Abstract

We consider the propagation in a dielectric medium of radiation emitted by a single-atom source. The source and dielectric atoms are assumed to be two-state systems, and the emitted light is incident on an ideal broadband detector. It is shown that the peak probability for producing a “click” at the detector can occur sooner than it could if there were no material medium between it and the source atom.

© 2001 Optical Society of America

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References

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  1. L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277 (2000).
    [CrossRef] [PubMed]
  2. Experiments by S. Chu and S. Wong [“Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738 (1982)] showed that vg can be >c, ±∞, or <0.
    [CrossRef]
  3. A. Katz and R. R. Alfano, “Pulse propagation in an absorbing medium,” Phys. Rev. Lett. 49, 1292 (1982),
    [CrossRef]
  4. S. Chu and S. Wong, “Chu and Wong respond,” Phys. Rev. Lett. 49, 1293 (1982).
    [CrossRef]
  5. P. W. Milonni, D. F. V. James, and H. Fearn, “Causality and photodetection in quantum optics,” Phys. Rev. A52, 1525 (1995).
  6. C. G. B. Garrett and D. E. McCumber, “Propagation of a gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A1, 305 (1970).
  7. L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).

2000 (1)

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277 (2000).
[CrossRef] [PubMed]

1995 (1)

P. W. Milonni, D. F. V. James, and H. Fearn, “Causality and photodetection in quantum optics,” Phys. Rev. A52, 1525 (1995).

1982 (3)

Experiments by S. Chu and S. Wong [“Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738 (1982)] showed that vg can be >c, ±∞, or <0.
[CrossRef]

A. Katz and R. R. Alfano, “Pulse propagation in an absorbing medium,” Phys. Rev. Lett. 49, 1292 (1982),
[CrossRef]

S. Chu and S. Wong, “Chu and Wong respond,” Phys. Rev. Lett. 49, 1293 (1982).
[CrossRef]

1970 (1)

C. G. B. Garrett and D. E. McCumber, “Propagation of a gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A1, 305 (1970).

Alfano, R. R.

A. Katz and R. R. Alfano, “Pulse propagation in an absorbing medium,” Phys. Rev. Lett. 49, 1292 (1982),
[CrossRef]

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).

Chu, S.

S. Chu and S. Wong, “Chu and Wong respond,” Phys. Rev. Lett. 49, 1293 (1982).
[CrossRef]

Experiments by S. Chu and S. Wong [“Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738 (1982)] showed that vg can be >c, ±∞, or <0.
[CrossRef]

Dogariu, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277 (2000).
[CrossRef] [PubMed]

Fearn, H.

P. W. Milonni, D. F. V. James, and H. Fearn, “Causality and photodetection in quantum optics,” Phys. Rev. A52, 1525 (1995).

Garrett, C. G. B.

C. G. B. Garrett and D. E. McCumber, “Propagation of a gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A1, 305 (1970).

James, D. F. V.

P. W. Milonni, D. F. V. James, and H. Fearn, “Causality and photodetection in quantum optics,” Phys. Rev. A52, 1525 (1995).

Katz, A.

A. Katz and R. R. Alfano, “Pulse propagation in an absorbing medium,” Phys. Rev. Lett. 49, 1292 (1982),
[CrossRef]

Kuzmich, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277 (2000).
[CrossRef] [PubMed]

McCumber, D. E.

C. G. B. Garrett and D. E. McCumber, “Propagation of a gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A1, 305 (1970).

Milonni, P. W.

P. W. Milonni, D. F. V. James, and H. Fearn, “Causality and photodetection in quantum optics,” Phys. Rev. A52, 1525 (1995).

Wang, L. J.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277 (2000).
[CrossRef] [PubMed]

Wong, S.

Experiments by S. Chu and S. Wong [“Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738 (1982)] showed that vg can be >c, ±∞, or <0.
[CrossRef]

S. Chu and S. Wong, “Chu and Wong respond,” Phys. Rev. Lett. 49, 1293 (1982).
[CrossRef]

Nature (1)

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277 (2000).
[CrossRef] [PubMed]

Phys. Rev. (2)

P. W. Milonni, D. F. V. James, and H. Fearn, “Causality and photodetection in quantum optics,” Phys. Rev. A52, 1525 (1995).

C. G. B. Garrett and D. E. McCumber, “Propagation of a gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A1, 305 (1970).

Phys. Rev. Lett. (3)

Experiments by S. Chu and S. Wong [“Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738 (1982)] showed that vg can be >c, ±∞, or <0.
[CrossRef]

A. Katz and R. R. Alfano, “Pulse propagation in an absorbing medium,” Phys. Rev. Lett. 49, 1292 (1982),
[CrossRef]

S. Chu and S. Wong, “Chu and Wong respond,” Phys. Rev. Lett. 49, 1293 (1982).
[CrossRef]

Other (1)

L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).

