Abstract

A laser-driven molecular species A, represented as a two-level system, is taken to react forming a finite-level molecular species B. Criteria are developed that, when satisfied, enable this model to be approximated by a two-level molecular A system reacting to form a single-level molecular species B. Further criteria are then developed that, when satisfied, enable this model to be approximated by a two-level molecular species A with irreversible population loss.

© 1980 Optical Society of America

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References

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  1. N. Bloembergen, E. Yablonovitch, Phys. Today 31, 23 (1978), and references therein; J. R. Ackerhalt, H. W. Galbraith, Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87545, to be published.
    [CrossRef]
  2. J. G. Black, P. Kolodner, M. J. Shutz, E. Yablonovitch, N. Bloembergen, Phys. Rev. A 19, 704 (1979).
    [CrossRef]
  3. M. P. Silverman, F. M. Pipkin, J. Phys. B 5, 1844 (1972).
    [CrossRef]
  4. M. F. Goodman, J. Stone, D. A. Dows, J. Chem. Phys. 65, 5052 (1976); M. F. Goodman, E. Thiele, Phys. Rev. A 5, 1355 (1972); J. Stone, M. F. Goodman, Phys. Rev. A 14, 380 (1976); J. Stone, M. F. Goodman, D. A. Dows, J. Chem. Phys. 65, 5062 (1976).
    [CrossRef]
  5. C. M. Bowden, N. M. Witriol, C. A. Coulter, Opt. Commun. 23, 389 (1977).
    [CrossRef]
  6. I. R. Senitzky, Phys. Rev. A 10, 1868 (1974).
    [CrossRef]
  7. R. Gilmore, C. M. Bowden, L. M. Narducci, Phys. Rev. A 12, 1019 (1975); “c-number representation for multilevel systems and the quantum-classical correspondence,” in Quantum Statistics and the Many-Body Problem, S. B. Trickey, W. P. Kirk, T. W. Dufty, eds. (Plenum, New York, 1975).
    [CrossRef]

1979 (1)

J. G. Black, P. Kolodner, M. J. Shutz, E. Yablonovitch, N. Bloembergen, Phys. Rev. A 19, 704 (1979).
[CrossRef]

1978 (1)

N. Bloembergen, E. Yablonovitch, Phys. Today 31, 23 (1978), and references therein; J. R. Ackerhalt, H. W. Galbraith, Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87545, to be published.
[CrossRef]

1977 (1)

C. M. Bowden, N. M. Witriol, C. A. Coulter, Opt. Commun. 23, 389 (1977).
[CrossRef]

1976 (1)

M. F. Goodman, J. Stone, D. A. Dows, J. Chem. Phys. 65, 5052 (1976); M. F. Goodman, E. Thiele, Phys. Rev. A 5, 1355 (1972); J. Stone, M. F. Goodman, Phys. Rev. A 14, 380 (1976); J. Stone, M. F. Goodman, D. A. Dows, J. Chem. Phys. 65, 5062 (1976).
[CrossRef]

1975 (1)

R. Gilmore, C. M. Bowden, L. M. Narducci, Phys. Rev. A 12, 1019 (1975); “c-number representation for multilevel systems and the quantum-classical correspondence,” in Quantum Statistics and the Many-Body Problem, S. B. Trickey, W. P. Kirk, T. W. Dufty, eds. (Plenum, New York, 1975).
[CrossRef]

1974 (1)

I. R. Senitzky, Phys. Rev. A 10, 1868 (1974).
[CrossRef]

1972 (1)

M. P. Silverman, F. M. Pipkin, J. Phys. B 5, 1844 (1972).
[CrossRef]

Black, J. G.

J. G. Black, P. Kolodner, M. J. Shutz, E. Yablonovitch, N. Bloembergen, Phys. Rev. A 19, 704 (1979).
[CrossRef]

Bloembergen, N.

J. G. Black, P. Kolodner, M. J. Shutz, E. Yablonovitch, N. Bloembergen, Phys. Rev. A 19, 704 (1979).
[CrossRef]

N. Bloembergen, E. Yablonovitch, Phys. Today 31, 23 (1978), and references therein; J. R. Ackerhalt, H. W. Galbraith, Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87545, to be published.
[CrossRef]

Bowden, C. M.

