Abstract

We report quantitative measurements of the effects of a phase-diffusing field on coherent transients when the detected signals are averaged over many shots. Experiments were made at a millimeter wavelength, and frequency fluctuations were simulated by deliberately applying a well-defined random Stark field to the gaseous sample: This permits a separate adjustment of the amplitude and the rate of fluctuations. In the case of slow frequency fluctuations, two- and three-pulse-induced photon echoes clearly exhibit a reversible behavior that is closely related to the definite shape of the frequency-autocorrelation function.

© 1986 Optical Society of America

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  1. P. T. Greenland, J. Phys. B 17, 1919–1925 (1984); M. Helm and P. Zoller, Opt. Commun. 49, 324–328 (1984); B. W. Shore, J. Opt. Soc. Am. B 1, 176–188 (1984).
    [Crossref]
  2. P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, and M. D. Levenson, J. Phys. B 11, 1733–1747 (1978); B. R. Marx, J. Simons, and L. Allen, J. Phys. B 11, L273–L277 (1978); A. T. Georges and P. Lambropoulos, Phys. Rev. A 20, 991–1004 (1979).
    [Crossref]
  3. F. Rohart and B. Macke, Appl. Phys. B 26, 23–30 (1981).
    [Crossref]
  4. D. S. Elliott, M. W. Hamilton, K. Arnett, and S. J. Smith, Phys. Rev. Lett. 53, 439–441 (1984).
    [Crossref]
  5. B. Macke, J. Mol. Structure 97, 203–214 (1983); H. Dève, Thèse de 3ème Cycle (Université de Lille I, Lille, 1983; unpublished).
    [Crossref]
  6. F. Rohart, H. Dève, and B. Macke, Appl. Phys. B 39, 19–27 (1986).
    [Crossref]
  7. K. Wodkiewicz, Phys. Rev. A 19, 1686–1696 (1979).
    [Crossref]
  8. J. Rutman, Proc. IEEE 66, 1048–1075 (1978); Thèse d’Etat (Office National d’ Etudes et de Recherches Aérospatiales, Paris, 1972).
    [Crossref]
  9. Recent results obtained in transient spectroscopy with incoherent light may be found in, e.g., R. Beach and S. R. Hartmann, Phys. Rev. Lett. 53, 663–666 (1984); N. Morita and T. Yajima, Phys. Rev. A 30, 2525–2536 (1984).
    [Crossref]
  10. See, for example, J. Mostowski and K. Rza̧żewski, Z. Phys. B 39, 183–185 (1980), and references therein.
    [Crossref]
  11. E. Hanamura, J. Phys. Soc. Jpn. 52, 2258–2266, 3265–3274, 3678–3684 (1983).
    [Crossref]
  12. J. Javanainen, Opt. Commun. 50, 26–30 (1984); M. Yamanoi and J. H. EberlyPhys. Rev. Lett. 52, 1353 (1984); A. Schenzle, M. Mitsunaga, R. G. De Voe, and R. G. Brewer, Phys. Rev. A 30, 325–335 (1984); K. Wodkiewicz and J. H. Eberly, Phys. Rev. A 32, 992–1001 (1985); P. R. Berman and R. G. Brewer, Phys. Rev. A 32, 2784–2796 (1985).
    [Crossref] [PubMed]
  13. Similar problems were considered previously in magnetic resonance; see, for example, B. Herzog and E. L. Hahn, Phys. Rev. 103, 148–166 (1956); P. Hu and S. R. Hartmann, Phys. Rev. B 9, 1–13 (1974).
    [Crossref]
  14. R. G. De Voe, A. Szabo, S. C. Rand, and R. G. Brewer, Phys. Rev. Lett. 42, 1560–1563 (1979); R. M. Macfarlane, R. M. Shelby, and R. L. Shoemaker, Phys. Rev. Lett. 43, 1726–1730 (1979).
    [Crossref]
  15. R. G. De Voe and R. G. Brewer, Phys. Rev. Lett. 50, 1269–1272 (1983); analogous effects are also reported on a gaseous sample; see A. G. Yodh, J. Golub, N. W. Carlson, and T. W. Mossberg, 53, 659–662 (1984).
    [Crossref]
  16. R. L. Shoemaker, in Laser and Coherence Spectroscopy, J. I. Steinfeld, ed. (Plenum, New York, 1978), pp. 197–371; R. H. Schwendeman, Ann. Rev. Phys. Chem. 29, 537–558 (1978); T. W. Mossberg, R. Kachru, S. R. Hartmann, and A. M. Flusberg, Phys. Rev. A 20, 1976–1996 (1979).
    [Crossref]
  17. A. Szabo and M. Kroll, Opt. Lett. 2, 10–12 (1978).
    [Crossref] [PubMed]
  18. L. S. Cutler and C. L. Searle, Proc. IEEE 54, 136–154 (1966).
    [Crossref]
  19. A discussion more specific to steady-state experiments and their connection with the e.m.-field bandwidth can be found in Ref. 6.
  20. F. Rohart and B. Macke, Z. Naturforsch,  36a, 929–936 (1981).
  21. D. W. Allan, Proc. IEEE 54, 221–230 (1966).
    [Crossref]
  22. P. R. Berman, J. M. Levy, and R. G. Brewer, Phys. Rev. A 11, 1668–1688 (1975).
    [Crossref]
  23. R. H. Dicke, Phys. Rev. 89, 472–473 (1953).
    [Crossref]
  24. H. Y. Carr and E. M. Purcell, Phys. Rev. 94, 630–638 (1954).
    [Crossref]
  25. F. Rohart, Thèse d’Etat (Université de Lille I, Lille, 1981; unpublished).
  26. Y. C. Chen, K. Chiang, and S. R. Hartmann, Opt. Commun. 29, 181–185 (1979); J. B. W. Morsink and D. A. Wiersma, Chem. Phys. Lett. 65, 105–108 (1979).
    [Crossref]
  27. P. R. Berman and R. G. Brewer, in Proceedings of 7th International Laser Spectroscopy Conference, T. W. Hänsch and Y. R. Shen, eds. (Springer-Verlag, Berlin, to be published).