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Equations (39)

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H = 1 2 ω o σ z + j = 1 N T 1 2 ω d σ zj + k λ ω k a k λ a k λ i d μ k λ C k λ [ a k λ a k λ ] σ x
i j = 1 N T k λ C k λ [ a k λ e i k · x j a k λ e i k · x j ] σ xj ,
E ( z , t ) = i k ( 2 π ω k V ) 1 2 a k ( t ) e i ω k z c + h . c .
= E o ( + ) ( z , t ) + i k ( 2 π d ω k V ) e i k z 0 t dt σ x ( t ) e i ω k ( t t )
+ i k j = 1 N T ( 2 πμ ω k V ) e i k ( z z j ) 0 t dt σ xj ( t ) e i ω k ( t t ) + h . c . ,
E o ( + ) ( z , t ) = i k ( 2 π ω k V ) 1 2 a k ( 0 ) e i ( ω k t kz ) ,
2 Re [ i k ( 2 π ω k V ) e ikz e i ω k ( t t ) ] Re i AL L 2 π c d ω ( 2 π ω ) e i ω ( t t + z c )
= 2 π Ac t δ ( t t + z c ) ,
E ( z , t ) = E o ( z , t ) 2 π d Ac σ ˙ x ( t z c ) θ ( t z c )
2 π d Ac j σ ˙ xj ( t z z j c ) θ ( t z z j c )
E ( z , t ) = d ω E ˜ ( z , ω ) e i ω t ,
σ x ( t ) = d ω σ ˜ x ( ω ) e i ω t ,
σ xj ( t ) = d ω σ ˜ xj ( ω ) e i ω t .
E ˜ ( z , ω ) = E ˜ o ( z , ω ) + 2 π id Ac ω e i ω z c σ ˜ x ( ω ) + 2 πiμ Ac ω j e i ω z z j c σ ˜ xj ( ω )
F ( z , ω ) + 2 πiμ Ac ω j σ ˜ xj ( ω ) e i ω z z j c
F ( z , ω ) + 2 π i μ ω c N z o dz σ ˜ x ( z , ω ) e i ω z z c ,
σ xj ̈ + 2 β σ ˙ xj + ω d 2 σ xj = 2 μ ω d E ( z j , t ) σ zj 2 μ ω d E ( z j , t ) ,
μ σ ˜ x ( z , ω ) = α ( ω ) E ˜ ( z , ω )
E ˜ ( z , ω ) = f ( ω ) e i ω z c + 2 π i ω c N α ( ω ) z o z dz E ˜ ( z , ω ) e i ω ( z z ) c
+ 2 π i ω c N α ( ω ) z dz E ˜ ( z , ω ) e i ω ( z z ) c ,
E ˜ ( z , ω ) = g ( ω ) e in ( ω ) ω z c
E ˜ ( z , ω ) = 2 n ( ω ) + 1 f ( ω ) e in ( ω ) ( z z o ) ω c e i ω z o c
E ( z , t ) = E o ( z , t ) + 2 id Ac dt σ x ( t ) d ω ω n ( ω ) + 1 e i ω [ t t + n ( ω ) z c ] ,
R ( z , t ) = dt dt σ x ( t ) σ x ( t ) d ω ω n * ( ω ) + 1 e i ω [ t t + n * ( ω ) z c ]
× d ω ω n ( ω ) + 1 e i ω [ t t + n ( ω ) z c ] .
σ x ( t ) σ x ( t ) = σ ( t ) σ ( t ) + σ ( t ) σ ( t ) + σ ( t ) σ ( t ) + σ ( t ) σ ( t ) .
R ( z , t ) = dt dt σ ( t ) σ ( t ) d ω ω n * ( ω ) + 1 e i ω [ t t + n * ( ω ) z c ]
× d ω ω n ( ω ) + 1 e i ω [ t t + n ( ω ) z c ] .
R ( z , t ) dt e i ω o t F o ( t ) d ω ω n ( ω ) + 1 e i ω [ t t + n ( ω ) z c ] 2
dt a ( t ) d ω ω n ( ω ) + 1 e i ω [ t t + n ( ω ) z c ] 2 ,
R ( z , t ) d ω ω n ( ω ) + 1 e i ω t e i ω n ( ω ) z c e 1 2 ( ω ω o ) 2 τ 2 2 .
dt F o ( t ) d ω ω n ( ω ) + 1 e i ( ω ω o ) t e i ω [ t n ( ω ) z c ]
ω o n ( ω o ) + 1 e ω o n I ( ω o ) z c dt F o ( t ) e i ω o t e i ω [ t t + n R ( ω ) z c ]
dt F o ( t ) e i ω o t d Δ e i ( ω o + Δ ) ( t t ) e i ( ω o + Δ ) [ n R ( ω o ) + Δ n R ( ω o ) ] z c
e i ω o [ t n R ( ω o ) z c ] dt F o ( t ) d Δ e i Δ ( t t ) e i Δ [ n R ( ω o ) + ω o n R ( ω o ) ] z c
= 2 π e i ω o [ t n R ( ω o ) z c ] F o ( t z υ g ) ,
R ( z , t ) e 2 ω o n I ( ω o ) z c P ( t z υ g ) ,
R ( z , t ) = dt 0 dt σ ( t ) σ ( t ) d ω ω n * ( ω ) + 1 e i ω [ t t + n * ( ω ) z c ]
× d ω ω n ( ω ) + 1 e i ω [ t t + n ( ω ) z c ] .

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