R. K. Lee, “Coherent control of optical bistability in an open Λ-type three-level atomic system,” J. Opt. Soc. Am. B 29, 2891–2896 (2012).
[CrossRef]

W. X. Yang, A. X. Chen, R. K. Lee, and Y. Wu, “Matched slow optical soliton pairs via biexciton coherence in quantum dots,” Phys. Rev. A 84, 013835 (2011).
[CrossRef]

Chen, H.

S. Y. Zhu, H. Chen, and H. Huang, “Quantum interference effects in spontaneous emission from an atom embedded in a photonic band gap structure,” Phys. Rev. Lett. 79, 205 (1997).
[CrossRef]

Chen, H. X.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
[CrossRef]

Chen, X.

Y. Bai, H. Guo, H. Sun, D. Han, C. Liu, and X. Chen, “Effects of spontaneously generated coherence on the conditions for exhibiting lasing without inversion in a V system,” Phys. Rev. A 69, 043814 (2004).
[CrossRef]

Cheng, D.

D. Cheng, C. Liu, and S. Gong, “Optical bistability and multistability via the effect of spontaneously generated coherence in a three-level ladder-type atomic system,” Phys. Lett. A 332, 244–249 (2004).
[CrossRef]

Deng, L.

Du, S.

S. Gong, S. Du, Z. Xu, and S. Pan, “Optical bistability via a phase fluctuation effect of the control field,” Phys. Lett. A 222, 237–240 (1996).
[CrossRef]

Dynes, J. F.

J. F. Dynes and E. Paspalakis, “Phase control of electron population, absorption, and dispersion properties of a semiconductor quantum well,” Phys. Rev. B 73, 233305 (2006).
[CrossRef]

Evers, J.

J. Evers, D. Bullock, and C. H. Keitel, “Dark state suppression and narrow fluorescent feature in a laser-driven Λ atom,” Opt. Commun. 209, 173–179 (2002).
[CrossRef]

Fan, H.

Z. P. Wang and H. Fan, “Phase-dependent optical bistability and multistability in a semiconductor quantum well system,” J. Lumin. 130, 2084–2088 (2010).
[CrossRef]

Fan, X.

C. Liu, S. Gong, X. Fan, and Z. Xu, “Phase control of spontaneously generated coherence induced bistability,” Opt. Commun. 239, 383–388 (2004).
[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, 063820 (2012).
[CrossRef]

Fleischhauer, M.

M. O. Scully and M. Fleischhauer, “High-sensitivity magnetometer based on index-enhanced media,” Phys. Rev. Lett. 69, 1360 (1992).
[CrossRef]

Gao, J. Y.

J. H. Wu and J. Y. Gao, “Phase control of light amplification without inversion in a Λ system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
[CrossRef]

Gea-Banacloche, J.

H. B. 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]

N. A. Ansari, J. Gea-Banacloche, and M. S. Zubairy, “Phase-sensitive amplification in a three-level atomic system,” Phys. Rev. A 41, 5179 (1990).
[CrossRef]

Ghafoor, F.

F. Ghafoor, S. Y. Zhu, and M. S. Zubairy, “Amplitude and phase control of spontaneous emission,” Phys. Rev. A 62, 013811 (2000).
[CrossRef]

Gong, S.

D. Cheng, C. Liu, and S. Gong, “Optical bistability and multistability via the effect of spontaneously generated coherence in a three-level ladder-type atomic system,” Phys. Lett. A 332, 244–249 (2004).
[CrossRef]

C. Liu, S. Gong, X. Fan, and Z. Xu, “Phase control of spontaneously generated coherence induced bistability,” Opt. Commun. 239, 383–388 (2004).
[CrossRef]

S. Gong, S. Du, Z. Xu, and S. Pan, “Optical bistability via a phase fluctuation effect of the control field,” Phys. Lett. A 222, 237–240 (1996).
[CrossRef]

Guo, H.

Y. Bai, H. Guo, H. Sun, D. Han, C. Liu, and X. Chen, “Effects of spontaneously generated coherence on the conditions for exhibiting lasing without inversion in a V system,” Phys. Rev. A 69, 043814 (2004).
[CrossRef]

Hagley, E. W.

Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Efficient multiwave mixing in the ultraslow propagation regime and the role of multiphoton quantum destructive interference,” Opt. Lett. 29, 2294–2296 (2004).
[CrossRef]

Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Preparation of multiparty entangled states using pairwise perfectly efficient single-probe photon four-wave mixing,” Phys. Rev. A 69, 063803 (2004).
[CrossRef]

Hakuta, K.

K. Hakuta, L. Marmet, and B. P. Stoicheff, “Electric-field-induced second-harmonic generation with reduced absorption in atomic hydrogen,” Phys. Rev. Lett. 66, 596 (1991).
[CrossRef]

Han, D.

Y. Bai, H. Guo, H. Sun, D. Han, C. Liu, and X. Chen, “Effects of spontaneously generated coherence on the conditions for exhibiting lasing without inversion in a V system,” Phys. Rev. A 69, 043814 (2004).
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W. X. Yang, J. M. Hou, Y. Y. Lin, and R. K. Lee, “Detuning management of optical solitons in coupled quantum wells,” Phys. Rev. A 79, 033825 (2009).
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X. M. Hu and Z. Z. Xu, “Phase control of amplitude-fluctuation-induced bistability,” J. Opt. B Quant. Semiclass. Opt. 3, 35–38 (2001).
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X.-M. Hu and J.-S. Peng, “Quantum interference from spontaneous decay in Lamba systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
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S. Y. Zhu, H. Chen, and H. Huang, “Quantum interference effects in spontaneous emission from an atom embedded in a photonic band gap structure,” Phys. Rev. Lett. 79, 205 (1997).
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J.-H. Li, X.-Y. Lü, J.-M. Luo, and Q.-J. Huang, “Optical bistability and multistability via atomic coherence in an N-type atomic medium,” Phys. Rev. A 74, 035801 (2006).
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A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on the dynamics of multi-level atomic systems,” Phys. Lett. A 325, 30–36 (2004).
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A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on optical bistability in three-level Λ-type atomic system,” Phys. Lett. A 315, 203–207 (2003).
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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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Z. Wang, A. X. Chen, Y. Bai, W. X. Yang, and R. K. Lee, “Coherent control of optical bistability in an open Λ-type three-level atomic system,” J. Opt. Soc. Am. B 29, 2891–2896 (2012).
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Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
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J.-H. Li, X.-Y. Lü, J.-M. Luo, and Q.-J. Huang, “Optical bistability and multistability via atomic coherence in an N-type atomic medium,” Phys. Rev. A 74, 035801 (2006).
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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, 063820 (2012).
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W. X. Yang, J. M. Hou, Y. Y. Lin, and R. K. Lee, “Detuning management of optical solitons in coupled quantum wells,” Phys. Rev. A 79, 033825 (2009).
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D. Cheng, C. Liu, and S. Gong, “Optical bistability and multistability via the effect of spontaneously generated coherence in a three-level ladder-type atomic system,” Phys. Lett. A 332, 244–249 (2004).
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X.-Y. Lü, J.-H. Li, J.-B. Liu, and J.-M. Luo, “Optical bistability via quantum interference in a four-level atomic medium,” J. Phys. B 39, 5161–5171 (2006).

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Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
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X.-Y. Lü, J.-H. Li, J.-B. Liu, and J.-M. Luo, “Optical bistability via quantum interference in a four-level atomic medium,” J. Phys. B 39, 5161–5171 (2006).

