Abstract

We study a four-level double-Λ system with spontaneously generated coherence driven by a standing-wave coupling field. It is found that two well-developed photonic bandgaps with reflectivities of about 90% can be generated on the probe resonance in the presence of maximal spontaneously generated coherence. The induced double photonic bandgaps become, however, severely malformed when spontaneously generated coherence vanishes. Dynamic control of the double photonic bandgaps may be exploited to achieve a novel two-port double-channel routing scheme for weak light signals in quantum networks.

© 2010 Optical Society of America

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  1. J. Mompart and R. Corbalan, J. Opt. B 2, R7 (2004).
    [CrossRef]
  2. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
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  3. K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
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    [CrossRef] [PubMed]
  5. J.-H. Wu, H.-F. Zhang, and J.-Y. Gao, Opt. Lett. 28, 654 (2003).
    [CrossRef] [PubMed]
  6. Y. P. Niu and S. Q. Gong, Phys. Rev. A 73, 053811 (2006).
    [CrossRef]
  7. X.-H. Yang and S.-Y. Zhu, Phys. Rev. A 77, 063822 (2008).
    [CrossRef]
  8. V. Yannopapas, E. Paspalakis, and N. V. Vitanov, Phys. Rev. Lett. 103, 063602 (2009).
    [CrossRef] [PubMed]
  9. M. Artoni and G. C. La Rocca, Phys. Rev. Lett. 96, 073905 (2006).
    [CrossRef] [PubMed]
  10. Q.-Y. He, Y. Xue, M. Artoni, G. C. La Rocca, J.-H. Xu, and J.-Y. Gao, Phys. Rev. B 73, 195124 (2006).
    [CrossRef]
  11. A. W. Brown and M. Xiao, Opt. Lett. 30, 699 (2005).
    [CrossRef] [PubMed]
  12. J.-H. Wu, M. Artoni, and G. C. La Rocca, Phys. Rev. Lett. 103, 133601 (2009).
    [CrossRef] [PubMed]
  13. M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge Univ. Press, 1980).
  14. J.-W. Gao, J.-H. Wu, N. Ba, C.-L. Cui, and X.-X. Tian, Phys. Rev. A 81, 013804 (2010).
    [CrossRef]
  15. C.-L. Wang, A.-J. Li, X.-Y. Zhou, Z.-H. Kang, Y. Jiang, and J.-Y. Gao, Opt. Lett. 33, 687 (2008).
    [CrossRef] [PubMed]
  16. J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
    [CrossRef] [PubMed]

2010 (1)

J.-W. Gao, J.-H. Wu, N. Ba, C.-L. Cui, and X.-X. Tian, Phys. Rev. A 81, 013804 (2010).
[CrossRef]

2009 (2)

V. Yannopapas, E. Paspalakis, and N. V. Vitanov, Phys. Rev. Lett. 103, 063602 (2009).
[CrossRef] [PubMed]

J.-H. Wu, M. Artoni, and G. C. La Rocca, Phys. Rev. Lett. 103, 133601 (2009).
[CrossRef] [PubMed]

2008 (2)

2006 (3)

M. Artoni and G. C. La Rocca, Phys. Rev. Lett. 96, 073905 (2006).
[CrossRef] [PubMed]

Q.-Y. He, Y. Xue, M. Artoni, G. C. La Rocca, J.-H. Xu, and J.-Y. Gao, Phys. Rev. B 73, 195124 (2006).
[CrossRef]

Y. P. Niu and S. Q. Gong, Phys. Rev. A 73, 053811 (2006).
[CrossRef]

2005 (3)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

A. W. Brown and M. Xiao, Opt. Lett. 30, 699 (2005).
[CrossRef] [PubMed]

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef] [PubMed]

2004 (1)

J. Mompart and R. Corbalan, J. Opt. B 2, R7 (2004).
[CrossRef]

2003 (1)

1998 (1)

K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

1996 (1)

S. Y. Zhu and M. O. Scully, Phys. Rev. Lett. 76, 388 (1996).
[CrossRef] [PubMed]

Artoni, M.

J.-H. Wu, M. Artoni, and G. C. La Rocca, Phys. Rev. Lett. 103, 133601 (2009).
[CrossRef] [PubMed]

M. Artoni and G. C. La Rocca, Phys. Rev. Lett. 96, 073905 (2006).
[CrossRef] [PubMed]

Q.-Y. He, Y. Xue, M. Artoni, G. C. La Rocca, J.-H. Xu, and J.-Y. Gao, Phys. Rev. B 73, 195124 (2006).
[CrossRef]

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef] [PubMed]

Ba, N.

J.-W. Gao, J.-H. Wu, N. Ba, C.-L. Cui, and X.-X. Tian, Phys. Rev. A 81, 013804 (2010).
[CrossRef]

Bassani, F.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef] [PubMed]

Bergmann, K.

K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge Univ. Press, 1980).

Brown, A. W.

Corbalan, R.

