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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. T. Greenland, J. Phys. B 17, 1919–1925 (1984); M. Helm, 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, M. D. Levenson, J. Phys. B 11, 1733–1747 (1978); B. R. Marx, J. Simons, L. Allen, J. Phys. B 11, L273–L277 (1978); A. T. Georges, P. Lambropoulos, Phys. Rev. A 20, 991–1004 (1979).
    [CrossRef]
  3. F. Rohart, B. Macke, Appl. Phys. B 26, 23–30 (1981).
    [CrossRef]
  4. D. S. Elliott, M. W. Hamilton, K. Arnett, 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 Structure 97, 203–214 (1983); H. Dève, Thèse de 3ème Cycle (Université de Lille I, Lille, 1983; unpublished).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, 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, S. R. Hartmann, Phys. Rev. Lett. 53, 663–666 (1984); N. Morita, T. Yajima, Phys. Rev. A 30, 2525–2536 (1984).
    [CrossRef]
  10. See, for example, J. Mostowski, 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, J. H. EberlyPhys. Rev. Lett. 52, 1353 (1984); A. Schenzle, M. Mitsunaga, R. G. De Voe, R. G. Brewer, Phys. Rev. A 30, 325–335 (1984); K. Wodkiewicz, J. H. Eberly, Phys. Rev. A 32, 992–1001 (1985); P. R. Berman, 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, E. L. Hahn, Phys. Rev. 103, 148–166 (1956); P. Hu, S. R. Hartmann, Phys. Rev. B 9, 1–13 (1974).
    [CrossRef]
  14. R. G. De Voe, A. Szabo, S. C. Rand, R. G. Brewer, Phys. Rev. Lett. 42, 1560–1563 (1979); R. M. Macfarlane, R. M. Shelby, R. L. Shoemaker, Phys. Rev. Lett. 43, 1726–1730 (1979).
    [CrossRef]
  15. R. G. De Voe, 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, 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, A. M. Flusberg, Phys. Rev. A 20, 1976–1996 (1979).
    [CrossRef]
  17. A. Szabo, M. Kroll, Opt. Lett. 2, 10–12 (1978).
    [CrossRef] [PubMed]
  18. L. S. Cutler, 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, 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, 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, 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, S. R. Hartmann, Opt. Commun. 29, 181–185 (1979); J. B. W. Morsink, D. A. Wiersma, Chem. Phys. Lett. 65, 105–108 (1979).
    [CrossRef]
  27. P. R. Berman, R. G. Brewer, in Proceedings of 7th International Laser Spectroscopy Conference, T. W. Hänsch, Y. R. Shen, eds. (Springer-Verlag, Berlin, to be published).

1986 (1)

F. Rohart, H. Dève, 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, S. R. Hartmann, Phys. Rev. Lett. 53, 663–666 (1984); N. Morita, T. Yajima, Phys. Rev. A 30, 2525–2536 (1984).
[CrossRef]

P. T. Greenland, J. Phys. B 17, 1919–1925 (1984); M. Helm, 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, S. J. Smith, Phys. Rev. Lett. 53, 439–441 (1984).
[CrossRef]

J. Javanainen, Opt. Commun. 50, 26–30 (1984); M. Yamanoi, J. H. EberlyPhys. Rev. Lett. 52, 1353 (1984); A. Schenzle, M. Mitsunaga, R. G. De Voe, R. G. Brewer, Phys. Rev. A 30, 325–335 (1984); K. Wodkiewicz, J. H. Eberly, Phys. Rev. A 32, 992–1001 (1985); P. R. Berman, 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, 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, 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, B. Macke, Z. Naturforsch, 36a, 929–936 (1981).

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

1980 (1)

See, for example, J. Mostowski, 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, R. G. Brewer, Phys. Rev. Lett. 42, 1560–1563 (1979); R. M. Macfarlane, R. M. Shelby, R. L. Shoemaker, Phys. Rev. Lett. 43, 1726–1730 (1979).
[CrossRef]

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

1978 (3)

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

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

1975 (1)

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

1966 (2)

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

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

1956 (1)

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

1954 (1)

H. Y. Carr, 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, M. D. Levenson, J. Phys. B 11, 1733–1747 (1978); B. R. Marx, J. Simons, L. Allen, J. Phys. B 11, L273–L277 (1978); A. T. Georges, 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, 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, S. R. Hartmann, Phys. Rev. Lett. 53, 663–666 (1984); N. Morita, T. Yajima, Phys. Rev. A 30, 2525–2536 (1984).
[CrossRef]

Berman, P. R.

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

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

Brewer, R. G.

R. G. De Voe, 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, T. W. Mossberg, 53, 659–662 (1984).
[CrossRef]

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

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

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

Carr, H. Y.

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

Chen, Y. C.

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

Chiang, K.

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

Cutler, L. S.

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

De Voe, R. G.

R. G. De Voe, 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, T. W. Mossberg, 53, 659–662 (1984).
[CrossRef]

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

Dève, H.