1986 (1)

F. Rohart, H. Dève, and B. Macke, Appl. Phys. B 39, 19–27 (1986).
[Crossref]

1984 (4)

Recent results obtained in transient spectroscopy with incoherent light may be found in, e.g., R. Beach and S. R. Hartmann, Phys. Rev. Lett. 53, 663–666 (1984); N. Morita and T. Yajima, Phys. Rev. A 30, 2525–2536 (1984).
[Crossref]

P. T. Greenland, J. Phys. B 17, 1919–1925 (1984); M. Helm and P. Zoller, Opt. Commun. 49, 324–328 (1984); B. W. Shore, J. Opt. Soc. Am. B 1, 176–188 (1984).
[Crossref]

D. S. Elliott, M. W. Hamilton, K. Arnett, and S. J. Smith, Phys. Rev. Lett. 53, 439–441 (1984).
[Crossref]

J. Javanainen, Opt. Commun. 50, 26–30 (1984); M. Yamanoi and J. H. EberlyPhys. Rev. Lett. 52, 1353 (1984); A. Schenzle, M. Mitsunaga, R. G. De Voe, and R. G. Brewer, Phys. Rev. A 30, 325–335 (1984); K. Wodkiewicz and J. H. Eberly, Phys. Rev. A 32, 992–1001 (1985); P. R. Berman and R. G. Brewer, Phys. Rev. A 32, 2784–2796 (1985).
[Crossref] [PubMed]

1983 (3)

E. Hanamura, J. Phys. Soc. Jpn. 52, 2258–2266, 3265–3274, 3678–3684 (1983).
[Crossref]

R. G. De Voe and R. G. Brewer, Phys. Rev. Lett. 50, 1269–1272 (1983); analogous effects are also reported on a gaseous sample; see A. G. Yodh, J. Golub, N. W. Carlson, and T. W. Mossberg, 53, 659–662 (1984).
[Crossref]

B. Macke, J. Mol. Structure 97, 203–214 (1983); H. Dève, Thèse de 3ème Cycle (Université de Lille I, Lille, 1983; unpublished).
[Crossref]

1981 (2)