J. Mompart and R. Corbalan, J. Opt. B 2, R7 (2004).
[CrossRef]

Cui, C.-L.

J.-W. Gao, J.-H. Wu, N. Ba, C.-L. Cui, and X.-X. Tian, Phys. Rev. A 81, 013804 (2010).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Gao, J.-W.

J.-W. Gao, J.-H. Wu, N. Ba, C.-L. Cui, and X.-X. Tian, Phys. Rev. A 81, 013804 (2010).
[CrossRef]

Gao, J.-Y.

C.-L. Wang, A.-J. Li, X.-Y. Zhou, Z.-H. Kang, Y. Jiang, and J.-Y. Gao, Opt. Lett. 33, 687 (2008).
[CrossRef] [PubMed]

Q.-Y. He, Y. Xue, M. Artoni, G. C. La Rocca, J.-H. Xu, and J.-Y. Gao, Phys. Rev. B 73, 195124 (2006).
[CrossRef]

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef] [PubMed]

J.-H. Wu, H.-F. Zhang, and J.-Y. Gao, Opt. Lett. 28, 654 (2003).
[CrossRef] [PubMed]

Gong, S. Q.

Y. P. Niu and S. Q. Gong, Phys. Rev. A 73, 053811 (2006).
[CrossRef]

He, Q.-Y.

Q.-Y. He, Y. Xue, M. Artoni, G. C. La Rocca, J.-H. Xu, and J.-Y. Gao, Phys. Rev. B 73, 195124 (2006).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Jiang, Y.

Kang, Z.-H.

La Rocca, G. C.

J.-H. Wu, M. Artoni, and G. C. La Rocca, Phys. Rev. Lett. 103, 133601 (2009).
[CrossRef] [PubMed]

M. Artoni and G. C. La Rocca, Phys. Rev. Lett. 96, 073905 (2006).
[CrossRef] [PubMed]

Q.-Y. He, Y. Xue, M. Artoni, G. C. La Rocca, J.-H. Xu, and J.-Y. Gao, Phys. Rev. B 73, 195124 (2006).
[CrossRef]

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef] [PubMed]

Li, A.-J.

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Mompart, J.

J. Mompart and R. Corbalan, J. Opt. B 2, R7 (2004).
[CrossRef]

Niu, Y. P.

Y. P. Niu and S. Q. Gong, Phys. Rev. A 73, 053811 (2006).
[CrossRef]

Paspalakis, E.

V. Yannopapas, E. Paspalakis, and N. V. Vitanov, Phys. Rev. Lett. 103, 063602 (2009).
[CrossRef] [PubMed]

Scully, M. O.

S. Y. Zhu and M. O. Scully, Phys. Rev. Lett. 76, 388 (1996).
[CrossRef] [PubMed]

Shore, B. W.

K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

Silvestri, L.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef] [PubMed]

Theuer, H.

K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

Tian, X.-X.

J.-W. Gao, J.-H. Wu, N. Ba, C.-L. Cui, and X.-X. Tian, Phys. Rev. A 81, 013804 (2010).
[CrossRef]

Vitanov, N. V.

V. Yannopapas, E. Paspalakis, and N. V. Vitanov, Phys. Rev. Lett. 103, 063602 (2009).
[CrossRef] [PubMed]

Wang, C.-L.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge Univ. Press, 1980).

Wu, J.-H.

J.-W. Gao, J.-H. Wu, N. Ba, C.-L. Cui, and X.-X. Tian, Phys. Rev. A 81, 013804 (2010).
[CrossRef]

J.-H. Wu, M. Artoni, and G. C. La Rocca, Phys. Rev. Lett. 103, 133601 (2009).
[CrossRef] [PubMed]

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef] [PubMed]

J.-H. Wu, H.-F. Zhang, and J.-Y. Gao, Opt. Lett. 28, 654 (2003).
[CrossRef] [PubMed]

Xiao, M.

Xu, J.-H.

Q.-Y. He, Y. Xue, M. Artoni, G. C. La Rocca, J.-H. Xu, and J.-Y. Gao, Phys. Rev. B 73, 195124 (2006).
[CrossRef]

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef] [PubMed]

Xue, Y.

Q.-Y. He, Y. Xue, M. Artoni, G. C. La Rocca, J.-H. Xu, and J.-Y. Gao, Phys. Rev. B 73, 195124 (2006).
[CrossRef]

Yang, X.-H.

X.-H. Yang and S.-Y. Zhu, Phys. Rev. A 77, 063822 (2008).
[CrossRef]

Yannopapas, V.

V. Yannopapas, E. Paspalakis, and N. V. Vitanov, Phys. Rev. Lett. 103, 063602 (2009).
[CrossRef] [PubMed]

Zhang, H.-F.

Zhou, X.-Y.

Zhu, S. Y.

S. Y. Zhu and M. O. Scully, Phys. Rev. Lett. 76, 388 (1996).
[CrossRef] [PubMed]

Zhu, S.-Y.

