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.

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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, _1 , 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).

Other (7)

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

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, _1 , 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]

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).

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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