C. M. Bowden, N. M. Witriol, C. A. Coulter, Opt. Commun. 23, 389 (1977).
[CrossRef]

R. Gilmore, C. M. Bowden, L. M. Narducci, Phys. Rev. A 12, 1019 (1975); “c-number representation for multilevel systems and the quantum-classical correspondence,” in Quantum Statistics and the Many-Body Problem, S. B. Trickey, W. P. Kirk, T. W. Dufty, eds. (Plenum, New York, 1975).
[CrossRef]

Coulter, C. A.

C. M. Bowden, N. M. Witriol, C. A. Coulter, Opt. Commun. 23, 389 (1977).
[CrossRef]

Dows, D. A.

M. F. Goodman, J. Stone, D. A. Dows, J. Chem. Phys. 65, 5052 (1976); M. F. Goodman, E. Thiele, Phys. Rev. A 5, 1355 (1972); J. Stone, M. F. Goodman, Phys. Rev. A 14, 380 (1976); J. Stone, M. F. Goodman, D. A. Dows, J. Chem. Phys. 65, 5062 (1976).
[CrossRef]

Gilmore, R.

R. Gilmore, C. M. Bowden, L. M. Narducci, Phys. Rev. A 12, 1019 (1975); “c-number representation for multilevel systems and the quantum-classical correspondence,” in Quantum Statistics and the Many-Body Problem, S. B. Trickey, W. P. Kirk, T. W. Dufty, eds. (Plenum, New York, 1975).
[CrossRef]

Goodman, M. F.

M. F. Goodman, J. Stone, D. A. Dows, J. Chem. Phys. 65, 5052 (1976); M. F. Goodman, E. Thiele, Phys. Rev. A 5, 1355 (1972); J. Stone, M. F. Goodman, Phys. Rev. A 14, 380 (1976); J. Stone, M. F. Goodman, D. A. Dows, J. Chem. Phys. 65, 5062 (1976).
[CrossRef]

Kolodner, P.

J. G. Black, P. Kolodner, M. J. Shutz, E. Yablonovitch, N. Bloembergen, Phys. Rev. A 19, 704 (1979).
[CrossRef]

Narducci, L. M.

R. Gilmore, C. M. Bowden, L. M. Narducci, Phys. Rev. A 12, 1019 (1975); “c-number representation for multilevel systems and the quantum-classical correspondence,” in Quantum Statistics and the Many-Body Problem, S. B. Trickey, W. P. Kirk, T. W. Dufty, eds. (Plenum, New York, 1975).
[CrossRef]

Pipkin, F. M.

M. P. Silverman, F. M. Pipkin, J. Phys. B 5, 1844 (1972).
[CrossRef]

Senitzky, I. R.

I. R. Senitzky, Phys. Rev. A 10, 1868 (1974).
[CrossRef]

Shutz, M. J.

J. G. Black, P. Kolodner, M. J. Shutz, E. Yablonovitch, N. Bloembergen, Phys. Rev. A 19, 704 (1979).
[CrossRef]

Silverman, M. P.

M. P. Silverman, F. M. Pipkin, J. Phys. B 5, 1844 (1972).
[CrossRef]

Stone, J.

M. F. Goodman, J. Stone, D. A. Dows, J. Chem. Phys. 65, 5052 (1976); M. F. Goodman, E. Thiele, Phys. Rev. A 5, 1355 (1972); J. Stone, M. F. Goodman, Phys. Rev. A 14, 380 (1976); J. Stone, M. F. Goodman, D. A. Dows, J. Chem. Phys. 65, 5062 (1976).
[CrossRef]

Witriol, N. M.

C. M. Bowden, N. M. Witriol, C. A. Coulter, Opt. Commun. 23, 389 (1977).
[CrossRef]

Yablonovitch, E.

