Abstract

Coherent and incoherent manifestations of light-pressure effects are considered. A simple analytical solution of the quantum problem of atomic scattering in a standing-wave field for arbitrarily large numbers of spontaneous transitions is obtained. Attractors of the light-pressure force in a strong field, i.e., the critical velocities at which a bunching of the particles takes place, are found. The one-dimensional problem of self-localization of an atomic ensemble in the field of counterpropagating waves is treated for a gas with an arbitrary optical thickness.

© 1989 Optical Society of America

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  1. A. P. Kazantsev and G. I. Surdutovich, Pis’ma Zh. Eksp. Teor. Fiz. 21, 346 (1975).
  2. G. A. Delone, V. A. Grinchuk, A. P. Kazantsev, and G. I. Surdutovich, Opt. Commun. 25, 399 (1978).
    [CrossRef]
  3. R. J. Cook and A. F. Bernhardt, Phys. Rev. A 18, 2533 (1978).
    [CrossRef]
  4. A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Pis’ma Zh. Eksp. Teor. Fiz. 31, 542 (1980).
  5. B. Ya. Dubetsky, A. P. Kazantsev, V. P. Chebotaev, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 89, 1190 (1985).
  6. D. E. Pitchard and P. L. Gould, J. Opt. Soc. Am. B 2, 1799 (1985).
    [CrossRef]
  7. A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 80, 541 (1981).
  8. A. P. Kazantsev, G. A. Ryabenko, G. I. Surdutovich, and V. P. Yakovlev. Phys. Rep.129, 75 (1985).
    [CrossRef]
  9. P. L. Gould, Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1986).
  10. A. P. Kazantsev, Zh. Eksp. Teor. Fiz. 66, 1599 (1974).
  11. J. P. Gordon and A. Ashkin, Phys. Rev. A 21, 1606 (1980).
    [CrossRef]
  12. A. P. Kazantsev, V. S. Smirnov, G. I. Surdutovich, D. O. Chudesnikov, and V. P. Yakovlev, J. Opt. Soc. Am. B 2, 1731 (1985).
    [CrossRef]
  13. J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1707 (1985).
    [CrossRef]
  14. A. P. Kazantsev, D. O. Chudesnikov, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 90, 1619 (1986).
  15. A. Aspect, J. Dalibard, A. Heidmann, C. Salomon, and C. Cohen-Tannoudji, Phys. Rev. Lett. 57, 1688 (1986).
    [CrossRef] [PubMed]
  16. P. E. Moskowitz, P. L. Gould, S. R. Atlas, and D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
    [CrossRef]
  17. P. E. Moskowitz, P. L. Gould, and D. E. Pritchard, J. Opt. Soc. Am. B 2, 1784 (1985).
    [CrossRef]
  18. E. Arimondo, H. Lew, and T. Oka, Phys. Rev. Lett. 43, 753 (1979).
    [CrossRef]
  19. V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Phys. Lett. A 86, 136 (1981).
    [CrossRef]
  20. A. P. Kazantsev, G. I. Surdutovich, D. O. Chudesnikov, and V. P. Yakovlev, Opt. Commun. 52, 311 (1985).
    [CrossRef]
  21. C. Tanguy, S. Roynaud, and C. Cohen-Tannoudji, J. Phys. B 17, 4623 (1984).
    [CrossRef]
  22. B. H. Hendriks and G. Nienhuis, Opt. Commun. 63, 233 (1987).
    [CrossRef]
  23. A. P. Gavriluk, I. V. Krasnov, and D. V. Sizikh. Opt. Commun. 62, 21 (1987).
    [CrossRef]
  24. J. W. Early, Opt. Commun. 65, 250 (1988).
    [CrossRef]
  25. A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Opt. Commun. 68, 103 (1988).
    [CrossRef]
  26. C. Solomon, J. Dalibard, A. Aspect, H. Metcalf, and C. Cohen-Tannoudji, Phys. Rev. Lett. 59, 1660 (1987).
  27. D. O. Chudesnikov, A. V. Tsventov, and V. P. Yakovlev, Opt. Commun. 66, 191 (1988).
    [CrossRef]
  28. B. Mollow, Phys. Rev. 188, 1969 (1969).
    [CrossRef]
  29. V. M. Dubovik, O. G. Melikyan, D. O. Chudesnikov, and V. P. Yakovlev, “Spektroskopiya rezonansnoi fluorestcenteii i sila treniya,” Preprint MIFI 026-87 (Mifi, Moscow, 1987), p. 24.
  30. A. P. Kazantsev, D. O. Chudesnikov, and V. P. Yakovlev, Problemy Kvantovoi Optiki (Dubna, Moscow, 1988),p. 49.
  31. M. G. Prentiss and S. Ezekiel, Phys. Rev. Lett. 56, 46 (1986).
    [CrossRef] [PubMed]
  32. S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, Phys. Rev. Lett. 55, 46 (1985).
    [CrossRef]
  33. T. Dalibard, Opt. Commun. 68, 203 (1988).
    [CrossRef]

