Abstract

A two-level system coupled to a one-dimensional continuum is investigated. By using a real-space model Hamiltonian, we show that spontaneous emission can coherently interfere with the continuum modes and gives interesting transport properties. The technique is applied to various related problems with different configurations, and analytical solutions are given.

© 2005 Optical Society of America

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  1. S. John, Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef] [PubMed]
  2. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  3. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
    [CrossRef] [PubMed]
  4. R. H. Dicke, Phys. Rev. 93, 99 (1953).
    [CrossRef]
  5. P. W. Anderson, Phys. Rev. 124, 41 (1961).
    [CrossRef]
  6. P. B. Wiegmann and A. M. Tsvelick, J. Phys. C 16, 2281 (1983).
    [CrossRef]
  7. V. I. Rupasov and V. I. Yudson, Sov. Phys. JETP 60, 927 (1984).
  8. H. A. Haus and Y. Lai, J. Lightwave Technol. 9, 754 (1991).
    [CrossRef]
  9. Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
    [CrossRef]
  10. S. Fan, Appl. Phys. Lett. 80, 908 (2002).
    [CrossRef]
  11. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  12. S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. A 20, 569 (2003).
    [CrossRef]
  13. U. Fano, Phys. Rev. 124, 1866 (1961).
    [CrossRef]
  14. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
    [CrossRef]

2004 (1)

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

S. Fan, Appl. Phys. Lett. 80, 908 (2002).
[CrossRef]

2000 (1)

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

1999 (1)

1991 (1)

H. A. Haus and Y. Lai, J. Lightwave Technol. 9, 754 (1991).
[CrossRef]

1987 (2)

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

1984 (1)

V. I. Rupasov and V. I. Yudson, Sov. Phys. JETP 60, 927 (1984).

1983 (1)

P. B. Wiegmann and A. M. Tsvelick, J. Phys. C 16, 2281 (1983).
[CrossRef]

1961 (2)

P. W. Anderson, Phys. Rev. 124, 41 (1961).
[CrossRef]

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

1953 (1)

R. H. Dicke, Phys. Rev. 93, 99 (1953).
[CrossRef]

Anderson, P. W.

P. W. Anderson, Phys. Rev. 124, 41 (1961).
[CrossRef]

Deppe, D. G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Dicke, R. H.

R. H. Dicke, Phys. Rev. 93, 99 (1953).
[CrossRef]

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Fan, S.

Fano, U.

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Gibbs, H. M.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Haus, H. A.

H. A. Haus and Y. Lai, J. Lightwave Technol. 9, 754 (1991).
[CrossRef]

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Hendrickson, J.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Joannopoulos, J. D.

John, S.

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Khitrova, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Lai, Y.

H. A. Haus and Y. Lai, J. Lightwave Technol. 9, 754 (1991).
[CrossRef]

Lee, R. K.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
[CrossRef]

Li, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

Rupasov, V. I.

V. I. Rupasov and V. I. Yudson, Sov. Phys. JETP 60, 927 (1984).

Rupper, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Scherer, A.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
[CrossRef]

Shchekin, O. B.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Suh, W.

Tsvelick, A. M.

P. B. Wiegmann and A. M. Tsvelick, J. Phys. C 16, 2281 (1983).
[CrossRef]

Wiegmann, P. B.

P. B. Wiegmann and A. M. Tsvelick, J. Phys. C 16, 2281 (1983).
[CrossRef]

Xu, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Yariv, A.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
[CrossRef]

Yoshie, T.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Yudson, V. I.

V. I. Rupasov and V. I. Yudson, Sov. Phys. JETP 60, 927 (1984).

Appl. Phys. Lett. (1)

S. Fan, Appl. Phys. Lett. 80, 908 (2002).
[CrossRef]

J. Lightwave Technol. (1)

H. A. Haus and Y. Lai, J. Lightwave Technol. 9, 754 (1991).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. C (1)

P. B. Wiegmann and A. M. Tsvelick, J. Phys. C 16, 2281 (1983).
[CrossRef]

Nature (1)

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. (3)

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

R. H. Dicke, Phys. Rev. 93, 99 (1953).
[CrossRef]

P. W. Anderson, Phys. Rev. 124, 41 (1961).
[CrossRef]

Phys. Rev. E (1)

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

V. I. Rupasov and V. I. Yudson, Sov. Phys. JETP 60, 927 (1984).

Other (1)

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

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Figures (4)

Fig. 1
Fig. 1

Schematics of the systems: (a) An atom embedded in a one-dimensional waveguide. (b) An atom surrounded by two partial reflectors denoted by black vertical bars. (c) A chain of atoms. (d) An atom couples to two parallel waveguides. The waveguide is denoted by two horizontal black lines. The light shaded region denotes the photonic bandgap crystal. The atom is indicated by the black dot. The arrow indicates the direction of the input light.

Fig. 2
Fig. 2

Transmission spectrum (solid curve) and the reflection spectrum (dashed curve) for an atom in a one-dimensional waveguide as shown in Fig. 1(a). V 2 Ω v g = 0.05 .

Fig. 3
Fig. 3

Transmission spectra through the optical system as shown in Fig. 1(b). V 2 v g = 0.002 ( 2 π c L ) . The resonance energy is Ω = 0.325 ( 2 π c L ) . 2 L is the distance between the two partially reflecting elements. (a) r = 0.4 . The dashed curve represents the transmission spectrum through the two partially reflecting elements, without the presence of the atom. (b) r = 0.9 .

Fig. 4
Fig. 4

Dispersion relation between frequency ω and Bloch wave vector K. λ r 2 π v g Ω is the wavelength at resonance for a single atom. v g = 1 . (a) d λ r = 3.4 × 10 3 , (b) d λ r = 3.4 × 10 2 , (c) d λ r = 6.8 × 10 2 , (d) d λ r = 3.4 × 10 1 . The line at ω Ω = 1 is a visual aid.

Equations (9)

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H = k ω k a k a k + 1 2 Ω S z + k V k ( a k + a k ) ( S + + S ) ,
H = d x { i v g c R ( x ) x c R ( x ) + i v g c L ( x ) x c L ( x ) + V δ ( x ) [ c R ( x ) S + c R ( x ) S + + c L ( x ) S + c L ( x ) S + ] } + E e a e a e + E g a g a e ,
E k = d x [ ϕ k , R + ( x ) c R ( x ) + ϕ k , L + ( x ) c L ( x ) ] 0 , + e k a e a g 0 , ,
ϕ k , R + ( x ) [ exp ( i k x ) θ ( x ) + t exp ( i k x ) θ ( x ) ] ,
ϕ k , L + ( x ) r exp ( i k x ) θ ( x ) ,
t = cos b e i b , r = i sin b e i b , e k = v g V sin b e i b ,
R r 2 = sin 2 { arctan [ V 2 v g ( Ω E k ) ] } = ( V 2 v g ) 2 ( Ω E k ) 2 + ( V 2 v g ) 2 ,
( a b ) = [ 1 i V 2 v g ( Ω E k ) i V 2 v g ( Ω E k ) + i V 2 v g ( Ω E k ) 1 + i V 2 v g ( Ω E k ) ] ( a b ) .
T p = 1 i 1 r 2 [ 1 r r 1 ] ,

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