J.-H. Li, X.-Y. Lü, J.-M. Luo, and Q.-J. Huang, “Optical bistability and multistability via atomic coherence in an N-type atomic medium,” Phys. Rev. A 74, 035801 (2006).
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M. Sahrai, S. H. Asadpour, H. Mahrami, and R. Sadighi-Bonabi, “Controlling the optical bistability via quantum interference in a four-level N-type atomic system,” J. Lumin. 131, 1682–1686 (2011).
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M. A. G. Martinez, P. R. Herezfeld, C. Samuels, L. M. Narducci, and C. H. Keitel, “Quantum interference effects in spontaneous atomic emission: dependence of the resonance fluorescence spectrum on the phase of the driving field,” Phys. Rev. A 55, 4483 (1997).
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Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
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Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Efficient multiwave mixing in the ultraslow propagation regime and the role of multiphoton quantum destructive interference,” Opt. Lett. 29, 2294–2296 (2004).
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X.-M. Hu and J.-S. Peng, “Quantum interference from spontaneous decay in Lamba systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
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M. Sahrai, S. H. Asadpour, H. Mahrami, and R. Sadighi-Bonabi, “Controlling the optical bistability via quantum interference in a four-level N-type atomic system,” J. Lumin. 131, 1682–1686 (2011).
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M. Sahrai, S. H. Asadpour, H. Mahrami, and R. Sadighi-Bonabi, “Controlling the optical bistability via quantum interference in a four-level N-type atomic system,” J. Lumin. 131, 1682–1686 (2011).
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M. A. G. Martinez, P. R. Herezfeld, C. Samuels, L. M. Narducci, and C. H. Keitel, “Quantum interference effects in spontaneous atomic emission: dependence of the resonance fluorescence spectrum on the phase of the driving field,” Phys. Rev. A 55, 4483 (1997).
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Y. Bai, H. Guo, H. Sun, D. Han, C. Liu, and X. Chen, “Effects of spontaneously generated coherence on the conditions for exhibiting lasing without inversion in a V system,” Phys. Rev. A 69, 043814 (2004).
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P. Zhou and S. Swain, “Phase-dependent spectra in a driven two-level atom,” Phys. Rev. Lett. 82, 2500 (1999).
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A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67, 041801(R) (2003).
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Wang, Z. G.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
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Z. P. Wang and B. Yu, “Optical bistability via dual electromagnetically induced transparency in a coupled quantum-well nanostructure,” J. Appl. Phys. 113, 113101 (2013).
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Z. P. Wang and H. Fan, “Phase-dependent optical bistability and multistability in a semiconductor quantum well system,” J. Lumin. 130, 2084–2088 (2010).
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H. B. 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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J. H. Wu and J. Y. Gao, “Phase control of light amplification without inversion in a Λ system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
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W. X. Yang, A. X. Chen, R. K. Lee, and Y. Wu, “Matched slow optical soliton pairs via biexciton coherence in quantum dots,” Phys. Rev. A 84, 013835 (2011).
[CrossRef]

Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Preparation of multiparty entangled states using pairwise perfectly efficient single-probe photon four-wave mixing,” Phys. Rev. A 69, 063803 (2004).
[CrossRef]

Y. Wu and X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70, 053818 (2004).
[CrossRef]

Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Efficient multiwave mixing in the ultraslow propagation regime and the role of multiphoton quantum destructive interference,” Opt. Lett. 29, 2294–2296 (2004).
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Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
[CrossRef]

U. Khadka, Y. P. Zhang, and M. Xiao, “Control of multitransparency windows via dark-state phase manipulation,” Phys. Rev. A 81, 023830 (2010).
[CrossRef]

H. B. 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]

A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on the dynamics of multi-level atomic systems,” Phys. Lett. A 325, 30–36 (2004).
[CrossRef]

A. Joshi, W. Yang, and M. Xiao, “Effect of quantum interference on optical bistability in the three-level V-type atomic system,” Phys. Rev. A 68, 015806 (2003).
[CrossRef]

A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on optical bistability in three-level Λ-type atomic system,” Phys. Lett. A 315, 203–207 (2003).
[CrossRef]

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

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

Xu, Z.

C. Liu, S. Gong, X. Fan, and Z. Xu, “Phase control of spontaneously generated coherence induced bistability,” Opt. Commun. 239, 383–388 (2004).
[CrossRef]

S. Gong, S. Du, Z. Xu, and S. Pan, “Optical bistability via a phase fluctuation effect of the control field,” Phys. Lett. A 222, 237–240 (1996).
[CrossRef]

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X. M. Hu and Z. Z. Xu, “Phase control of amplitude-fluctuation-induced bistability,” J. Opt. B Quant. Semiclass. Opt. 3, 35–38 (2001).
[CrossRef]

Yang, W.