F. Rohart and B. Macke, Z. Naturforsch,  36a, 929–936 (1981).

F. Rohart and B. Macke, Appl. Phys. B 26, 23–30 (1981).
[Crossref]

1980 (1)

See, for example, J. Mostowski and K. Rza̧żewski, Z. Phys. B 39, 183–185 (1980), and references therein.
[Crossref]

1979 (3)

K. Wodkiewicz, Phys. Rev. A 19, 1686–1696 (1979).
[Crossref]

R. G. De Voe, A. Szabo, S. C. Rand, and R. G. Brewer, Phys. Rev. Lett. 42, 1560–1563 (1979); R. M. Macfarlane, R. M. Shelby, and R. L. Shoemaker, Phys. Rev. Lett. 43, 1726–1730 (1979).
[Crossref]

Y. C. Chen, K. Chiang, and S. R. Hartmann, Opt. Commun. 29, 181–185 (1979); J. B. W. Morsink and D. A. Wiersma, Chem. Phys. Lett. 65, 105–108 (1979).
[Crossref]

1978 (3)

A. Szabo and M. Kroll, Opt. Lett. 2, 10–12 (1978).
[Crossref] [PubMed]

J. Rutman, Proc. IEEE 66, 1048–1075 (1978); Thèse d’Etat (Office National d’ Etudes et de Recherches Aérospatiales, Paris, 1972).
[Crossref]

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, and M. D. Levenson, J. Phys. B 11, 1733–1747 (1978); B. R. Marx, J. Simons, and L. Allen, J. Phys. B 11, L273–L277 (1978); A. T. Georges and P. Lambropoulos, Phys. Rev. A 20, 991–1004 (1979).
[Crossref]

1975 (1)

P. R. Berman, J. M. Levy, and R. G. Brewer, Phys. Rev. A 11, 1668–1688 (1975).
[Crossref]

1966 (2)

D. W. Allan, Proc. IEEE 54, 221–230 (1966).
[Crossref]

L. S. Cutler and C. L. Searle, Proc. IEEE 54, 136–154 (1966).
[Crossref]

1956 (1)

Similar problems were considered previously in magnetic resonance; see, for example, B. Herzog and E. L. Hahn, Phys. Rev. 103, 148–166 (1956); P. Hu and S. R. Hartmann, Phys. Rev. B 9, 1–13 (1974).
[Crossref]

1954 (1)

H. Y. Carr and E. M. Purcell, Phys. Rev. 94, 630–638 (1954).
[Crossref]

1953 (1)

R. H. Dicke, Phys. Rev. 89, 472–473 (1953).
[Crossref]

Agostini, P.

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, and M. D. Levenson, J. Phys. B 11, 1733–1747 (1978); B. R. Marx, J. Simons, and L. Allen, J. Phys. B 11, L273–L277 (1978); A. T. Georges and P. Lambropoulos, Phys. Rev. A 20, 991–1004 (1979).
[Crossref]

Allan, D. W.

D. W. Allan, Proc. IEEE 54, 221–230 (1966).
[Crossref]

Arnett, K.

D. S. Elliott, M. W. Hamilton, K. Arnett, and S. J. Smith, Phys. Rev. Lett. 53, 439–441 (1984).
[Crossref]

Beach, R.

Recent results obtained in transient spectroscopy with incoherent light may be found in, e.g., R. Beach and S. R. Hartmann, Phys. Rev. Lett. 53, 663–666 (1984); N. Morita and T. Yajima, Phys. Rev. A 30, 2525–2536 (1984).
[Crossref]

Berman, P. R.

P. R. Berman, J. M. Levy, and R. G. Brewer, Phys. Rev. A 11, 1668–1688 (1975).
[Crossref]

P. R. Berman and R. G. Brewer, in Proceedings of 7th International Laser Spectroscopy Conference, T. W. Hänsch and Y. R. Shen, eds. (Springer-Verlag, Berlin, to be published).

Brewer, R. G.