1988 (4)

J. W. Early, Opt. Commun. 65, 250 (1988).
[CrossRef]

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Opt. Commun. 68, 103 (1988).
[CrossRef]

D. O. Chudesnikov, A. V. Tsventov, and V. P. Yakovlev, Opt. Commun. 66, 191 (1988).
[CrossRef]

T. Dalibard, Opt. Commun. 68, 203 (1988).
[CrossRef]

1987 (3)

C. Solomon, J. Dalibard, A. Aspect, H. Metcalf, and C. Cohen-Tannoudji, Phys. Rev. Lett. 59, 1660 (1987).

B. H. Hendriks and G. Nienhuis, Opt. Commun. 63, 233 (1987).
[CrossRef]

A. P. Gavriluk, I. V. Krasnov, and D. V. Sizikh. Opt. Commun. 62, 21 (1987).
[CrossRef]

1986 (3)

A. P. Kazantsev, D. O. Chudesnikov, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 90, 1619 (1986).

A. Aspect, J. Dalibard, A. Heidmann, C. Salomon, and C. Cohen-Tannoudji, Phys. Rev. Lett. 57, 1688 (1986).
[CrossRef] [PubMed]

M. G. Prentiss and S. Ezekiel, Phys. Rev. Lett. 56, 46 (1986).
[CrossRef] [PubMed]

1985 (7)

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, Phys. Rev. Lett. 55, 46 (1985).
[CrossRef]

J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1707 (1985).
[CrossRef]

A. P. Kazantsev, V. S. Smirnov, G. I. Surdutovich, D. O. Chudesnikov, and V. P. Yakovlev, J. Opt. Soc. Am. B 2, 1731 (1985).
[CrossRef]

P. E. Moskowitz, P. L. Gould, and D. E. Pritchard, J. Opt. Soc. Am. B 2, 1784 (1985).
[CrossRef]

D. E. Pitchard and P. L. Gould, J. Opt. Soc. Am. B 2, 1799 (1985).
[CrossRef]

A. P. Kazantsev, G. I. Surdutovich, D. O. Chudesnikov, and V. P. Yakovlev, Opt. Commun. 52, 311 (1985).
[CrossRef]

B. Ya. Dubetsky, A. P. Kazantsev, V. P. Chebotaev, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 89, 1190 (1985).

1984 (1)

C. Tanguy, S. Roynaud, and C. Cohen-Tannoudji, J. Phys. B 17, 4623 (1984).
[CrossRef]

1983 (1)

P. E. Moskowitz, P. L. Gould, S. R. Atlas, and D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
[CrossRef]

1981 (2)

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Phys. Lett. A 86, 136 (1981).
[CrossRef]

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 80, 541 (1981).

1980 (2)

J. P. Gordon and A. Ashkin, Phys. Rev. A 21, 1606 (1980).
[CrossRef]

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Pis’ma Zh. Eksp. Teor. Fiz. 31, 542 (1980).

1979 (1)

E. Arimondo, H. Lew, and T. Oka, Phys. Rev. Lett. 43, 753 (1979).
[CrossRef]

1978 (2)

G. A. Delone, V. A. Grinchuk, A. P. Kazantsev, and G. I. Surdutovich, Opt. Commun. 25, 399 (1978).
[CrossRef]

R. J. Cook and A. F. Bernhardt, Phys. Rev. A 18, 2533 (1978).
[CrossRef]

1975 (1)

A. P. Kazantsev and G. I. Surdutovich, Pis’ma Zh. Eksp. Teor. Fiz. 21, 346 (1975).

1974 (1)

A. P. Kazantsev, Zh. Eksp. Teor. Fiz. 66, 1599 (1974).

1969 (1)

B. Mollow, Phys. Rev. 188, 1969 (1969).
[CrossRef]

Arimondo, E.

E. Arimondo, H. Lew, and T. Oka, Phys. Rev. Lett. 43, 753 (1979).
[CrossRef]

Ashkin, A.

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, Phys. Rev. Lett. 55, 46 (1985).
[CrossRef]

J. P. Gordon and A. Ashkin, Phys. Rev. A 21, 1606 (1980).
[CrossRef]

Aspect, A.

C. Solomon, J. Dalibard, A. Aspect, H. Metcalf, and C. Cohen-Tannoudji, Phys. Rev. Lett. 59, 1660 (1987).

A. Aspect, J. Dalibard, A. Heidmann, C. Salomon, and C. Cohen-Tannoudji, Phys. Rev. Lett. 57, 1688 (1986).
[CrossRef] [PubMed]

Atlas, S. R.

