Abstract

Interactions between a three-level atom and two amplitude-fluctuating lasers are studied theoretically. One interesting feature of the interactions is the influence of the finite laser bandwidth and the two-laser cross-bandwidth on the absorption rate into the third level. As an example, it is shown how the partially saturated absorption process depends on both the autocorrelated and cross-correlated laser bandwidths.

© 1977 Optical Society of America

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  1. An excellent review of work in the atomic multiphoton field up to 1975 has been prepared by P. Lambropoulos, in Advances in Atomic and Molecular Physics, D. R. Bates, ed. (Academic, New York, 1976), Vol. 12. More recent work, especially concerning multiphoton processes in molecules, has yet to be reviewed.
    [CrossRef]
  2. An early exception is P. Lambropoulos, Phys. Rev. A 9, 1992 (1974).See also these papers presented at the International Conference on Multiphoton Processes, Rochester, N.Y., June 1977:L. Armstrong, in Multiphoton Processes, J. H. Eberly, P. Lambropoulos, eds. (Wiley, New York, in press);M. Crance, in ICOMP Abstracts, (available from Department of Physics and Astronomy, University of Rochester), p. 97;J. R. Ackerhalt, in ICOMP Abstracts, p. 99.
    [CrossRef]
  3. See the review by G. Mainfray, in Multiphoton Processes,and the recent results of P. Agostiniet al., in ICOMP Abstracts,2 p. 95.
  4. R. V. Ambartzumian, N. P. Furzikov, Yu. Gorokhov, V. S. Letokhov, G. N. Makarov, A. A. Puretzky, Opt. Lett. 1, 22 (1977);see also V. S. Letokhov, in Multiphoton Processes.2
    [CrossRef] [PubMed]
  5. The correlation function ansatz used in Eqs. (3) is a generalization of a simpler ansatz found convenient in the theory of strong-field resonance fluorescence: J. H. Eberly, Phys. Rev. Lett. 37, 1387 (1976).For a comparison of several stochastic models of laser light in coherent interactions, see P. Zoller, F. Ehlotzky, in ICOMP Abstracts,2 p. 109. Note also that Eqs. (3) are far from sufficient to specify all the statistical features of our lasers. In particular, they do not specify relations among γ1, γ2, and γ12. However, it is clear that some relations must be implied. For example, it appears quite unphysical that γ1 ≠ 0, γ2 ≠ 0, and γ12 = 0 should be possible. Using one particular phase-diffusion model, K. Wódkiewicz, Institute of Theoretical Physics, Warsaw University, 00-681 Warsaw, Poland (private communication) finds that stationarity of the crosscorrelation is possible only if γ12 = 1/2(γ1 + γ2), thus providing one example of a relation among the bandwidths.
    [CrossRef]
  6. P. W. Milonni, Phys. Rep. 25C, 1 (1976);see also J. R. Ackerhalt, J. H. Eberly, Phys. Rev. A 14, 1705 (1976) for an application to high-power excitation of a three-level system.
    [CrossRef]
  7. N. C. Wong (Senior Thesis, Department of Physics and Astronomy, University of Rochester, 1977).
  8. Equation (5) demonstrates the utility of the concept of Rabi frequency in a discussion of transition rates. Basically, a transition rate is given simply by the square of the Rabi frequency divided by the effective linewidth of the transition. A discussion of the relation among Rabi frequencies, linewidths, and transition rates is given in J. R. Ackerhalt and J. H. Eberly, Ref. 6, particularly in the appendix.

1977 (1)

1976 (2)

The correlation function ansatz used in Eqs. (3) is a generalization of a simpler ansatz found convenient in the theory of strong-field resonance fluorescence: J. H. Eberly, Phys. Rev. Lett. 37, 1387 (1976).For a comparison of several stochastic models of laser light in coherent interactions, see P. Zoller, F. Ehlotzky, in ICOMP Abstracts,2 p. 109. Note also that Eqs. (3) are far from sufficient to specify all the statistical features of our lasers. In particular, they do not specify relations among γ1, γ2, and γ12. However, it is clear that some relations must be implied. For example, it appears quite unphysical that γ1 ≠ 0, γ2 ≠ 0, and γ12 = 0 should be possible. Using one particular phase-diffusion model, K. Wódkiewicz, Institute of Theoretical Physics, Warsaw University, 00-681 Warsaw, Poland (private communication) finds that stationarity of the crosscorrelation is possible only if γ12 = 1/2(γ1 + γ2), thus providing one example of a relation among the bandwidths.
[CrossRef]