R. G. De Voe and R. G. Brewer, Phys. Rev. Lett. 50, 1269–1272 (1983); analogous effects are also reported on a gaseous sample; see A. G. Yodh, J. Golub, N. W. Carlson, and T. W. Mossberg, 53, 659–662 (1984).
[Crossref]

R. G. De Voe, A. Szabo, S. C. Rand, and R. G. Brewer, Phys. Rev. Lett. 42, 1560–1563 (1979); R. M. Macfarlane, R. M. Shelby, and R. L. Shoemaker, Phys. Rev. Lett. 43, 1726–1730 (1979).
[Crossref]

P. R. Berman, J. M. Levy, and R. G. Brewer, Phys. Rev. A 11, 1668–1688 (1975).
[Crossref]

P. R. Berman and R. G. Brewer, in Proceedings of 7th International Laser Spectroscopy Conference, T. W. Hänsch and Y. R. Shen, eds. (Springer-Verlag, Berlin, to be published).

Carr, H. Y.

H. Y. Carr and E. M. Purcell, Phys. Rev. 94, 630–638 (1954).
[Crossref]

Chen, Y. C.

Y. C. Chen, K. Chiang, and S. R. Hartmann, Opt. Commun. 29, 181–185 (1979); J. B. W. Morsink and D. A. Wiersma, Chem. Phys. Lett. 65, 105–108 (1979).
[Crossref]

Chiang, K.

Y. C. Chen, K. Chiang, and S. R. Hartmann, Opt. Commun. 29, 181–185 (1979); J. B. W. Morsink and D. A. Wiersma, Chem. Phys. Lett. 65, 105–108 (1979).
[Crossref]

Cutler, L. S.

L. S. Cutler and C. L. Searle, Proc. IEEE 54, 136–154 (1966).
[Crossref]

De Voe, R. G.

R. G. De Voe and R. G. Brewer, Phys. Rev. Lett. 50, 1269–1272 (1983); analogous effects are also reported on a gaseous sample; see A. G. Yodh, J. Golub, N. W. Carlson, and T. W. Mossberg, 53, 659–662 (1984).
[Crossref]

R. G. De Voe, A. Szabo, S. C. Rand, and R. G. Brewer, Phys. Rev. Lett. 42, 1560–1563 (1979); R. M. Macfarlane, R. M. Shelby, and R. L. Shoemaker, Phys. Rev. Lett. 43, 1726–1730 (1979).
[Crossref]

Dève, H.

F. Rohart, H. Dève, and B. Macke, Appl. Phys. B 39, 19–27 (1986).
[Crossref]

Dicke, R. H.

R. H. Dicke, Phys. Rev. 89, 472–473 (1953).
[Crossref]

Elliott, D. S.

D. S. Elliott, M. W. Hamilton, K. Arnett, and S. J. Smith, Phys. Rev. Lett. 53, 439–441 (1984).
[Crossref]

Georges, A. T.

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, and M. D. Levenson, J. Phys. B 11, 1733–1747 (1978); B. R. Marx, J. Simons, and L. Allen, J. Phys. B 11, L273–L277 (1978); A. T. Georges and P. Lambropoulos, Phys. Rev. A 20, 991–1004 (1979).
[Crossref]

Greenland, P. T.

P. T. Greenland, J. Phys. B 17, 1919–1925 (1984); M. Helm and P. Zoller, Opt. Commun. 49, 324–328 (1984); B. W. Shore, J. Opt. Soc. Am. B 1, 176–188 (1984).
[Crossref]

Hahn, E. L.

Similar problems were considered previously in magnetic resonance; see, for example, B. Herzog and E. L. Hahn, Phys. Rev. 103, 148–166 (1956); P. Hu and S. R. Hartmann, Phys. Rev. B 9, 1–13 (1974).
[Crossref]

Hamilton, M. W.

D. S. Elliott, M. W. Hamilton, K. Arnett, and S. J. Smith, Phys. Rev. Lett. 53, 439–441 (1984).
[Crossref]

Hanamura, E.

E. Hanamura, J. Phys. Soc. Jpn. 52, 2258–2266, 3265–3274, 3678–3684 (1983).
[Crossref]

Hartmann, S. R.