P. E. Moskowitz, P. L. Gould, S. R. Atlas, and D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
[CrossRef]

Bernhardt, A. F.

R. J. Cook and A. F. Bernhardt, Phys. Rev. A 18, 2533 (1978).
[CrossRef]

Bjorkholm, J. E.

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, Phys. Rev. Lett. 55, 46 (1985).
[CrossRef]

Cable, A.

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, Phys. Rev. Lett. 55, 46 (1985).
[CrossRef]

Chebotaev, V. P.

B. Ya. Dubetsky, A. P. Kazantsev, V. P. Chebotaev, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 89, 1190 (1985).

Chu, S.

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, Phys. Rev. Lett. 55, 46 (1985).
[CrossRef]

Chudesnikov, D. O.

D. O. Chudesnikov, A. V. Tsventov, and V. P. Yakovlev, Opt. Commun. 66, 191 (1988).
[CrossRef]

A. P. Kazantsev, D. O. Chudesnikov, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 90, 1619 (1986).

A. P. Kazantsev, V. S. Smirnov, G. I. Surdutovich, D. O. Chudesnikov, and V. P. Yakovlev, J. Opt. Soc. Am. B 2, 1731 (1985).
[CrossRef]

A. P. Kazantsev, G. I. Surdutovich, D. O. Chudesnikov, and V. P. Yakovlev, Opt. Commun. 52, 311 (1985).
[CrossRef]

V. M. Dubovik, O. G. Melikyan, D. O. Chudesnikov, and V. P. Yakovlev, “Spektroskopiya rezonansnoi fluorestcenteii i sila treniya,” Preprint MIFI 026-87 (Mifi, Moscow, 1987), p. 24.

A. P. Kazantsev, D. O. Chudesnikov, and V. P. Yakovlev, Problemy Kvantovoi Optiki (Dubna, Moscow, 1988),p. 49.

Cohen-Tannoudji, C.

C. Solomon, J. Dalibard, A. Aspect, H. Metcalf, and C. Cohen-Tannoudji, Phys. Rev. Lett. 59, 1660 (1987).

A. Aspect, J. Dalibard, A. Heidmann, C. Salomon, and C. Cohen-Tannoudji, Phys. Rev. Lett. 57, 1688 (1986).
[CrossRef] [PubMed]

J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1707 (1985).
[CrossRef]

C. Tanguy, S. Roynaud, and C. Cohen-Tannoudji, J. Phys. B 17, 4623 (1984).
[CrossRef]

Cook, R. J.

R. J. Cook and A. F. Bernhardt, Phys. Rev. A 18, 2533 (1978).
[CrossRef]

Dalibard, J.

C. Solomon, J. Dalibard, A. Aspect, H. Metcalf, and C. Cohen-Tannoudji, Phys. Rev. Lett. 59, 1660 (1987).

A. Aspect, J. Dalibard, A. Heidmann, C. Salomon, and C. Cohen-Tannoudji, Phys. Rev. Lett. 57, 1688 (1986).
[CrossRef] [PubMed]

J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1707 (1985).
[CrossRef]

Dalibard, T.

T. Dalibard, Opt. Commun. 68, 203 (1988).
[CrossRef]

Delone, G. A.

G. A. Delone, V. A. Grinchuk, A. P. Kazantsev, and G. I. Surdutovich, Opt. Commun. 25, 399 (1978).
[CrossRef]

Dubetsky, B. Ya.

B. Ya. Dubetsky, A. P. Kazantsev, V. P. Chebotaev, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 89, 1190 (1985).

Dubovik, V. M.

V. M. Dubovik, O. G. Melikyan, D. O. Chudesnikov, and V. P. Yakovlev, “Spektroskopiya rezonansnoi fluorestcenteii i sila treniya,” Preprint MIFI 026-87 (Mifi, Moscow, 1987), p. 24.

Early, J. W.

J. W. Early, Opt. Commun. 65, 250 (1988).
[CrossRef]

Ezekiel, S.

M. G. Prentiss and S. Ezekiel, Phys. Rev. Lett. 56, 46 (1986).
[CrossRef] [PubMed]

Gavriluk, A. P.

A. P. Gavriluk, I. V. Krasnov, and D. V. Sizikh. Opt. Commun. 62, 21 (1987).
[CrossRef]

Gordon, J. P.

J. P. Gordon and A. Ashkin, Phys. Rev. A 21, 1606 (1980).
[CrossRef]

Gould, P. L.

P. E. Moskowitz, P. L. Gould, and D. E. Pritchard, J. Opt. Soc. Am. B 2, 1784 (1985).
[CrossRef]

D. E. Pitchard and P. L. Gould, J. Opt. Soc. Am. B 2, 1799 (1985).
[CrossRef]

P. E. Moskowitz, P. L. Gould, S. R. Atlas, and D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
[CrossRef]

P. L. Gould, Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1986).

Grinchuk, V. A.

