Abstract

We consider a category of transient processes that is usually hidden from view in coherent-transient experiments. These are the very fast noise processes that give rise to relaxation effects. We present different Markov-type models of a class of these noise processes, namely, laser phase and frequency fluctuations. These models lead to different forms for the laser-field autocorrelation function, depending on which quantity, the phase or the frequency, is the primary source of noise. We show that it is possible to establish a regime such that all these kinds of noise will lead to a Lorentzian laser power spectrum. Despite this common feature, N-photon absorption exhibits observable differences depending on the source of fluctuations. For example, for diffusive noises the absorption linewidth increases as N2, but for jumplike or shotlike phase fluctuations it can be N independent.

© 1986 Optical Society of America

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References

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  1. P. Zoller and P. Lambropoulos, J. Phys. B 12, L547 (1979); S. N. Dixit, P. Zoller, and P. Lambropoulos, Phys. Rev. A 21, 1289 (1980).
    [Crossref]
  2. J. J. Yeh and J. H. Eberly, Phys. Rev. A 24, 888 (1981).
    [Crossref]
  3. K. Wódkiewicz, Phys. Rev. A 19, 1686 (1979).
    [Crossref]
  4. J. H. Eberly, K. Wódkiewicz, and B. W. Shore, Phys. Rev. A 30, 2381 (1984).
    [Crossref]
  5. K. Wódkiewicz, B. W. Shore, and J. H. Eberly, Phys. Rev. A 30, 2390 (1984).
    [Crossref]
  6. K. Wódkiewicz, B. W. Shore, and J. H. Eberly, J. Opt. Soc. Am. B 1, 398 (1984).
    [Crossref]
  7. K. Wódkiewicz and J. H. Eberly, Phys. Rev. A 31, 2314 (1985).
    [Crossref]
  8. K. Wódkiewicz and J. J. Yeh, in Coherence and Quantum Optics V, L. Mandel and E. Wolf, eds. (Plenum, New York, 1984), p. 397 and references therein.
  9. M. Helm and P. Zoller, Opt. Commun. 49, 324 (1984); P. T. Greenland, J. Phys. B 17, 1919 (1984).
    [Crossref]
  10. We have recently also treated resonant excitation in which the Rabi frequency was comparable to the reservoir noise rate 1/τ. For a Gaussian model see M. Yamanoi and J. H. Eberly, J. Opt. Soc. Am. B 1, 751 (1984); for a jumptype model see K. Wódkiewicz and J. H. Eberly, Phys. Rev. 32, 992 (1985).
    [Crossref]
  11. B. R. Mollow, Phys. Rev. 175, 1555 (1968); G. S. Agarwal, Phys. Rev. A 1, 1445 (1970).
    [Crossref]
  12. D. S. Elliot, M. W. Hamilton, K. Arnett, and S. J. Smith, Phys. Rev. Lett. 53, 439 (1984); Phys. Rev. A 32, 887 (1985).
    [Crossref]

1985 (1)

K. Wódkiewicz and J. H. Eberly, Phys. Rev. A 31, 2314 (1985).
[Crossref]

1984 (6)

M. Helm and P. Zoller, Opt. Commun. 49, 324 (1984); P. T. Greenland, J. Phys. B 17, 1919 (1984).
[Crossref]

We have recently also treated resonant excitation in which the Rabi frequency was comparable to the reservoir noise rate 1/τ. For a Gaussian model see M. Yamanoi and J. H. Eberly, J. Opt. Soc. Am. B 1, 751 (1984); for a jumptype model see K. Wódkiewicz and J. H. Eberly, Phys. Rev. 32, 992 (1985).
[Crossref]

J. H. Eberly, K. Wódkiewicz, and B. W. Shore, Phys. Rev. A 30, 2381 (1984).
[Crossref]

K. Wódkiewicz, B. W. Shore, and J. H. Eberly, Phys. Rev. A 30, 2390 (1984).
[Crossref]

K. Wódkiewicz, B. W. Shore, and J. H. Eberly, J. Opt. Soc. Am. B 1, 398 (1984).
[Crossref]

D. S. Elliot, M. W. Hamilton, K. Arnett, and S. J. Smith, Phys. Rev. Lett. 53, 439 (1984); Phys. Rev. A 32, 887 (1985).
[Crossref]

1981 (1)

J. J. Yeh and J. H. Eberly, Phys. Rev. A 24, 888 (1981).
[Crossref]

1979 (2)

K. Wódkiewicz, Phys. Rev. A 19, 1686 (1979).
[Crossref]

P. Zoller and P. Lambropoulos, J. Phys. B 12, L547 (1979); S. N. Dixit, P. Zoller, and P. Lambropoulos, Phys. Rev. A 21, 1289 (1980).
[Crossref]

1968 (1)

B. R. Mollow, Phys. Rev. 175, 1555 (1968); G. S. Agarwal, Phys. Rev. A 1, 1445 (1970).
[Crossref]

Arnett, K.