Recent results obtained in transient spectroscopy with incoherent light may be found in, e.g., R. Beach and S. R. Hartmann, Phys. Rev. Lett. 53, 663–666 (1984); N. Morita and T. Yajima, Phys. Rev. A 30, 2525–2536 (1984).
[Crossref]

Y. C. Chen, K. Chiang, and S. R. Hartmann, Opt. Commun. 29, 181–185 (1979); J. B. W. Morsink and D. A. Wiersma, Chem. Phys. Lett. 65, 105–108 (1979).
[Crossref]

Herzog, B.

Similar problems were considered previously in magnetic resonance; see, for example, B. Herzog and E. L. Hahn, Phys. Rev. 103, 148–166 (1956); P. Hu and S. R. Hartmann, Phys. Rev. B 9, 1–13 (1974).
[Crossref]

Javanainen, J.

J. Javanainen, Opt. Commun. 50, 26–30 (1984); M. Yamanoi and J. H. EberlyPhys. Rev. Lett. 52, 1353 (1984); A. Schenzle, M. Mitsunaga, R. G. De Voe, and R. G. Brewer, Phys. Rev. A 30, 325–335 (1984); K. Wodkiewicz and J. H. Eberly, Phys. Rev. A 32, 992–1001 (1985); P. R. Berman and R. G. Brewer, Phys. Rev. A 32, 2784–2796 (1985).
[Crossref] [PubMed]

Kroll, M.

Lambropoulos, P.

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, and M. D. Levenson, J. Phys. B 11, 1733–1747 (1978); B. R. Marx, J. Simons, and L. Allen, J. Phys. B 11, L273–L277 (1978); A. T. Georges and P. Lambropoulos, Phys. Rev. A 20, 991–1004 (1979).
[Crossref]

Levenson, M. D.

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, and M. D. Levenson, J. Phys. B 11, 1733–1747 (1978); B. R. Marx, J. Simons, and L. Allen, J. Phys. B 11, L273–L277 (1978); A. T. Georges and P. Lambropoulos, Phys. Rev. A 20, 991–1004 (1979).
[Crossref]

Levy, J. M.

P. R. Berman, J. M. Levy, and R. G. Brewer, Phys. Rev. A 11, 1668–1688 (1975).
[Crossref]

Macke, B.

F. Rohart, H. Dève, and B. Macke, Appl. Phys. B 39, 19–27 (1986).
[Crossref]

B. Macke, J. Mol. Structure 97, 203–214 (1983); H. Dève, Thèse de 3ème Cycle (Université de Lille I, Lille, 1983; unpublished).
[Crossref]

F. Rohart and B. Macke, Appl. Phys. B 26, 23–30 (1981).
[Crossref]

F. Rohart and B. Macke, Z. Naturforsch,  36a, 929–936 (1981).

Mostowski, J.

See, for example, J. Mostowski and K. Rza̧żewski, Z. Phys. B 39, 183–185 (1980), and references therein.
[Crossref]

Purcell, E. M.

H. Y. Carr and E. M. Purcell, Phys. Rev. 94, 630–638 (1954).
[Crossref]

Rand, S. C.

R. G. De Voe, A. Szabo, S. C. Rand, and R. G. Brewer, Phys. Rev. Lett. 42, 1560–1563 (1979); R. M. Macfarlane, R. M. Shelby, and R. L. Shoemaker, Phys. Rev. Lett. 43, 1726–1730 (1979).
[Crossref]

Rohart, F.

F. Rohart, H. Dève, and B. Macke, Appl. Phys. B 39, 19–27 (1986).
[Crossref]

F. Rohart and B. Macke, Appl. Phys. B 26, 23–30 (1981).
[Crossref]

F. Rohart and B. Macke, Z. Naturforsch,  36a, 929–936 (1981).

F. Rohart, Thèse d’Etat (Université de Lille I, Lille, 1981; unpublished).

Rutman, J.

J. Rutman, Proc. IEEE 66, 1048–1075 (1978); Thèse d’Etat (Office National d’ Etudes et de Recherches Aérospatiales, Paris, 1972).
[Crossref]

Rza¸zewski, K.

See, for example, J. Mostowski and K. Rza̧żewski, Z. Phys. B 39, 183–185 (1980), and references therein.
[Crossref]

Searle, C. L.

L. S. Cutler and C. L. Searle, Proc. IEEE 54, 136–154 (1966).
[Crossref]

Shoemaker, R. L.