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Phys. Lett. A 86, 136 (1981).
[CrossRef]

G. A. Delone, V. A. Grinchuk, A. P. Kazantsev, and G. I. Surdutovich, Opt. Commun. 25, 399 (1978).
[CrossRef]

Heidmann, A.

A. Aspect, J. Dalibard, A. Heidmann, C. Salomon, and C. Cohen-Tannoudji, Phys. Rev. Lett. 57, 1688 (1986).
[CrossRef] [PubMed]

Hendriks, B. H.

B. H. Hendriks and G. Nienhuis, Opt. Commun. 63, 233 (1987).
[CrossRef]

Hollberg, L.

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, Phys. Rev. Lett. 55, 46 (1985).
[CrossRef]

Kazantsev, A. P.

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Opt. Commun. 68, 103 (1988).
[CrossRef]

A. P. Kazantsev, D. O. Chudesnikov, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 90, 1619 (1986).

A. P. Kazantsev, V. S. Smirnov, G. I. Surdutovich, D. O. Chudesnikov, and V. P. Yakovlev, J. Opt. Soc. Am. B 2, 1731 (1985).
[CrossRef]

A. P. Kazantsev, G. I. Surdutovich, D. O. Chudesnikov, and V. P. Yakovlev, Opt. Commun. 52, 311 (1985).
[CrossRef]

B. Ya. Dubetsky, A. P. Kazantsev, V. P. Chebotaev, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 89, 1190 (1985).

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 80, 541 (1981).

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Phys. Lett. A 86, 136 (1981).
[CrossRef]

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Pis’ma Zh. Eksp. Teor. Fiz. 31, 542 (1980).

G. A. Delone, V. A. Grinchuk, A. P. Kazantsev, and G. I. Surdutovich, Opt. Commun. 25, 399 (1978).
[CrossRef]

A. P. Kazantsev and G. I. Surdutovich, Pis’ma Zh. Eksp. Teor. Fiz. 21, 346 (1975).

A. P. Kazantsev, Zh. Eksp. Teor. Fiz. 66, 1599 (1974).

A. P. Kazantsev, G. A. Ryabenko, G. I. Surdutovich, and V. P. Yakovlev. Phys. Rep.129, 75 (1985).
[CrossRef]

A. P. Kazantsev, D. O. Chudesnikov, and V. P. Yakovlev, Problemy Kvantovoi Optiki (Dubna, Moscow, 1988),p. 49.

Krasnov, I. V.

A. P. Gavriluk, I. V. Krasnov, and D. V. Sizikh. Opt. Commun. 62, 21 (1987).
[CrossRef]

Kuzin, E. F.

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Phys. Lett. A 86, 136 (1981).
[CrossRef]

Lew, H.

E. Arimondo, H. Lew, and T. Oka, Phys. Rev. Lett. 43, 753 (1979).
[CrossRef]

Melikyan, O. G.

V. M. Dubovik, O. G. Melikyan, D. O. Chudesnikov, and V. P. Yakovlev, “Spektroskopiya rezonansnoi fluorestcenteii i sila treniya,” Preprint MIFI 026-87 (Mifi, Moscow, 1987), p. 24.

Metcalf, H.

C. Solomon, J. Dalibard, A. Aspect, H. Metcalf, and C. Cohen-Tannoudji, Phys. Rev. Lett. 59, 1660 (1987).

Mollow, B.

B. Mollow, Phys. Rev. 188, 1969 (1969).
[CrossRef]

Moskowitz, P. E.

P. E. Moskowitz, P. L. Gould, and D. E. Pritchard, J. Opt. Soc. Am. B 2, 1784 (1985).
[CrossRef]

P. E. Moskowitz, P. L. Gould, S. R. Atlas, and D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
[CrossRef]

Nagaeva, M. L.

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Phys. Lett. A 86, 136 (1981).
[CrossRef]

Nienhuis, G.

B. H. Hendriks and G. Nienhuis, Opt. Commun. 63, 233 (1987).
[CrossRef]

Oka, T.

E. Arimondo, H. Lew, and T. Oka, Phys. Rev. Lett. 43, 753 (1979).
[CrossRef]

Pitchard, D. E.

Prentiss, M. G.

M. G. Prentiss and S. Ezekiel, Phys. Rev. Lett. 56, 46 (1986).
[CrossRef] [PubMed]

Pritchard, D. E.

P. E. Moskowitz, P. L. Gould, and D. E. Pritchard, J. Opt. Soc. Am. B 2, 1784 (1985).
[CrossRef]

P. E. Moskowitz, P. L. Gould, S. R. Atlas, and D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
[CrossRef]

Roynaud, S.

C. Tanguy, S. Roynaud, and C. Cohen-Tannoudji, J. Phys. B 17, 4623 (1984).
[CrossRef]

Ryabenko, G. A.