D. S. Elliot, M. W. Hamilton, K. Arnett, and S. J. Smith, Phys. Rev. Lett. 53, 439 (1984); Phys. Rev. A 32, 887 (1985).
[Crossref]

Eberly, J. H.

Elliot, D. S.

D. S. Elliot, M. W. Hamilton, K. Arnett, and S. J. Smith, Phys. Rev. Lett. 53, 439 (1984); Phys. Rev. A 32, 887 (1985).
[Crossref]

Hamilton, M. W.

D. S. Elliot, M. W. Hamilton, K. Arnett, and S. J. Smith, Phys. Rev. Lett. 53, 439 (1984); Phys. Rev. A 32, 887 (1985).
[Crossref]

Helm, M.

M. Helm and P. Zoller, Opt. Commun. 49, 324 (1984); P. T. Greenland, J. Phys. B 17, 1919 (1984).
[Crossref]

Lambropoulos, P.

P. Zoller and P. Lambropoulos, J. Phys. B 12, L547 (1979); S. N. Dixit, P. Zoller, and P. Lambropoulos, Phys. Rev. A 21, 1289 (1980).
[Crossref]

Mollow, B. R.

B. R. Mollow, Phys. Rev. 175, 1555 (1968); G. S. Agarwal, Phys. Rev. A 1, 1445 (1970).
[Crossref]

Shore, B. W.

K. Wódkiewicz, B. W. Shore, and J. H. Eberly, J. Opt. Soc. Am. B 1, 398 (1984).
[Crossref]

J. H. Eberly, K. Wódkiewicz, and B. W. Shore, Phys. Rev. A 30, 2381 (1984).
[Crossref]

K. Wódkiewicz, B. W. Shore, and J. H. Eberly, Phys. Rev. A 30, 2390 (1984).
[Crossref]

Smith, S. J.

D. S. Elliot, M. W. Hamilton, K. Arnett, and S. J. Smith, Phys. Rev. Lett. 53, 439 (1984); Phys. Rev. A 32, 887 (1985).
[Crossref]

Wódkiewicz, K.

K. Wódkiewicz and J. H. Eberly, Phys. Rev. A 31, 2314 (1985).
[Crossref]

K. Wódkiewicz, B. W. Shore, and J. H. Eberly, J. Opt. Soc. Am. B 1, 398 (1984).
[Crossref]

K. Wódkiewicz, B. W. Shore, and J. H. Eberly, Phys. Rev. A 30, 2390 (1984).
[Crossref]

J. H. Eberly, K. Wódkiewicz, and B. W. Shore, Phys. Rev. A 30, 2381 (1984).
[Crossref]

K. Wódkiewicz, Phys. Rev. A 19, 1686 (1979).
[Crossref]

K. Wódkiewicz and J. J. Yeh, in Coherence and Quantum Optics V, L. Mandel and E. Wolf, eds. (Plenum, New York, 1984), p. 397 and references therein.

Yamanoi, M.

Yeh, J. J.

J. J. Yeh and J. H. Eberly, Phys. Rev. A 24, 888 (1981).
[Crossref]

K. Wódkiewicz and J. J. Yeh, in Coherence and Quantum Optics V, L. Mandel and E. Wolf, eds. (Plenum, New York, 1984), p. 397 and references therein.

Zoller, P.

M. Helm and P. Zoller, Opt. Commun. 49, 324 (1984); P. T. Greenland, J. Phys. B 17, 1919 (1984).
[Crossref]

P. Zoller and P. Lambropoulos, J. Phys. B 12, L547 (1979); S. N. Dixit, P. Zoller, and P. Lambropoulos, Phys. Rev. A 21, 1289 (1980).
[Crossref]

J. Opt. Soc. Am. B (2)

J. Phys. B (1)

P. Zoller and P. Lambropoulos, J. Phys. B 12, L547 (1979); S. N. Dixit, P. Zoller, and P. Lambropoulos, Phys. Rev. A 21, 1289 (1980).
[Crossref]

Opt. Commun. (1)

M. Helm and P. Zoller, Opt. Commun. 49, 324 (1984); P. T. Greenland, J. Phys. B 17, 1919 (1984).
[Crossref]

Phys. Rev. (1)

B. R. Mollow, Phys. Rev. 175, 1555 (1968); G. S. Agarwal, Phys. Rev. A 1, 1445 (1970).
[Crossref]

Phys. Rev. A (5)

K. Wódkiewicz and J. H. Eberly, Phys. Rev. A 31, 2314 (1985).
[Crossref]

J. J. Yeh and J. H. Eberly, Phys. Rev. A 24, 888 (1981).
[Crossref]

K. Wódkiewicz, Phys. Rev. A 19, 1686 (1979).
[Crossref]

J. H. Eberly, K. Wódkiewicz, and B. W. Shore, Phys. Rev. A 30, 2381 (1984).
[Crossref]

K. Wódkiewicz, B. W. Shore, and J. H. Eberly, Phys. Rev. A 30, 2390 (1984).
[Crossref]

Phys. Rev. Lett. (1)

D. S. Elliot, M. W. Hamilton, K. Arnett, and S. J. Smith, Phys. Rev. Lett. 53, 439 (1984); Phys. Rev. A 32, 887 (1985).
[Crossref]

Other (1)

K. Wódkiewicz and J. J. Yeh, in Coherence and Quantum Optics V, L. Mandel and E. Wolf, eds. (Plenum, New York, 1984), p. 397 and references therein.