J. G. Black, P. Kolodner, M. J. Shutz, E. Yablonovitch, N. Bloembergen, Phys. Rev. A 19, 704 (1979).
[CrossRef]

N. Bloembergen, E. Yablonovitch, Phys. Today 31, 23 (1978), and references therein; J. R. Ackerhalt, H. W. Galbraith, Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87545, to be published.
[CrossRef]

J. Chem. Phys. (1)

M. F. Goodman, J. Stone, D. A. Dows, J. Chem. Phys. 65, 5052 (1976); M. F. Goodman, E. Thiele, Phys. Rev. A 5, 1355 (1972); J. Stone, M. F. Goodman, Phys. Rev. A 14, 380 (1976); J. Stone, M. F. Goodman, D. A. Dows, J. Chem. Phys. 65, 5062 (1976).
[CrossRef]

J. Phys. B (1)

M. P. Silverman, F. M. Pipkin, J. Phys. B 5, 1844 (1972).
[CrossRef]

Opt. Commun. (1)

C. M. Bowden, N. M. Witriol, C. A. Coulter, Opt. Commun. 23, 389 (1977).
[CrossRef]

Phys. Rev. A (3)

I. R. Senitzky, Phys. Rev. A 10, 1868 (1974).
[CrossRef]

R. Gilmore, C. M. Bowden, L. M. Narducci, Phys. Rev. A 12, 1019 (1975); “c-number representation for multilevel systems and the quantum-classical correspondence,” in Quantum Statistics and the Many-Body Problem, S. B. Trickey, W. P. Kirk, T. W. Dufty, eds. (Plenum, New York, 1975).
[CrossRef]

J. G. Black, P. Kolodner, M. J. Shutz, E. Yablonovitch, N. Bloembergen, Phys. Rev. A 19, 704 (1979).
[CrossRef]

Phys. Today (1)

N. Bloembergen, E. Yablonovitch, Phys. Today 31, 23 (1978), and references therein; J. R. Ackerhalt, H. W. Galbraith, Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87545, to be published.
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Schematic diagrams of a two-level A molecule (a) reacting from the upper level to form M levels of a B molecule, which are in turn coupled to a reservoir; (b) reacting from the upper level to form a B molecule, which in turn is coupled to a reservoir; (c) with the upper level coupled directly to a reservoir.

Equations (12)

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α ˙ 0 = - i ω R a 1 exp ( - i Ω t ) , a ˙ 1 = - i ω R a 0 exp ( i Ω t ) - i j = 1 M g j * b j exp ( - i σ j t ) , b ˙ j = - i g j a 1 exp ( i σ j t ) - γ j b j ,             j = 1 , , M ,
a 1 ( s ) = - i ω R × [ 1 s 2 - i Ω s + ω R 2 + ( s - i Ω ) ( j = 1 M g j 2 s + γ j + i σ j ) ] .
a ˙ 0 = - i ω R a 1 exp ( - i Ω t ) , a ˙ 1 = - i ω R a 0 exp ( i Ω t ) - i g * b exp ( - i σ t ) , b ˙ = i g a 1 exp ( i σ t ) - γ B b ,
a 1 ( s ) = - i ω R [ 1 s 2 - i Ω s + ω R 2 + ( s - i Ω ) g 2 ( s + γ B + i σ ) ] .
σ j σ k , j , k = 1 , , M , γ j γ k , j , k = 1 , , M ,
σ σ j , γ γ j , g 2 j = 1 M g j 2 ;
γ = γ j γ k , j , k = 1 , , M , γ j σ j , j = 1 , , M ,
γ γ j , g 2 = j = 1 M g j 2 , σ = j = 1 M g j 2 σ j g 2 .
a ˙ 0 = - i ω R a 1 exp ( - i Ω t ) , a ˙ 1 = - i ω R a 0 exp ( i Ω t ) - γ A a 1 .
a 1 ( s ) = - i ω R [ 1 s 2 + ( γ A - i Ω ) s + ( ω R 2 - i Ω γ A ) ] .
γ B 2 + ω R 2 g 2 , γ B , ω R σ , Ω ,
γ A = g 2 γ B γ B 2 + ω R 2 .

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