R. L. Shoemaker, in Laser and Coherence Spectroscopy, J. I. Steinfeld, ed. (Plenum, New York, 1978), pp. 197–371; R. H. Schwendeman, Ann. Rev. Phys. Chem. 29, 537–558 (1978); T. W. Mossberg, R. Kachru, S. R. Hartmann, and A. M. Flusberg, Phys. Rev. A 20, 1976–1996 (1979).
[Crossref]

Smith, S. J.

D. S. Elliott, M. W. Hamilton, K. Arnett, and S. J. Smith, Phys. Rev. Lett. 53, 439–441 (1984).
[Crossref]

Szabo, A.

R. G. De Voe, A. Szabo, S. C. Rand, and R. G. Brewer, Phys. Rev. Lett. 42, 1560–1563 (1979); R. M. Macfarlane, R. M. Shelby, and R. L. Shoemaker, Phys. Rev. Lett. 43, 1726–1730 (1979).
[Crossref]

A. Szabo and M. Kroll, Opt. Lett. 2, 10–12 (1978).
[Crossref] [PubMed]

Wheatley, S. E.

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, and M. D. Levenson, J. Phys. B 11, 1733–1747 (1978); B. R. Marx, J. Simons, and L. Allen, J. Phys. B 11, L273–L277 (1978); A. T. Georges and P. Lambropoulos, Phys. Rev. A 20, 991–1004 (1979).
[Crossref]

Wodkiewicz, K.

K. Wodkiewicz, Phys. Rev. A 19, 1686–1696 (1979).
[Crossref]

Appl. Phys. B (2)

F. Rohart and B. Macke, Appl. Phys. B 26, 23–30 (1981).
[Crossref]

F. Rohart, H. Dève, and B. Macke, Appl. Phys. B 39, 19–27 (1986).
[Crossref]

J. Mol. Structure (1)

B. Macke, J. Mol. Structure 97, 203–214 (1983); H. Dève, Thèse de 3ème Cycle (Université de Lille I, Lille, 1983; unpublished).
[Crossref]

J. Phys. B (2)

P. T. Greenland, J. Phys. B 17, 1919–1925 (1984); M. Helm and P. Zoller, Opt. Commun. 49, 324–328 (1984); B. W. Shore, J. Opt. Soc. Am. B 1, 176–188 (1984).
[Crossref]

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, and M. D. Levenson, J. Phys. B 11, 1733–1747 (1978); B. R. Marx, J. Simons, and L. Allen, J. Phys. B 11, L273–L277 (1978); A. T. Georges and P. Lambropoulos, Phys. Rev. A 20, 991–1004 (1979).
[Crossref]

J. Phys. Soc. Jpn. (1)

E. Hanamura, J. Phys. Soc. Jpn. 52, 2258–2266, 3265–3274, 3678–3684 (1983).
[Crossref]

Opt. Commun. (2)

J. Javanainen, Opt. Commun. 50, 26–30 (1984); M. Yamanoi and J. H. EberlyPhys. Rev. Lett. 52, 1353 (1984); A. Schenzle, M. Mitsunaga, R. G. De Voe, and R. G. Brewer, Phys. Rev. A 30, 325–335 (1984); K. Wodkiewicz and J. H. Eberly, Phys. Rev. A 32, 992–1001 (1985); P. R. Berman and R. G. Brewer, Phys. Rev. A 32, 2784–2796 (1985).
[Crossref] [PubMed]

Y. C. Chen, K. Chiang, and S. R. Hartmann, Opt. Commun. 29, 181–185 (1979); J. B. W. Morsink and D. A. Wiersma, Chem. Phys. Lett. 65, 105–108 (1979).
[Crossref]

Opt. Lett. (1)

Phys. Rev. (3)

Similar problems were considered previously in magnetic resonance; see, for example, B. Herzog and E. L. Hahn, Phys. Rev. 103, 148–166 (1956); P. Hu and S. R. Hartmann, Phys. Rev. B 9, 1–13 (1974).
[Crossref]

R. H. Dicke, Phys. Rev. 89, 472–473 (1953).
[Crossref]

H. Y. Carr and E. M. Purcell, Phys. Rev. 94, 630–638 (1954).
[Crossref]

Phys. Rev. A (2)