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Equations (29)

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E ( t ) = E 0 exp [ - i ω L t - i ϕ ( t ) L ] ,
d ϕ ( t ) d t = μ ( t ) ,
μ ( t ) = 0 ,             μ ( t ) μ ( t + τ ) = a μ 2 exp ( - τ τ μ ) ,
t p ( μ t μ 0 t 0 ) = ( 1 τ μ μ μ + a μ 2 τ μ 2 μ 2 ) p ( μ t μ 0 t 0 ) .
t p ( ϕ t ϕ 0 t 0 ) = a μ 2 τ μ { 1 - exp [ - ( t / τ μ ) ] } 2 ϕ 2 p ( ϕ t ϕ 0 t 0 ) .
t p ( ϕ t ϕ 0 t 0 ) = γ μ 2 ϕ 2 p ( ϕ t ϕ 0 t 0 ) .
t p ( μ t μ 0 t 0 ) = D μ 2 μ 2 p ( μ t μ 0 t 0 ) ,
E ( t ) E * ( t + τ ) = E 0 2 exp ( i ω L τ ) C ( τ ) ,
C ( τ ) = exp [ - a μ 2 τ μ ( τ + τ μ { exp [ - ( τ / τ μ ) ] - 1 } ) ] .
ϕ ( t ) = 0 , ϕ ( t ) ϕ ( t + τ ) = a ϕ 2 exp [ - ( τ / τ ϕ ) ] ,
t p ( ϕ t ϕ 0 t 0 ) = ( 1 τ ϕ ϕ ϕ + a ϕ 2 τ ϕ 2 ϕ 2 ) p ( ϕ t ϕ 0 t 0 ) ,
C ( τ ) = exp ( - a ϕ 2 { 1 - exp [ - ( τ / τ ϕ ) ] } ) .
μ ( t ) = 0 ,             μ ( t + τ ) μ ( t ) = a μ 2 exp ( - τ τ μ ) ,
t p ( ϕ t ϕ 0 t 0 ) = a μ 2 t 0 t d s exp [ - ( t - s ) / τ μ ] 2 ϕ 2 p ( ϕ s ϕ 0 t 0 ) .
C ( τ ) = 1 2 ( 1 2 τ μ λ + 1 ) exp [ - ( 1 / 2 τ μ - λ ) τ ] - 1 2 ( 1 2 τ μ λ - 1 ) exp [ ( 1 / 2 τ μ + λ ) τ ] ,
t p ( ϕ t ϕ 0 t 0 ) = - 1 2 τ ϕ p ( ϕ t ϕ 0 t 0 ) + 1 2 τ ϕ p ( - ϕ t ϕ 0 t 0 ) ,
C ( τ ) = cos 2 a ϕ + sin 2 a ϕ exp ( - τ τ ϕ ) .
ϕ ( t ) = i = 1 n ϕ i θ ( t - t i )
t p ( ϕ t ϕ 0 t 0 ) = - 1 2 τ ϕ p ( ϕ t ϕ 0 t 0 ) + 1 2 τ ϕ d ϕ g ( ϕ - ϕ ) p ( ϕ t ϕ 0 t 0 ) .
C ( τ ) = exp ( - Γ ϕ τ ) ,
Γ ϕ = 1 2 τ ϕ [ 1 - d ϕ g ( ϕ ) e i ϕ ] .
μ ( t ) = d ϕ d t = i = 1 n ϕ i δ ( t - t i )
R I = R 2 c 4 β Ω N 2 0 d τ exp [ - ( β + i Δ ) τ ] C N ( τ ) ,
C N ( τ ) = exp { i N [ ϕ ( t + τ ) - ϕ ( t ) ] } .
Γ ϕ ( N ) = 1 2 τ ϕ [ 1 - d ϕ g ( ϕ ) e i N ϕ ] .
C N ( τ ) = exp ( - N 2 γ μ τ )             for frequency fluctuations ,
C N ( τ ) = exp ( - N 2 D ϕ τ )             for phase fluctuations .
R I = R 2 c 4 β Ω N 2 β + N 2 γ ˜ Δ 2 + ( β 2 + N 2 γ ˜ ) 2 ,
R I = R 2 c 4 β Ω N 2 [ β cos 2 ( π N 2 ) Δ 2 + β 2 + ( β + 1 τ ϕ ) sin 2 ( π N 2 ) Δ 2 + ( β + 1 τ ϕ ) 2 ] .

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