A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on the dynamics of multi-level atomic systems,” Phys. Lett. A 325, 30–36 (2004).
[CrossRef]

A. Joshi, W. Yang, and M. Xiao, “Effect of quantum interference on optical bistability in the three-level V-type atomic system,” Phys. Rev. A 68, 015806 (2003).
[CrossRef]

A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on optical bistability in three-level Λ-type atomic system,” Phys. Lett. A 315, 203–207 (2003).
[CrossRef]

Yang, W. X.

Z. Wang, A. X. Chen, Y. Bai, W. X. Yang, and R. K. Lee, “Coherent control of optical bistability in an open Λ-type three-level atomic system,” J. Opt. Soc. Am. B 29, 2891–2896 (2012).
[CrossRef]

W. X. Yang, A. X. Chen, R. K. Lee, and Y. Wu, “Matched slow optical soliton pairs via biexciton coherence in quantum dots,” Phys. Rev. A 84, 013835 (2011).
[CrossRef]

W. X. Yang, J. M. Hou, Y. Y. Lin, and R. K. Lee, “Detuning management of optical solitons in coupled quantum wells,” Phys. Rev. A 79, 033825 (2009).
[CrossRef]

W. X. Yang, J. M. Hou, and R. K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838 (2008).
[CrossRef]

Yang, X.

Y. Wu and X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70, 053818 (2004).
[CrossRef]

Y. Wu and X. Yang, “Effective two-level model for a three-level atom in the Ξ configuration,” Phys. Rev. A 56, 2443–2446 (1997).
[CrossRef]

Yu, B.

Z. P. Wang and B. Yu, “Optical bistability via dual electromagnetically induced transparency in a coupled quantum-well nanostructure,” J. Appl. Phys. 113, 113101 (2013).
[CrossRef]

Yuan, J. M.

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, 063820 (2012).
[CrossRef]

Zhang, X.

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, 063820 (2012).
[CrossRef]

Zhang, Y. P.

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, 063820 (2012).
[CrossRef]

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106, 093904 (2011).
[CrossRef]

U. Khadka, Y. P. Zhang, and M. Xiao, “Control of multitransparency windows via dark-state phase manipulation,” Phys. Rev. A 81, 023830 (2010).
[CrossRef]

Zhang, Y. Q.

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, 063820 (2012).
[CrossRef]

Zheng, H. B.

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, 063820 (2012).
[CrossRef]

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P. Zhou and S. Swain, “Phase-dependent spectra in a driven two-level atom,” Phys. Rev. Lett. 82, 2500 (1999).
[CrossRef]

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F. Ghafoor, S. Y. Zhu, and M. S. Zubairy, “Amplitude and phase control of spontaneous emission,” Phys. Rev. A 62, 013811 (2000).
[CrossRef]

S. Y. Zhu, H. Chen, and H. Huang, “Quantum interference effects in spontaneous emission from an atom embedded in a photonic band gap structure,” Phys. Rev. Lett. 79, 205 (1997).
[CrossRef]

Zubairy, M. S.

F. Ghafoor, S. Y. Zhu, and M. S. Zubairy, “Amplitude and phase control of spontaneous emission,” Phys. Rev. A 62, 013811 (2000).
[CrossRef]

N. A. Ansari, J. Gea-Banacloche, and M. S. Zubairy, “Phase-sensitive amplification in a three-level atomic system,” Phys. Rev. A 41, 5179 (1990).
[CrossRef]

Europhys. Lett.

J. Javanainen, “Effect of state superpositions created by spontaneous emission on laser-driven transitions,” Europhys. Lett. 17, 407 (1992).
[CrossRef]

J. Appl. Phys.

Z. P. Wang and B. Yu, “Optical bistability via dual electromagnetically induced transparency in a coupled quantum-well nanostructure,” J. Appl. Phys. 113, 113101 (2013).
[CrossRef]

J. Lumin.

Z. P. Wang and H. Fan, “Phase-dependent optical bistability and multistability in a semiconductor quantum well system,” J. Lumin. 130, 2084–2088 (2010).
[CrossRef]

M. Sahrai, S. H. Asadpour, H. Mahrami, and R. Sadighi-Bonabi, “Controlling the optical bistability via quantum interference in a four-level N-type atomic system,” J. Lumin. 131, 1682–1686 (2011).
[CrossRef]

J. Opt. B Quant. Semiclass. Opt.

X. M. Hu and Z. Z. Xu, “Phase control of amplitude-fluctuation-induced bistability,” J. Opt. B Quant. Semiclass. Opt. 3, 35–38 (2001).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

X.-Y. Lü, J.-H. Li, J.-B. Liu, and J.-M. Luo, “Optical bistability via quantum interference in a four-level atomic medium,” J. Phys. B 39, 5161–5171 (2006).