P. R. Berman, J. M. Levy, and R. G. Brewer, Phys. Rev. A 11, 1668–1688 (1975).
[Crossref]

K. Wodkiewicz, Phys. Rev. A 19, 1686–1696 (1979).
[Crossref]

Phys. Rev. Lett. (4)

Recent results obtained in transient spectroscopy with incoherent light may be found in, e.g., R. Beach and S. R. Hartmann, Phys. Rev. Lett. 53, 663–666 (1984); N. Morita and T. Yajima, Phys. Rev. A 30, 2525–2536 (1984).
[Crossref]

D. S. Elliott, M. W. Hamilton, K. Arnett, and S. J. Smith, Phys. Rev. Lett. 53, 439–441 (1984).
[Crossref]

R. G. De Voe, A. Szabo, S. C. Rand, and R. G. Brewer, Phys. Rev. Lett. 42, 1560–1563 (1979); R. M. Macfarlane, R. M. Shelby, and R. L. Shoemaker, Phys. Rev. Lett. 43, 1726–1730 (1979).
[Crossref]

R. G. De Voe and R. G. Brewer, Phys. Rev. Lett. 50, 1269–1272 (1983); analogous effects are also reported on a gaseous sample; see A. G. Yodh, J. Golub, N. W. Carlson, and T. W. Mossberg, 53, 659–662 (1984).
[Crossref]

Proc. IEEE (3)

L. S. Cutler and C. L. Searle, Proc. IEEE 54, 136–154 (1966).
[Crossref]

J. Rutman, Proc. IEEE 66, 1048–1075 (1978); Thèse d’Etat (Office National d’ Etudes et de Recherches Aérospatiales, Paris, 1972).
[Crossref]

D. W. Allan, Proc. IEEE 54, 221–230 (1966).
[Crossref]

Z. Naturforsch (1)

F. Rohart and B. Macke, Z. Naturforsch,  36a, 929–936 (1981).

Z. Phys. B (1)

See, for example, J. Mostowski and K. Rza̧żewski, Z. Phys. B 39, 183–185 (1980), and references therein.
[Crossref]

Other (4)

A discussion more specific to steady-state experiments and their connection with the e.m.-field bandwidth can be found in Ref. 6.

R. L. Shoemaker, in Laser and Coherence Spectroscopy, J. I. Steinfeld, ed. (Plenum, New York, 1978), pp. 197–371; R. H. Schwendeman, Ann. Rev. Phys. Chem. 29, 537–558 (1978); T. W. Mossberg, R. Kachru, S. R. Hartmann, and A. M. Flusberg, Phys. Rev. A 20, 1976–1996 (1979).
[Crossref]

F. Rohart, Thèse d’Etat (Université de Lille I, Lille, 1981; unpublished).

P. R. Berman and R. G. Brewer, in Proceedings of 7th International Laser Spectroscopy Conference, T. W. Hänsch and Y. R. Shen, eds. (Springer-Verlag, Berlin, to be published).

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Figures (5)

Fig. 1
Fig. 1

Stark sequence used for the observation of three-pulse photon echoes: a, π/2 pulse; b and c, π pulses. The pulse durations, assumed to be negligible (θ0, θ1, θ2T), are enlarged for sake of visibility.

Fig. 2
Fig. 2

π/2 pulse amplitude A versus the rms frequency deviation σ ϕ ˙. Experimental results, normalized to the amplitude A0 observed without frequency fluctuations, are obtained in the reversible limit (frequency-correlation time 1/q = 3.5 μsec) with a Rabi frequency ω1/2π = 0.5 MHz. The curve is computed with the inhomogeneous broadening of Eq. (8).

Fig. 3
Fig. 3

Inhomogeneous broadening Δveff deduced from optical precession signals versus rms frequency deviation σ ϕ ˙ (quadratic scales). Experimental results are obtained in the reversible limit (frequency-correlation time 1/q = 3.5 μsec). Duration of polarizing π/2 pulse, θ0 = 0.35 μsec. The ( σ ϕ ˙= 0) intercept of the line [Eq. (8)] corresponds to the line Doppler broadening.