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Phys. Lett. A 86, 136 (1981).
[CrossRef]

A. P. Kazantsev, G. A. Ryabenko, G. I. Surdutovich, and V. P. Yakovlev. Phys. Rep.129, 75 (1985).
[CrossRef]

Salomon, C.

A. Aspect, J. Dalibard, A. Heidmann, C. Salomon, and C. Cohen-Tannoudji, Phys. Rev. Lett. 57, 1688 (1986).
[CrossRef] [PubMed]

Sizikh, D. V.

A. P. Gavriluk, I. V. Krasnov, and D. V. Sizikh. Opt. Commun. 62, 21 (1987).
[CrossRef]

Smirnov, V. S.

Solomon, C.

C. Solomon, J. Dalibard, A. Aspect, H. Metcalf, and C. Cohen-Tannoudji, Phys. Rev. Lett. 59, 1660 (1987).

Surdutovich, G. I.

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Opt. Commun. 68, 103 (1988).
[CrossRef]

A. P. Kazantsev, G. I. Surdutovich, D. O. Chudesnikov, and V. P. Yakovlev, Opt. Commun. 52, 311 (1985).
[CrossRef]

A. P. Kazantsev, V. S. Smirnov, G. I. Surdutovich, D. O. Chudesnikov, and V. P. Yakovlev, J. Opt. Soc. Am. B 2, 1731 (1985).
[CrossRef]

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Phys. Lett. A 86, 136 (1981).
[CrossRef]

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 80, 541 (1981).

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Pis’ma Zh. Eksp. Teor. Fiz. 31, 542 (1980).

G. A. Delone, V. A. Grinchuk, A. P. Kazantsev, and G. I. Surdutovich, Opt. Commun. 25, 399 (1978).
[CrossRef]

A. P. Kazantsev and G. I. Surdutovich, Pis’ma Zh. Eksp. Teor. Fiz. 21, 346 (1975).

A. P. Kazantsev, G. A. Ryabenko, G. I. Surdutovich, and V. P. Yakovlev. Phys. Rep.129, 75 (1985).
[CrossRef]

Tanguy, C.

C. Tanguy, S. Roynaud, and C. Cohen-Tannoudji, J. Phys. B 17, 4623 (1984).
[CrossRef]

Tsventov, A. V.

D. O. Chudesnikov, A. V. Tsventov, and V. P. Yakovlev, Opt. Commun. 66, 191 (1988).
[CrossRef]

Yakovlev, V. P.

D. O. Chudesnikov, A. V. Tsventov, and V. P. Yakovlev, Opt. Commun. 66, 191 (1988).
[CrossRef]

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Opt. Commun. 68, 103 (1988).
[CrossRef]

A. P. Kazantsev, D. O. Chudesnikov, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 90, 1619 (1986).

A. P. Kazantsev, V. S. Smirnov, G. I. Surdutovich, D. O. Chudesnikov, and V. P. Yakovlev, J. Opt. Soc. Am. B 2, 1731 (1985).
[CrossRef]

A. P. Kazantsev, G. I. Surdutovich, D. O. Chudesnikov, and V. P. Yakovlev, Opt. Commun. 52, 311 (1985).
[CrossRef]

B. Ya. Dubetsky, A. P. Kazantsev, V. P. Chebotaev, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 89, 1190 (1985).

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 80, 541 (1981).

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Phys. Lett. A 86, 136 (1981).
[CrossRef]

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Pis’ma Zh. Eksp. Teor. Fiz. 31, 542 (1980).

A. P. Kazantsev, G. A. Ryabenko, G. I. Surdutovich, and V. P. Yakovlev. Phys. Rep.129, 75 (1985).
[CrossRef]

A. P. Kazantsev, D. O. Chudesnikov, and V. P. Yakovlev, Problemy Kvantovoi Optiki (Dubna, Moscow, 1988),p. 49.

V. M. Dubovik, O. G. Melikyan, D. O. Chudesnikov, and V. P. Yakovlev, “Spektroskopiya rezonansnoi fluorestcenteii i sila treniya,” Preprint MIFI 026-87 (Mifi, Moscow, 1987), p. 24.

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A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Opt. Commun. 68, 103 (1988).
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D. O. Chudesnikov, A. V. Tsventov, and V. P. Yakovlev, Opt. Commun. 66, 191 (1988).
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A. P. Kazantsev, G. I. Surdutovich, D. O. Chudesnikov, and V. P. Yakovlev, Opt. Commun. 52, 311 (1985).
[CrossRef]

T. Dalibard, Opt. Commun. 68, 203 (1988).
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G. A. Delone, V. A. Grinchuk, A. P. Kazantsev, and G. I. Surdutovich, Opt. Commun. 25, 399 (1978).
[CrossRef]

Phys. Lett. A (1)

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Phys. Lett. A 86, 136 (1981).
[CrossRef]

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A. Aspect, J. Dalibard, A. Heidmann, C. Salomon, and C. Cohen-Tannoudji, Phys. Rev. Lett. 57, 1688 (1986).
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C. Solomon, J. Dalibard, A. Aspect, H. Metcalf, and C. Cohen-Tannoudji, Phys. Rev. Lett. 59, 1660 (1987).