X.-M. Hu and J.-S. Peng, “Quantum interference from spontaneous decay in Lamba systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
[CrossRef]

Opt. Commun.

J. Evers, D. Bullock, and C. H. Keitel, “Dark state suppression and narrow fluorescent feature in a laser-driven Λ atom,” Opt. Commun. 209, 173–179 (2002).
[CrossRef]

C. Liu, S. Gong, X. Fan, and Z. Xu, “Phase control of spontaneously generated coherence induced bistability,” Opt. Commun. 239, 383–388 (2004).
[CrossRef]

Opt. Lett.

Phys. Lett. A

S. Gong, S. Du, Z. Xu, and S. Pan, “Optical bistability via a phase fluctuation effect of the control field,” Phys. Lett. A 222, 237–240 (1996).
[CrossRef]

A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on the dynamics of multi-level atomic systems,” Phys. Lett. A 325, 30–36 (2004).
[CrossRef]

D. Cheng, C. Liu, and S. Gong, “Optical bistability and multistability via the effect of spontaneously generated coherence in a three-level ladder-type atomic system,” Phys. Lett. A 332, 244–249 (2004).
[CrossRef]

A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on optical bistability in three-level Λ-type atomic system,” Phys. Lett. A 315, 203–207 (2003).
[CrossRef]

Phys. Rev. A

J. H. Wu and J. Y. Gao, “Phase control of light amplification without inversion in a Λ system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
[CrossRef]

Y. Bai, H. Guo, H. Sun, D. Han, C. Liu, and X. Chen, “Effects of spontaneously generated coherence on the conditions for exhibiting lasing without inversion in a V system,” Phys. Rev. A 69, 043814 (2004).
[CrossRef]

N. A. Ansari, J. Gea-Banacloche, and M. S. Zubairy, “Phase-sensitive amplification in a three-level atomic system,” Phys. Rev. A 41, 5179 (1990).
[CrossRef]

M. A. G. Martinez, P. R. Herezfeld, C. Samuels, L. M. Narducci, and C. H. Keitel, “Quantum interference effects in spontaneous atomic emission: dependence of the resonance fluorescence spectrum on the phase of the driving field,” Phys. Rev. A 55, 4483 (1997).
[CrossRef]

S. Menon and G. S. Agarwal, “Effects of spontaneously generated coherence on the pump-probe response of a Λ system,” Phys. Rev. A 57, 4014 (1998).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Four-level Y-type atomic system interacting with a linear-polarized probe field Ωp (with angular frequency ωp) and a single elliptically polarized control field Ωc (with angular frequency ωc). The frequency detunings of the system are correspondingly defined by Δc and Δp. A realistic candidate for the proposed atomic system can be found in Rb87 atoms with the designated states chosen as follows: |5S1/2,F=1,mF=0 as |3, |5P1/2,F=2,mF=0 as |2, |5D3/2,F=2,mF=1 as |4, and |5D3/2,F=2,mF=1 as |1.

Fig. 2.
Fig. 2.

Schematic setup of the unidirectional ring cavity containing an atomic sample with the length L. EpI and EpT are the incident and transmitted fields, respectively. Ec represents the EPF control field that is not circulating inside the cavity.

Fig. 3.
Fig. 3.

(a) Curve diagrams of the input–output field intensity with different frequency detuning Δp with Ωc=γ. (b) Curve diagrams of the input–output field intensity with different intensities of the elliptically polarized field Ωc with Δp=γ. Other values of the parameters were chosen as γ1=γ2=γ, γ3=0.01γ, Δc=0.9γ, C=100γ, and η=0, ϕ=0.

