Abstract

We compare the collapse and revival occurring in the steady-state characteristics of the micromaser with the corresponding effects in the Jaynes–Cummings model.

© 1989 Optical Society of America

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References

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  1. E. T. Jaynes, F. W. Cummings, Proc. IEEE 51, 89 (1963).
    [Crossref]
  2. For a review see, e.g., S. M. Barnett, P. Filipowicz, J. Javanainen, P. L. Knight, P. Meystre, in Frontiers in Quantum Optics, E. R. Pike, S. Sarkar, eds. (Hilger, Bristol, U.K., 1986), p. 485.
  3. J. H. Eberly, N. B. Narozhny, J. J. Sanchez-Mondragon, Phys. Rev. Lett. 44, 1323 (1980); N. B. Narozhny, J. J. Sanchez-Mondragon, J. H. Eberly, Phys. Rev. A 23, 236 (1981).
    [Crossref]
  4. D. Meschede, H. Walther, G. Muller, Phys. Rev. Lett. 54, 551 (1985).
    [Crossref] [PubMed]
  5. M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, Phys. Rev. Lett. 59, 1899 (1987).
    [Crossref] [PubMed]
  6. G. Rempe, H. Walther, N. Klein, Phys. Rev. Lett. 58, 353 (1987).
    [Crossref] [PubMed]
  7. P. L. Knight, P. M. Radmore, Phys. Lett. 90A, 342 (1982).
  8. P. Meystre, G. Rempe, H. Walther, Opt. Lett. 13, 1078 (1988).
    [Crossref] [PubMed]
  9. P. Filipowicz, J. Javanainen, P. Meystre, Phys. Rev. A 34, 3077 (1986).
    [Crossref] [PubMed]
  10. F. W. Cummings, Phys. Rev. A 140, 1051 (1965).
  11. S. Stenholm, Phys. Rep. 6C, 1 (1973).
    [Crossref]
  12. P. Meystre, E. Geneux, A. Quattropani, A. Faist, Nuovo Cimento B 25, 521 (1975).
    [Crossref]
  13. T. von Foerster, J. Phys. A 8, 95 (1975).
    [Crossref]
  14. P. Filipowicz, J. Javanainen, P. Meystre, J. Opt. Soc. Am. B 3, 906 (1986).
    [Crossref]

1988 (1)

1987 (2)

M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, Phys. Rev. Lett. 59, 1899 (1987).
[Crossref] [PubMed]

G. Rempe, H. Walther, N. Klein, Phys. Rev. Lett. 58, 353 (1987).
[Crossref] [PubMed]

1986 (2)

P. Filipowicz, J. Javanainen, P. Meystre, Phys. Rev. A 34, 3077 (1986).
[Crossref] [PubMed]

P. Filipowicz, J. Javanainen, P. Meystre, J. Opt. Soc. Am. B 3, 906 (1986).
[Crossref]

1985 (1)

D. Meschede, H. Walther, G. Muller, Phys. Rev. Lett. 54, 551 (1985).
[Crossref] [PubMed]

1982 (1)

P. L. Knight, P. M. Radmore, Phys. Lett. 90A, 342 (1982).

1980 (1)

J. H. Eberly, N. B. Narozhny, J. J. Sanchez-Mondragon, Phys. Rev. Lett. 44, 1323 (1980); N. B. Narozhny, J. J. Sanchez-Mondragon, J. H. Eberly, Phys. Rev. A 23, 236 (1981).
[Crossref]

1975 (2)

P. Meystre, E. Geneux, A. Quattropani, A. Faist, Nuovo Cimento B 25, 521 (1975).
[Crossref]

T. von Foerster, J. Phys. A 8, 95 (1975).
[Crossref]

1973 (1)

S. Stenholm, Phys. Rep. 6C, 1 (1973).
[Crossref]

1965 (1)

F. W. Cummings, Phys. Rev. A 140, 1051 (1965).

1963 (1)

E. T. Jaynes, F. W. Cummings, Proc. IEEE 51, 89 (1963).
[Crossref]

Barnett, S. M.

For a review see, e.g., S. M. Barnett, P. Filipowicz, J. Javanainen, P. L. Knight, P. Meystre, in Frontiers in Quantum Optics, E. R. Pike, S. Sarkar, eds. (Hilger, Bristol, U.K., 1986), p. 485.

Brune, M.

M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, Phys. Rev. Lett. 59, 1899 (1987).
[Crossref] [PubMed]

Cummings, F. W.

F. W. Cummings, Phys. Rev. A 140, 1051 (1965).

E. T. Jaynes, F. W. Cummings, Proc. IEEE 51, 89 (1963).
[Crossref]

Davidovich, L.