Pis’ma Zh. Eksp. Teor. Fiz. (2)

A. P. Kazantsev and G. I. Surdutovich, Pis’ma Zh. Eksp. Teor. Fiz. 21, 346 (1975).

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Pis’ma Zh. Eksp. Teor. Fiz. 31, 542 (1980).

Zh. Eksp. Teor. Fiz. (4)

B. Ya. Dubetsky, A. P. Kazantsev, V. P. Chebotaev, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 89, 1190 (1985).

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 80, 541 (1981).

A. P. Kazantsev, Zh. Eksp. Teor. Fiz. 66, 1599 (1974).

A. P. Kazantsev, D. O. Chudesnikov, and V. P. Yakovlev, Zh. Eksp. Teor. Fiz. 90, 1619 (1986).

Other (4)

A. P. Kazantsev, G. A. Ryabenko, G. I. Surdutovich, and V. P. Yakovlev. Phys. Rep.129, 75 (1985).
[CrossRef]

P. L. Gould, Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1986).

V. M. Dubovik, O. G. Melikyan, D. O. Chudesnikov, and V. P. Yakovlev, “Spektroskopiya rezonansnoi fluorestcenteii i sila treniya,” Preprint MIFI 026-87 (Mifi, Moscow, 1987), p. 24.

A. P. Kazantsev, D. O. Chudesnikov, and V. P. Yakovlev, Problemy Kvantovoi Optiki (Dubna, Moscow, 1988),p. 49.

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Figures (5)

Fig. 1
Fig. 1

Distribution function of the scattered particles as given by formulas (2.11) and (2.12) for ni = 7, ns = 0.8.

Fig. 2
Fig. 2

Experimental results9 in scattering of the sodium atoms by a standing light wave at V0/γ = 5.7, Δ/γ = −9.3, γτ = 4.4.

Fig. 3
Fig. 3

Velocity potential [Eq. (3.6)] for (a) positive and (b) negative detunings when C2 > 1. The particles are bunching near a minimum of W(υ).

Fig. 4
Fig. 4

Evolution of the velocity distribution [Eq. (3.10)] for η = 0 (curve 1), η = 2 (curve 2), η = 5 (curve 3).

Fig. 5
Fig. 5

Coordinate dependence of the wave intensities, atomic density, and the effective potential for ξ2 = 2/3.

Equations (78)