F. Rohart, H. Dève, 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, S. J. Smith, Phys. Rev. Lett. 53, 439–441 (1984).
[CrossRef]

Georges, A. T.

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, M. D. Levenson, J. Phys. B 11, 1733–1747 (1978); B. R. Marx, J. Simons, L. Allen, J. Phys. B 11, L273–L277 (1978); A. T. Georges, 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, 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, E. L. Hahn, Phys. Rev. 103, 148–166 (1956); P. Hu, S. R. Hartmann, Phys. Rev. B 9, 1–13 (1974).
[CrossRef]

Hamilton, M. W.

D. S. Elliott, M. W. Hamilton, K. Arnett, 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, S. R. Hartmann, Phys. Rev. Lett. 53, 663–666 (1984); N. Morita, T. Yajima, Phys. Rev. A 30, 2525–2536 (1984).
[CrossRef]

Y. C. Chen, K. Chiang, S. R. Hartmann, Opt. Commun. 29, 181–185 (1979); J. B. W. Morsink, 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, E. L. Hahn, Phys. Rev. 103, 148–166 (1956); P. Hu, S. R. Hartmann, Phys. Rev. B 9, 1–13 (1974).
[CrossRef]

Javanainen, J.

J. Javanainen, Opt. Commun. 50, 26–30 (1984); M. Yamanoi, J. H. EberlyPhys. Rev. Lett. 52, 1353 (1984); A. Schenzle, M. Mitsunaga, R. G. De Voe, R. G. Brewer, Phys. Rev. A 30, 325–335 (1984); K. Wodkiewicz, J. H. Eberly, Phys. Rev. A 32, 992–1001 (1985); P. R. Berman, 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, M. D. Levenson, J. Phys. B 11, 1733–1747 (1978); B. R. Marx, J. Simons, L. Allen, J. Phys. B 11, L273–L277 (1978); A. T. Georges, P. Lambropoulos, Phys. Rev. A 20, 991–1004 (1979).
[CrossRef]

Levenson, M. D.

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

Levy, J. M.

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

Macke, B.

F. Rohart, H. Dève, 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, B. Macke, Appl. Phys. B 26, 23–30 (1981).
[CrossRef]

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

Mostowski, J.

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

Purcell, E. M.

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

Rand, S. C.

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

Rohart, F.

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

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

F. Rohart, 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, K. Rza̧żewski, Z. Phys. B 39, 183–185 (1980), and references therein.
[CrossRef]

Searle, C. L.

L. S. Cutler, 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, A. M. Flusberg, Phys. Rev. A 20, 1976–1996 (1979).
[CrossRef]

Smith, S. J.

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

Szabo, A.

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

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

Wheatley, S. E.

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, M. D. Levenson, J. Phys. B 11, 1733–1747 (1978); B. R. Marx, J. Simons, L. Allen, J. Phys. B 11, L273–L277 (1978); A. T. Georges, 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, B. Macke, Appl. Phys. B 26, 23–30 (1981).
[CrossRef]

F. Rohart, H. Dève, 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, 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, M. D. Levenson, J. Phys. B 11, 1733–1747 (1978); B. R. Marx, J. Simons, L. Allen, J. Phys. B 11, L273–L277 (1978); A. T. Georges, 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, J. H. EberlyPhys. Rev. Lett. 52, 1353 (1984); A. Schenzle, M. Mitsunaga, R. G. De Voe, R. G. Brewer, Phys. Rev. A 30, 325–335 (1984); K. Wodkiewicz, J. H. Eberly, Phys. Rev. A 32, 992–1001 (1985); P. R. Berman, R. G. Brewer, Phys. Rev. A 32, 2784–2796 (1985).
[CrossRef] [PubMed]

Y. C. Chen, K. Chiang, S. R. Hartmann, Opt. Commun. 29, 181–185 (1979); J. B. W. Morsink, 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, E. L. Hahn, Phys. Rev. 103, 148–166 (1956); P. Hu, S. R. Hartmann, Phys. Rev. B 9, 1–13 (1974).
[CrossRef]

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

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

Phys. Rev. A (2)

P. R. Berman, J. M. Levy, 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, S. R. Hartmann, Phys. Rev. Lett. 53, 663–666 (1984); N. Morita, T. Yajima, Phys. Rev. A 30, 2525–2536 (1984).
[CrossRef]

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

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

R. G. De Voe, 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, T. W. Mossberg, 53, 659–662 (1984).
[CrossRef]

Proc. IEEE (3)

L. S. Cutler, 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, B. Macke, Z. Naturforsch, 36a, 929–936 (1981).

Z. Phys. B (1)

See, for example, J. Mostowski, 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, 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, R. G. Brewer, in Proceedings of 7th International Laser Spectroscopy Conference, T. W. Hänsch, Y. R. Shen, eds. (Springer-Verlag, Berlin, to be published).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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)

Equations on this page are rendered with MathJax. Learn more.

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.

Metrics