Fig. 4
Fig. 4

Two-pulse photon-echo experiment: echo amplitude A versus the mean number of frequency jumps qt. For a fixed total sequence duration t = 2T = 13 μsec, the experiments were done for the rms frequency deviations σ ϕ ˙/2π (kHz): 55 (▲), 290 (●), and 450 (■). Theoretical curves are computed from Eqs. (7) and (12). In the reversible limit (qt ≪ 1) the echo amplitude A corresponds to the amplitude A0 obtained without frequency fluctuations ( σ ϕ ˙= 0).

Fig. 5
Fig. 5

Three-pulse photon echo experiment: amplitudes of the first echo (at time t1 = 2T = 9 μsec) and of the second echo (at time t2 = 4T = 18 μsec) versus the mean number of frequency jumps qt1 and qt2. The sequence duration was fixed, and the rms frequency deviation was σ ϕ ˙/2π = 450 kHz. Echo amplitudes are normalized to the respective values obtained without frequency fluctuations. Theoretical curves are computed from Eqs. (7), (12) (first echo), and (17) (second echo).

Equations (21)

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E ( t ) = ½ E 0 exp { i [ ω t + ϕ ( t ) ] } + c . c . ,
σ ϕ 2 ( τ ) = [ ϕ ( t + τ ) - ϕ ( t ) ] 2
σ ϕ 2 ( τ ) = τ - S ϕ ˙ ( Ω ) sinc 2 ( Ω τ / 2 ) d ( Ω τ / 2 π ) ,
σ ϕ 2 ( τ ) = τ S ϕ ˙ ( 0 ) ~ τ σ ϕ ˙ 2 / q .
σ ϕ 2 ( τ ) = τ 2 σ ϕ ˙ 2 ,
S ϕ ˙ ( Ω ) = 2 π ( σ ϕ ˙ 2 / q ) exp ( - Ω 2 / 2 q 2 )
σ ϕ 2 ( τ ) = σ ϕ ˙ 2 τ 2 { 2 π erf ( q τ / 2 ) / q τ - [ 1 - exp ( - q 2 τ 2 / 2 ) ] / ( q 2 τ 2 / 2 ) } .
Δ ω eff = ( Δ ω Dop 2 + 2 σ ϕ ˙ 2 log 2 ) 1 / 2 ,
ω 1 2 σ ϕ ˙ q ,
S ( t ) ~ exp [ - t / T 2 - t 2 / τ Dop 2 - σ ϕ 2 ( t ) / 2 ] .
S ( t = 2 T ) ~ exp [ - t / T 2 - φ 1 2 ( t ) / 2 ] ,
φ 1 2 ( t = 2 T ) = 4 σ ϕ 2 ( T ) - σ ϕ 2 ( 2 T ) .
σ a 2 ( 2 , T , T ) = ½ ( ω T ) - 2 [ t + T t + 2 T ϕ ˙ ( θ ) d θ - t t + T ϕ ˙ ( θ ) d θ ] 2 ,
φ 1 2 ( t = 2 T ) = 2 ω 2 T 2 σ a 2 ( 2 , T , T )
φ 1 2 ( t = 2 T ) = σ ϕ ˙ 2 q 2 t 4 / 16.
q t ~ 2 ( q 2 / σ ϕ ˙ ) 1 / 2 .
φ 1 2 ( t = 2 T ) = t S ϕ ˙ ( 0 ) ~ t σ ϕ ˙ 2 / q .
φ 2 2 ( t 2 = 4 T ) = σ ϕ 2 ( 4 T ) - 4 σ ϕ 2 ( 3 T ) + 4 σ ϕ 2 ( 2 T ) + 4 σ ϕ 2 ( T ) .
φ 2 2 ( t = 4 T ) = 3 σ ϕ ˙ 2 q 4 t 6 / 1024 ,
φ stim 2 ( t = 2 T + T ) = 2 σ ϕ ˙ 2 ( T ) - 2 0 T d θ 0 T d θ R ϕ ˙ ( θ + θ + T ) ,
φ stim 2 ( t = 4 T ) = 9 σ ϕ ˙ 2 q 2 t 4 / 256.

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