M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, Phys. Rev. Lett. 59, 1899 (1987).
[Crossref] [PubMed]

Eberly, J. H.

J. H. Eberly, N. B. Narozhny, J. J. Sanchez-Mondragon, Phys. Rev. Lett. 44, 1323 (1980); N. B. Narozhny, J. J. Sanchez-Mondragon, J. H. Eberly, Phys. Rev. A 23, 236 (1981).
[Crossref]

Faist, A.

P. Meystre, E. Geneux, A. Quattropani, A. Faist, Nuovo Cimento B 25, 521 (1975).
[Crossref]

Filipowicz, P.

P. Filipowicz, J. Javanainen, P. Meystre, J. Opt. Soc. Am. B 3, 906 (1986).
[Crossref]

P. Filipowicz, J. Javanainen, P. Meystre, Phys. Rev. A 34, 3077 (1986).
[Crossref] [PubMed]

For a review see, e.g., S. M. Barnett, P. Filipowicz, J. Javanainen, P. L. Knight, P. Meystre, in Frontiers in Quantum Optics, E. R. Pike, S. Sarkar, eds. (Hilger, Bristol, U.K., 1986), p. 485.

Geneux, E.

P. Meystre, E. Geneux, A. Quattropani, A. Faist, Nuovo Cimento B 25, 521 (1975).
[Crossref]

Goy, P.

M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, Phys. Rev. Lett. 59, 1899 (1987).
[Crossref] [PubMed]

Haroche, S.

M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, Phys. Rev. Lett. 59, 1899 (1987).
[Crossref] [PubMed]

Javanainen, J.

P. Filipowicz, J. Javanainen, P. Meystre, Phys. Rev. A 34, 3077 (1986).
[Crossref] [PubMed]

P. Filipowicz, J. Javanainen, P. Meystre, J. Opt. Soc. Am. B 3, 906 (1986).
[Crossref]

For a review see, e.g., S. M. Barnett, P. Filipowicz, J. Javanainen, P. L. Knight, P. Meystre, in Frontiers in Quantum Optics, E. R. Pike, S. Sarkar, eds. (Hilger, Bristol, U.K., 1986), p. 485.

Jaynes, E. T.

E. T. Jaynes, F. W. Cummings, Proc. IEEE 51, 89 (1963).
[Crossref]

Klein, N.

G. Rempe, H. Walther, N. Klein, Phys. Rev. Lett. 58, 353 (1987).
[Crossref] [PubMed]

Knight, P. L.

P. L. Knight, P. M. Radmore, Phys. Lett. 90A, 342 (1982).

For a review see, e.g., S. M. Barnett, P. Filipowicz, J. Javanainen, P. L. Knight, P. Meystre, in Frontiers in Quantum Optics, E. R. Pike, S. Sarkar, eds. (Hilger, Bristol, U.K., 1986), p. 485.

Meschede, D.

D. Meschede, H. Walther, G. Muller, Phys. Rev. Lett. 54, 551 (1985).
[Crossref] [PubMed]

Meystre, P.

P. Meystre, G. Rempe, H. Walther, Opt. Lett. 13, 1078 (1988).
[Crossref] [PubMed]

P. Filipowicz, J. Javanainen, P. Meystre, Phys. Rev. A 34, 3077 (1986).
[Crossref] [PubMed]

P. Filipowicz, J. Javanainen, P. Meystre, J. Opt. Soc. Am. B 3, 906 (1986).
[Crossref]

P. Meystre, E. Geneux, A. Quattropani, A. Faist, Nuovo Cimento B 25, 521 (1975).
[Crossref]

For a review see, e.g., S. M. Barnett, P. Filipowicz, J. Javanainen, P. L. Knight, P. Meystre, in Frontiers in Quantum Optics, E. R. Pike, S. Sarkar, eds. (Hilger, Bristol, U.K., 1986), p. 485.

Muller, G.

D. Meschede, H. Walther, G. Muller, Phys. Rev. Lett. 54, 551 (1985).
[Crossref] [PubMed]

Narozhny, N. B.

J. H. Eberly, N. B. Narozhny, J. J. Sanchez-Mondragon, Phys. Rev. Lett. 44, 1323 (1980); N. B. Narozhny, J. J. Sanchez-Mondragon, J. H. Eberly, Phys. Rev. A 23, 236 (1981).
[Crossref]

Quattropani, A.

P. Meystre, E. Geneux, A. Quattropani, A. Faist, Nuovo Cimento B 25, 521 (1975).
[Crossref]

Radmore, P. M.