P. W. Milonni, Phys. Rep. 25C, 1 (1976);see also J. R. Ackerhalt, J. H. Eberly, Phys. Rev. A 14, 1705 (1976) for an application to high-power excitation of a three-level system.
[CrossRef]

1974 (1)

An early exception is P. Lambropoulos, Phys. Rev. A 9, 1992 (1974).See also these papers presented at the International Conference on Multiphoton Processes, Rochester, N.Y., June 1977:L. Armstrong, in Multiphoton Processes, J. H. Eberly, P. Lambropoulos, eds. (Wiley, New York, in press);M. Crance, in ICOMP Abstracts, (available from Department of Physics and Astronomy, University of Rochester), p. 97;J. R. Ackerhalt, in ICOMP Abstracts, p. 99.
[CrossRef]

Ambartzumian, R. V.

Eberly, J. H.

The correlation function ansatz used in Eqs. (3) is a generalization of a simpler ansatz found convenient in the theory of strong-field resonance fluorescence: J. H. Eberly, Phys. Rev. Lett. 37, 1387 (1976).For a comparison of several stochastic models of laser light in coherent interactions, see P. Zoller, F. Ehlotzky, in ICOMP Abstracts,2 p. 109. Note also that Eqs. (3) are far from sufficient to specify all the statistical features of our lasers. In particular, they do not specify relations among γ1, γ2, and γ12. However, it is clear that some relations must be implied. For example, it appears quite unphysical that γ1 ≠ 0, γ2 ≠ 0, and γ12 = 0 should be possible. Using one particular phase-diffusion model, K. Wódkiewicz, Institute of Theoretical Physics, Warsaw University, 00-681 Warsaw, Poland (private communication) finds that stationarity of the crosscorrelation is possible only if γ12 = 1/2(γ1 + γ2), thus providing one example of a relation among the bandwidths.
[CrossRef]

Furzikov, N. P.

Gorokhov, Yu.

Lambropoulos, P.

An early exception is P. Lambropoulos, Phys. Rev. A 9, 1992 (1974).See also these papers presented at the International Conference on Multiphoton Processes, Rochester, N.Y., June 1977:L. Armstrong, in Multiphoton Processes, J. H. Eberly, P. Lambropoulos, eds. (Wiley, New York, in press);M. Crance, in ICOMP Abstracts, (available from Department of Physics and Astronomy, University of Rochester), p. 97;J. R. Ackerhalt, in ICOMP Abstracts, p. 99.
[CrossRef]

An excellent review of work in the atomic multiphoton field up to 1975 has been prepared by P. Lambropoulos, in Advances in Atomic and Molecular Physics, D. R. Bates, ed. (Academic, New York, 1976), Vol. 12. More recent work, especially concerning multiphoton processes in molecules, has yet to be reviewed.
[CrossRef]

Letokhov, V. S.

Mainfray, G.

See the review by G. Mainfray, in Multiphoton Processes,and the recent results of P. Agostiniet al., in ICOMP Abstracts,2 p. 95.

Makarov, G. N.

Milonni, P. W.

P. W. Milonni, Phys. Rep. 25C, 1 (1976);see also J. R. Ackerhalt, J. H. Eberly, Phys. Rev. A 14, 1705 (1976) for an application to high-power excitation of a three-level system.
[CrossRef]

Puretzky, A. A.

Wong, N. C.

N. C. Wong (Senior Thesis, Department of Physics and Astronomy, University of Rochester, 1977).

Opt. Lett. (1)

Phys. Rep. (1)

P. W. Milonni, Phys. Rep. 25C, 1 (1976);see also J. R. Ackerhalt, J. H. Eberly, Phys. Rev. A 14, 1705 (1976) for an application to high-power excitation of a three-level system.
[CrossRef]

Phys. Rev. A (1)

An early exception is P. Lambropoulos, Phys. Rev. A 9, 1992 (1974).See also these papers presented at the International Conference on Multiphoton Processes, Rochester, N.Y., June 1977:L. Armstrong, in Multiphoton Processes, J. H. Eberly, P. Lambropoulos, eds. (Wiley, New York, in press);M. Crance, in ICOMP Abstracts, (available from Department of Physics and Astronomy, University of Rochester), p. 97;J. R. Ackerhalt, in ICOMP Abstracts, p. 99.
[CrossRef]

Phys. Rev. Lett. (1)