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n i δ u eff τ , n s w γ τ ,
k υ x τ 1 .
i ( t ρ a a γ ̂ ρ b b ) = V 1 ρ b a + V 2 ρ a b ,
i ( t + γ ) ρ b b = V 1 ρ a b + V 2 ρ b a ,
( i t + ν ) ρ b a = V 1 ρ a a + V 2 ρ b b ,
φ ( x ) = 3 2 [ sin k x k x + cos k x ( k x ) 2 sin k x ( k x ) 3 ] , φ ( q ) = 3 8 k [ 1 + ( q | k ) 2 ] , | q | k .
F ( x 1 x 2 , t = ) = ρ a a ( x 1 x 2 , t = ) = F 0 ( x 1 x 2 ) .
F 0 = 1 .
Δ V 0 , γ , γ τ 1 ,
ρ b a = V 1 ν ρ a a , ρ a b V 2 ν * ρ a a , ρ b b V 1 V 2 | ν | 2 ρ a a .
t ρ a a ( x 1 , x 2 , t ) = [ ( V 1 2 ν V 2 2 ν * ) + γ ̂ V 1 V 2 | ν | 2 ] ρ a a ( x 1 , x 2 , t ) ,
F ( x 1 , x 2 ) = ρ a a ( x 1 , x 2 , t = ) = F 0 ( x 1 x 2 ) exp { τ [ i V 1 2 V 2 2 Δ + γ 2 V 1 2 + V 2 2 Δ 2 γ φ ( x 1 x 2 ) V 1 V 2 Δ 2 ] } .
W ( p ) = 1 2 π F ( x 1 x 2 ) exp ( i p x ) d x .
n i ( x ) = U ( x ) τ , U ( x ) = V 2 ( x ) / Δ , U ( x ) = V 2 ( x ) / Δ ,
n s ( x ) = w ( x ) γ τ , w ( x ) = V 2 ( x ) / Δ 2
n s = V 0 2 γ τ / ( 2 Δ 2 ) .
W ( p ) = n = { W 2 n δ ( p 2 n k ) + W 2 n + 1 φ [ p ( 2 n + 1 ) k ] } ,
W 2 n = ( 1 n s ) J n 2 ( ξ ) , W 2 n + 1 = n s 2 [ J n 2 ( ξ ) + J n + 1 2 ( ξ ) ] , ξ = n i = V 0 2 τ 2 Δ .
n s 1 .
n s ( x ) 2 n s ( k δ x ) 2 < 1 , i . e . , for k δ x n s 1 / 2 1 .
P d f r k n c , n c n i n s V 0 ( τ / δ ) 1 / 2 .
k p d f f p d f r p 0 .
F = F d f r + F n c h ,
F d f r = exp [ i τ ( V 1 2 ν V 2 2 ν * ) ]
F n c h = F F d f r .
W dfr ( p ) = n W 2 n δ ( p 2 n k ) , W 2 n = exp ( n s ) | J n ( ξ ) | 2 , ξ = V 0 2 τ 2 ν , n s = V 0 2 τ γ 2 | ν | 2 .
ρ α β ( x 1 x 2 t ) = ψ β * ( x 2 t ) ψ α ( x 1 t ) , i t [ ψ β ψ α ] = [ Δ + i γ / 2 V V 0 ] [ ψ β ψ α ] , V = V 0 ( t sin k x ) .
i ψ a t = U eff ψ a , U eff = V 2 Δ + i γ / 2 .
W d f r = n W 2 n = exp ( n s ) I 0 ( n s ) ,
P d f r 2 ¯ = p 2 W d f r ( p ) d p = 2 k 2 n c 2 exp ( n s ) I 1 ( n s ) , n c 2 = V 0 2 τ / γ = 2 n i 2 / n s .
W 2 n = 1 2 π n i exp ( n 2 / n c 2 ) , W d f r = ( 2 π n s ) 1 / 2 1 , ( p d f r k ) 2 ¯ = ( 2 π ) 1 / 2 n c 2 n s V 0 Δ γ 2 γ τ .
W 2 n = exp ( 2 ξ ) I n 2 ( ξ ) , ξ = V 0 2 τ / γ
W ( 1 ) ( p ) = ( 4 π D τ ) 1 / 2 exp [ ( p τ f g ) 2 4 D τ ] , f g = d U d x , D = γ 2 Δ 2 [ ( d U d x ) 2 + 2 5 k 2 V 2 ] ,
W ( 2 ) ( p ) = 1 4 π k n i exp [ ( p 2 k n c ) 2 ] [ ( p 2 k n c ) 2 χ ( p ) 1 ] , χ ( p ) = 3 π 2 s = 1 s 2 cos π p s k = 1 4 ( 3 q 2 1 ) , q = p k ( 2 n + 1 ) , | q | 1 .
δ p D τ k n s p 0 .
p 2 ¯ = f g 2 τ 2 + 2 D τ
W N = 1 N ! [ n s ( X ) ] N exp [ n s ( X ) ] ,
N ¯ = n s ( X ) = n s , ( Δ N ) 2 ¯ = n s + n s 2 ( X ) n s 2 = n s + n s 2 / 2 > N ¯ ,
m d υ d t = f ( υ ) ,
f ( υ g ) = 0 , d d υ g f ( υ g ) < 0 .
f ( υ ) = d W d υ .
f ( υ ) = 2 a υ [ 1 C 2 γ 2 γ 2 + ( 2 k υ ) 2 ] , a = γ k 2 V 0 2 / 2 Δ 3 , C = V 0 2 / γ | Δ | .
υ c = γ 2 k C 2 1 .
W ( υ ) = a υ 2 + a ( γ C 2 k ) 2 ln [ 1 + ( 2 k υ / γ ) 2 ]
F t + υ [ f ( υ ) F / m ] = 0 , F ( υ t ) = F 0 [ υ 0 ( υ t ) ] d υ 0 ( υ t ) d υ ,