X.-H. Yang and S.-Y. Zhu, Phys. Rev. A 77, 063822 (2008).
[CrossRef]

J. Opt. B (1)

J. Mompart and R. Corbalan, J. Opt. B 2, R7 (2004).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (3)

J.-W. Gao, J.-H. Wu, N. Ba, C.-L. Cui, and X.-X. Tian, Phys. Rev. A 81, 013804 (2010).
[CrossRef]

Y. P. Niu and S. Q. Gong, Phys. Rev. A 73, 053811 (2006).
[CrossRef]

X.-H. Yang and S.-Y. Zhu, Phys. Rev. A 77, 063822 (2008).
[CrossRef]

Phys. Rev. B (1)

Q.-Y. He, Y. Xue, M. Artoni, G. C. La Rocca, J.-H. Xu, and J.-Y. Gao, Phys. Rev. B 73, 195124 (2006).
[CrossRef]

Phys. Rev. Lett. (5)

J.-H. Wu, M. Artoni, and G. C. La Rocca, Phys. Rev. Lett. 103, 133601 (2009).
[CrossRef] [PubMed]

V. Yannopapas, E. Paspalakis, and N. V. Vitanov, Phys. Rev. Lett. 103, 063602 (2009).
[CrossRef] [PubMed]

M. Artoni and G. C. La Rocca, Phys. Rev. Lett. 96, 073905 (2006).
[CrossRef] [PubMed]

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef] [PubMed]

S. Y. Zhu and M. O. Scully, Phys. Rev. Lett. 76, 388 (1996).
[CrossRef] [PubMed]

Rev. Mod. Phys. (2)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

Other (1)

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge Univ. Press, 1980).

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Figures (3)

Fig. 1
Fig. 1

Left, schematic of a four-level double Λ system with two closely lying levels |3⟩ and |4⟩ strongly coupled via spontaneous emission. An SW coupling field ω c simultaneously acts on transitions | 2 | 3 and | 2 | 4 , while a weak probe field ω p interacts with both transitions | 1 | 3 and | 1 | 4 . Right, arrangement of the probe (coupling) electric field E p ( E c ) and relevant dipole moments d 13 and d 14 ( d 23 and d 24 ).

Fig. 2
Fig. 2

(a) PBG structures and (b) probe reflectivity spectra with p 1 = 1 (black-solid); p 1 = 0.8 (red-dashed); p 1 = 0.5 (green-dotted); p 1 = 0 (blue-dash–dotted). Other parameters are Γ 31 = Γ 41 = γ , Γ 32 = Γ 42 = 0.1 γ , γ 21 = 0.001 γ , p 2 = 0 , Δ = 12 γ , Ω c 0 = 1.4 γ , Δ c = 0 , d 1 = d 2 = 1.5 × 10 29 C m , λ p = 780.792 nm , λ c = 780.778 nm , N 0 = 1.0 × 10 12 cm 3 , L = 1.5 mm , and γ = 6.0 MHz .

Fig. 3
Fig. 3

(a) Probe absorption spectra at the SW nodes with Ω c = 0 and (b) the SW antinodes with Ω c = 2 Ω c 0 . Other parameters and curve notations are the same as in Fig. 2. The two insets show more detail about the probe absorption at the SW nodes and antinodes.

Equations (10)

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| Ω c ( z ) | 2 = 4 Ω c 0 2 cos 2 ( k c z ) ,
t ρ 21 = γ 21 ρ 21 i Ω c ρ 31 + i Ω c ρ 41 ,
t ρ 31 = γ 31 ρ 31 + i Ω p i Ω c * ρ 12 γ 34 ρ 41 ,
t ρ 41 = γ 41 ρ 41 + i Ω p + i Ω c * ρ 12 γ 34 ρ 31 ,
ρ 31 = i Ω p γ 21 [ γ 21 ( γ 41 γ 34 ) + 2 | Ω c | 2 ] ( γ 21 γ 31 + | Ω c | 2 ) ( γ 21 γ 41 + | Ω c | 2 ) + ( γ 21 γ 34 | Ω c | 2 ) 2 ,
ρ 41 = i Ω p γ 21 [ γ 21 ( γ 31 γ 34 ) + 2 | Ω c | 2 ] ( γ 21 γ 31 + | Ω c | 2 ) ( γ 21 γ 41 + | Ω c | 2 ) + ( γ 21 γ 34 | Ω c | 2 ) 2 ,
χ p ( Δ p , z ) = N 0 d 1 2 2 ϵ 0 ρ 31 ( Δ p , z ) + ρ 41 ( Δ p , z ) Ω p ,
( E p + ( z + a ) E p ( z + a ) ) = M ( Δ p ) ( E p + ( z ) E p ( z ) ) = ( e i k a E p + ( z ) e i k a E p ( z ) ) ,
e 2 i k a Tr ( M ) e i k a + 1 = 0 .
R ( Δ p ) = | M N ( 12 ) ( Δ p ) M N ( 22 ) ( Δ p ) | 2 ,

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