P. L. Knight, P. M. Radmore, Phys. Lett. 90A, 342 (1982).

Raimond, J. M.

M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, Phys. Rev. Lett. 59, 1899 (1987).
[Crossref] [PubMed]

Rempe, G.

Sanchez-Mondragon, J. J.

J. H. Eberly, N. B. Narozhny, J. J. Sanchez-Mondragon, Phys. Rev. Lett. 44, 1323 (1980); N. B. Narozhny, J. J. Sanchez-Mondragon, J. H. Eberly, Phys. Rev. A 23, 236 (1981).
[Crossref]

Stenholm, S.

S. Stenholm, Phys. Rep. 6C, 1 (1973).
[Crossref]

von Foerster, T.

T. von Foerster, J. Phys. A 8, 95 (1975).
[Crossref]

Walther, H.

P. Meystre, G. Rempe, H. Walther, Opt. Lett. 13, 1078 (1988).
[Crossref] [PubMed]

G. Rempe, H. Walther, N. Klein, Phys. Rev. Lett. 58, 353 (1987).
[Crossref] [PubMed]

D. Meschede, H. Walther, G. Muller, Phys. Rev. Lett. 54, 551 (1985).
[Crossref] [PubMed]

J. Opt. Soc. Am. B (1)

J. Phys. A (1)

T. von Foerster, J. Phys. A 8, 95 (1975).
[Crossref]

Nuovo Cimento B (1)

P. Meystre, E. Geneux, A. Quattropani, A. Faist, Nuovo Cimento B 25, 521 (1975).
[Crossref]

Opt. Lett. (1)

Phys. Lett. (1)

P. L. Knight, P. M. Radmore, Phys. Lett. 90A, 342 (1982).

Phys. Rep. (1)

S. Stenholm, Phys. Rep. 6C, 1 (1973).
[Crossref]

Phys. Rev. A (2)

P. Filipowicz, J. Javanainen, P. Meystre, Phys. Rev. A 34, 3077 (1986).
[Crossref] [PubMed]

F. W. Cummings, Phys. Rev. A 140, 1051 (1965).

Phys. Rev. Lett. (4)

J. H. Eberly, N. B. Narozhny, J. J. Sanchez-Mondragon, Phys. Rev. Lett. 44, 1323 (1980); N. B. Narozhny, J. J. Sanchez-Mondragon, J. H. Eberly, Phys. Rev. A 23, 236 (1981).
[Crossref]

D. Meschede, H. Walther, G. Muller, Phys. Rev. Lett. 54, 551 (1985).
[Crossref] [PubMed]

M. Brune, J. M. Raimond, P. Goy, L. Davidovich, S. Haroche, Phys. Rev. Lett. 59, 1899 (1987).
[Crossref] [PubMed]

G. Rempe, H. Walther, N. Klein, Phys. Rev. Lett. 58, 353 (1987).
[Crossref] [PubMed]

Proc. IEEE (1)

E. T. Jaynes, F. W. Cummings, Proc. IEEE 51, 89 (1963).
[Crossref]

Other (1)

For a review see, e.g., S. M. Barnett, P. Filipowicz, J. Javanainen, P. L. Knight, P. Meystre, in Frontiers in Quantum Optics, E. R. Pike, S. Sarkar, eds. (Hilger, Bristol, U.K., 1986), p. 485.

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Figures (4)

Fig. 1
Fig. 1

Mean photon number 〈n〉 as a function of the pump parameter θ for Nex = 50 and (a) nb = 5, (b) nb = 0.5, (c) nb = 0.05.

Fig. 2
Fig. 2

(a) Mean photon number 〈n〉 as a function of the pump parameter θ for Nex = 50 and nb = 2.

Fig. 3
Fig. 3

Steady-state photon statistics of the micromaser for Nex = 50, θ = 10π, and (a) nb = 5, (b) nb = 0.5, (c) nb = 0.05.

Fig. 4
Fig. 4

Comparison between the exact (solid curve) and Fokker–Planck (dashed line) predictions of the mean photon number 〈n(d)〉 for Nex = 15 and nb = 1. In the collapse region the two curves coincide exactly.

Equations (5)

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p ¯ n = C ( n b 1 + n b ) n k = 1 n [ 1 + N ex n b k sin 2 ( θ k / N ex ) ] .
n = k = 0 k p ¯ k ,
p a = k = 0 p ¯ k cos 2 { θ [ ( k + 1 ) / N ex ] 1 / 2 } .
n = n b + N ex ( 1 p a ) ,
P τ = ν [ q ( ν ) P ] + 1 2 N ex 2 ν 2 [ g ( ν ) P ] ,

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