ξ = 2 k υ γ , ξ c = 2 k υ c γ , η = γ k 2 V 0 2 m | Δ | 3 t , ( C 2 > 1 ) .
η = ξ 0 ξ d ξ f ( ξ ) = 1 2 ξ c 2 [ ( 1 + ξ c 2 ) ln | ξ c 2 ξ 0 2 ξ c 2 ξ 2 | + ln ( ξ ξ c ) 2 ] .
ξ 0 ( ξ , η ) = ( α 2 + 1 ) 1 / 2 α , α = 1 ξ 2 2 ξ exp ( η ) ( ξ , ξ 0 > 0 ) .
F ( ξ , η ) = F 0 ( ξ 0 ) 1 + ξ 2 2 ξ 2 exp ( η ) × { 1 ( 1 ξ 2 ) [ ( 1 ξ 2 ) 2 + 4 ξ 2 exp ( 2 η ) ] 1 / 2 } .
f ( υ ) = 2 k 2 υ Δ τ ( 1 υ c 2 υ 2 ) , υ c 2 = γ Δ 2 4 V 0 k 2 ln ( 2 γ k υ V 0 ) .
( t + Γ ̂ ) ρ ( t ) = i [ Ĥ ( t ) ρ ( t ) ] ,
( t + Γ ̂ ) R ( t , t ) = i [ Ĥ ( t ) R ( t , t ) ] , t > t ,
Ĥ ( t ) = ( Δ / 2 ) σ 3 V ( t ) σ + V * ( t ) σ , V ( t ) = V ( x = υ t ) ,
Γ ̂ ρ = [ γ ρ b b ( γ / 2 ) ρ b a ( γ / 2 ) ρ a b γ ρ b b ] , Γ ̂ R = [ γ R b b ( γ / 2 ) R b a ( γ / 2 ) R a b γ R b b ] .
R α β ( t t ) = δ β , a ρ α b ( t ) .
I ( ν , n ) = γ π φ ( n ) Re 0 d τ exp [ i ( ν + k nv ) τ ] R b a ( t , t + τ ) , φ ( n ) = ( 3 / 8 π ) [ 1 ( dn ) 2 / d 2 ] .
d n ν I ( ν , n ) d ν = γ Re [ i t R b a ( t , t ) ] t = t + 0 .
i t R b a ( t t ) = ( Δ + i γ / 2 ) R b a ( t t ) + V ( t ) × [ R b b ( t t ) R a a ( t t ) ] .
γ Re [ i t R b a ( t t ) ] t = t + 0 = γ Re [ ( Δ + i γ / 2 ) ρ b b ( t ) + V ( t ) ρ a b ( t ) ] = Δ 2 d Q d t + V * ( t ) d P d t + c . c . = P d V * d t + c . c . υ f ( t ) .
f ( t ) = 1 υ ( P d V * d t + c . c . ) .
I d n ν I ( ν , n ) d ν = υ f .
I = ( d E d t ) ω rad > ω ( d E d t ) ω rad < ω .
I = d n ω rad I d ω rad ω d n Id ν = ( d E d t ) rad ( d E d t ) abs ,
( d E d t ) abs = ω γ ρ b b ( t ) = 2 ω Im P V * ,
( d E d t ) abs = ( d E d t ) rad + υ f
E ( x t ) = ½ [ E 1 ( x ) e i k x + E 2 ( x ) e i k x ] e i Δ t .
V 1 , 2 ( x ) = d E 1 , 2 ( x ) | Δ + i γ / 2 | .
F t + υ F x + p { [ f s ( x ) + f fr ( x ) ] F } = 2 p 2 [ D ( x ) F ] ,
f s ( x ) = k γ | ν | 2 [ I 1 ( x ) I 2 ( x ) ] , I 1 , 2 ( x ) = | V 1 , 2 ( x ) | 2 ,
f fr ( x ) = κ ( x ) υ , κ ( x ) = 2 k 2 γ Δ | ν | 4 [ I 1 ( x ) + I 2 ( x ) ] ,
D ( x ) = 7 10 γ k 2 | ν | 2 [ I 1 ( x ) + I 2 ( x ) ] , ν = Δ + i γ / 2 .
d V 1 d x = i 2 π k d 2 ν n ( x ) V 1 , d V 2 d x = i 2 π k d 2 ν n ( x ) V 2 ,
F ( x p ) = F 0 exp { 1 T [ p 2 2 m + U ( x ) ] } , n ( x ) = n 0 exp [ U ( x ) / T ] , U ( x ) = 0 x f s ( x ) d x , T = D ( x ) κ ( x ) = 7 20 | ν 2 Δ | , Δ < 0 .
d I 1 d x + 2 π d 2 k γ | ν | 2 n ( x ) I 1 = 0 , d I 2 d x 2 π d 2 k γ | ν | 2 n ( x ) I 2 = 0 , n ( x ) = n 0 exp [ k γ T | ν | 2 0 x ( I 1 I 2 ) d x ] .
I 1 ( x ) + I 2 ( x ) + 2 π T d 2 n ( x ) = I in + I out ,
I 1 ( x ) I 2 ( x ) = I in I out .
d I 1 d x = k γ T | ν | 2 ( I 1 I in ) ( I 1 I out ) .
I 1 ( x ) = I 2 ( x ) = I in ξ ξ + exp ( α x ) 1 + ξ exp ( α x ) , n ( x ) = n 0 [ 1 + 4 ξ ( 1 + ξ ) 2 s h 2 ( α x 2 ) ] 1 , n 0 = I in ( 1 ξ ) 2 2 π T d 2 , ξ 2 = I out / I in < 1 , U ( x ) = T ln [ 1 + 4 ξ ( 1 + ξ ) 2 s h 2 α x 2 ] , α = 1 l = I in ( 1 ξ 2 ) k γ T | ν | 2 .

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