The correlation function ansatz used in Eqs. (3) is a generalization of a simpler ansatz found convenient in the theory of strong-field resonance fluorescence: J. H. Eberly, Phys. Rev. Lett. 37, 1387 (1976).For a comparison of several stochastic models of laser light in coherent interactions, see P. Zoller, F. Ehlotzky, in ICOMP Abstracts,2 p. 109. Note also that Eqs. (3) are far from sufficient to specify all the statistical features of our lasers. In particular, they do not specify relations among γ1, γ2, and γ12. However, it is clear that some relations must be implied. For example, it appears quite unphysical that γ1 ≠ 0, γ2 ≠ 0, and γ12 = 0 should be possible. Using one particular phase-diffusion model, K. Wódkiewicz, Institute of Theoretical Physics, Warsaw University, 00-681 Warsaw, Poland (private communication) finds that stationarity of the crosscorrelation is possible only if γ12 = 1/2(γ1 + γ2), thus providing one example of a relation among the bandwidths.
[CrossRef]

Other (4)

See the review by G. Mainfray, in Multiphoton Processes,and the recent results of P. Agostiniet al., in ICOMP Abstracts,2 p. 95.

N. C. Wong (Senior Thesis, Department of Physics and Astronomy, University of Rochester, 1977).

Equation (5) demonstrates the utility of the concept of Rabi frequency in a discussion of transition rates. Basically, a transition rate is given simply by the square of the Rabi frequency divided by the effective linewidth of the transition. A discussion of the relation among Rabi frequencies, linewidths, and transition rates is given in J. R. Ackerhalt and J. H. Eberly, Ref. 6, particularly in the appendix.

An excellent review of work in the atomic multiphoton field up to 1975 has been prepared by P. Lambropoulos, in Advances in Atomic and Molecular Physics, D. R. Bates, ed. (Academic, New York, 1976), Vol. 12. More recent work, especially concerning multiphoton processes in molecules, has yet to be reviewed.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

The model three-level atom, showing relative linewidths.

Fig. 2
Fig. 2

Two views of the same absorption-rate surface. The height of the surface above the axis plane indicates the absorption rate into the atom's third level as a function of the second laser's Rabi frequency and bandwidth. The regions numbered 1, 2, and 3 correspond to the expressions given in Eqs. (7)(9) in the text. For analytic expressions appropriate to other portions of the rate surface, see Wong.7

Equations (12)

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E ( t ) = 12 ( t ) e i ν 12 t + 23 ( t ) e i ν 23 t + c . c . ,
Ω 1 ( t ) = 2 D 12 12 ( t ) ,
Ω 2 ( t ) = 2 D 23 23 ( t ) ,
Ω 1 ( t ) Ω 1 ( t ) = Ω 10 2 exp ( 1 2 γ 1 | t t | ) ,
Ω 2 ( t ) Ω 2 ( t ) = Ω 20 2 exp ( 1 2 γ 2 | t t | ) ,
Ω 1 ( t ) Ω 2 ( t ) = Ω 10 Ω 20 exp ( 1 2 γ 12 | t t | ) ,
σ ˙ 33 = Ω 1 2 1 / τ 2 + γ 1 1 1 / τ 2 Ω 2 2 1 / τ 3 .
σ ˙ 33 = [ Ω 1 2 1 / τ 2 + Ω 2 2 / ( 1 / τ 3 + γ 2 ) ] [ 1 1 / τ 2 Ω 2 2 / 1 / τ 3 1 / τ 2 + Ω 2 2 / 1 / τ 3 + γ 2 ( 1 / τ 2 + γ 2 ) ( 1 / τ 2 + γ 12 ) 2 ] ( Ω 2 2 1 / τ 3 + γ 2 ) .
σ ˙ 33 = Ω 1 2 1 / τ 2 1 1 / τ 2 Ω 2 2 1 / τ 3 + γ 2 ,
γ 12 ~ γ 2 1 / τ 2 , σ ˙ 33 = Ω 1 2 Ω 2 2 / 1 / τ 3 ;
γ 12 ~ γ 2 ~ 1 / τ 2 , σ ˙ 33 = Ω 1 2 1 / τ 2 [ 1 1 / τ 2 ( 1 / τ 2 + γ 2 ) ( 1 / τ 2 + γ 12 ) 2 ] ;
γ 12 ~ γ 2 1 / τ 3 , σ ˙ 33 = Ω 1 2 1 / τ 2 1 1 / τ 2 + Ω 2 2 / γ 2 Ω 2 2 γ 2 .

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