Fig. 4.
Fig. 4.

Density plot of the probe absorption Imρ23 versus the Ωc and the detuning Δp with Ωp=Ωp*=0.01γ. Other values of the parameters were chosen as γ1=γ2=γ, γ3=0.01γ, Δc=0.9γ, and ϕ=0, η=0.

Fig. 5.
Fig. 5.

Curve diagrams of the input–output field intensity with different cooperation parameters C. Other values of the parameters were chosen as γ1=γ2=γ, γ3=0.01γ, Δc=0.9γ, η=0, ϕ=0, and Ωc=γ, Δp=γ.

Fig. 6.
Fig. 6.

(a) Curve diagrams of the input–output field intensity for different values of the SGC effect η and different phase differences ϕ between two components of the polarized electric field of the EPF with Δp=0. (b) Curve diagrams of the input–output field intensity for different values of the SGC effect η with Δp=γ and ϕ=0. (c) Curve diagrams of the input–output field intensity for different phase differences ϕ with Δp=0 and η=0. (d) Curve diagrams of the input–output field intensity for different phase differences ϕ with Δp=γ and η=0.9. Other values of the parameters were chosen as γ1=γ2=γ, γ3=0.01γ, Δc=0.9γ, C=100γ, and Ωc=γ.

Fig. 7.
Fig. 7.

Density plot of the probe absorption Imρ23 versus the detuning Δp and the phase difference ϕ between two components of the polarized electric field of the EPF. Other values of the parameters were chosen as γ1=γ2=γ, γ3=0.01γ, Δc=0.9γ, Ωc=γ, η=0.9, and Ωp=0.01γ.

Equations (18)

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Hint=(Δc+Δp)|11|+(ΔpΔc)|44|+Δp|22|[Ωp|23|+Ωc+|12|+Ωc|42|+H.c.],
ρ˙11=γ1ρ11+iΩc+ρ21i(Ωc+)*ρ12η2γ1γ2(ρ14+ρ41),
ρ˙22=γ3ρ22+γ1ρ11+γ2ρ44+i(Ωc+)*ρ12iΩc+ρ21+iΩpρ32iΩp*ρ23+i(Ωc+)*ρ42iΩc+ρ24+ηγ1γ2(ρ41+ρ14),
ρ˙44=γ2ρ44+iΩcρ24i(Ωc)*ρ42η2γ1γ2(ρ14+ρ41),
ρ˙12=(γ12+γ32+iΔc)ρ12iΩc+(ρ11ρ22)iΩp*ρ13iΩcρ14η2γ1γ2ρ42,
ρ˙13=[γ12+i(Δc+Δp)]ρ13+iΩc+ρ23iΩpρ12η2γ1γ2ρ43,
ρ˙14=(γ12+γ22+2iΔc)ρ14+iΩc+ρ24i(Ωc)*ρ12η2γ1γ2(ρ11+ρ44),
ρ˙23=(γ32+iΔp)ρ23+i(Ωc+)*ρ13+iΩp(ρ33ρ22)+i(Ωc)*ρ43,
ρ˙42=(γ22+γ32iΔc)ρ42iΩc+ρ41iΩp*ρ43+iΩc(ρ22ρ44)η2γ1γ2ρ12,
ρ˙43=[γ22+i(ΔpΔc)]ρ43+iΩcρ23iΩpρ42η2γ1γ2ρ13,
2E⃗1c22E⃗t2=1ε0c22P⃗t2,
P⃗=N[μ⃗23ρ32ei(k⃗pr⃗ωpt)+(μ⃗12ρ21+μ⃗42ρ24)ei(k⃗cr⃗ωct)+c.c.],
1cEpt+Epz=iωp2cε0P(ωp),
Epz=iωp2cε0P(ωp).
EpT=TEp(L),
Ep(0)=TEpI(L)+REp(L),
y=xiCρ23,
ρ23(1)=i(4bcη2γ12)Ωpaη2γ124η(cos(2ϕ))2γ1Ωc2+4[abc+(b+c)Ωc2+(bc)sin(2ϕ)Ωc2],

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