Abstract

Formation of coherent transients by incoherent light pulses has stimulated renewed interest in time-resolved coherent spectroscopy. Standard theories conveniently account for the weak-field regime experiments, but they fail to interpret the power effects that occur during resonant excitation of a sample by time-delayed, correlated, broadband laser pulses. We report on a new approach to this problem. We have been able to determine the expectation value of the population grating induced by two time-delayed, correlated, broadband light pulses under the limitation that one of the fields is weak. We have developed a diagrammatic technique that seems promising for the calculation of actual coherent-transient signals in the strong-field regime.

© 1988 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, “Accumulated photon echoes with incoherent light in Nd3+ doped silicate glass,” Phys. Rev A 29, 2286–2289 (1984).
    [CrossRef]
  2. H. Nakatsuka, M. Tomita, M. Fujiwara, S. Asaka, “Subpicosecond photon echoes by using nanosecond laser pulses,” Opt. Commun. 52, 150–152 (1984).
    [CrossRef]
  3. N. Morita, T. Yajima, “Ultra-high-resolution coherent transient spectroscopy with incoherent light,” Phys. Rev. A 30, 2525–2536 (1984).
    [CrossRef]
  4. M. Fujiwara, R. Kuroda, H. Nakatsuka, “Measurement of ultrafast dephasing time of cresyl fast violet in cellulose by photon echoes with incoherent light,” J. Opt. Soc. Am. B 2, 1634–1639 (1985).
    [CrossRef]
  5. J. E. Golub, T. W. Mossberg, “Studies of picosecond collisional dephasing in atomic sodium vapor using broad-bandwidth transient four-wave mixing,” J. Opt. Soc. Am. B 3, 554–559 (1986).
    [CrossRef]
  6. M. Tomita, M. Matsuoka, “Ultrafast pump–probe measurement using intensity correlation of incoherent light,” J. Opt. Soc. Am. B 3, 560–563 (1986).
    [CrossRef]
  7. M. Defour, J.-C. Keller, J.-L. Le Gouët, “Broadband excitation and inhomogeneous broadening in photon-echo experiments,” J. Opt. Soc. Am. B 3, 544–547 (1986).
    [CrossRef]
  8. J. E. Golub, T. W. Mossberg, “Ultra-high frequency interference beats in transient, incoherent-light four-wave mixing,” Opt. Lett. 11, 431–433 (1986).
    [CrossRef] [PubMed]
  9. R. Beach, D. De Beer, S. R. Hartmann, “Time-delayed fourwave mixing using intense incoherent light,” Phys. Rev. A 32, 3467–3474 (1985).
    [CrossRef] [PubMed]
  10. I. D. Abella, N. A. Kurnit, S. R. Hartmann, “Photon echoes,” Phys. Rev. 141, 391–406 (1966).
    [CrossRef]
  11. P. F. Liao, N. P. Economou, R. R. Freeman, “Two-photon coherent transient measurements of Doppler-free linewidths with broad excitation,” Phys. Rev. Lett. 39, 1473–1476 (1977).
    [CrossRef]
  12. R. G. Brewer, R. L. Shoemaker, “Optical free induction decay,” Phys. Rev. A 6, 2001–2007 (1972);R. G. de Voe, A. Szabo, S. C. Rand, R. G. Brewer, “Ultraslow optical dephasing of LaF3:Pr3+,” Phys. Rev. Lett. 42, 1560–1563 (1979).
    [CrossRef]
  13. A. Laubereau, W. Kaiser, “Vibrational dynamics of liquids and solids investigated by picosecond light pulses,” Rev. Mod. Phys. 50, 607–665 (1978);S. M. George, A. L. Harris, M. Berg, C. B. Harris, “Picosecond studies of the temperature dependence of homogeneous and inhomogeneous vibrational line width broadening in liquid acetonitrile,” J. Chem. Phys. 80, 83–94 (1984).
    [CrossRef]
  14. M. Defour, J.-C. Keller, J.-L. Le Gouët, “Power effects in broadband optical transients,” Phys. Rev. A 36, 5226–5234 (1987).
    [CrossRef] [PubMed]
  15. R. Friedberg, S. R. Hartmann, “A diagrammatic technique for calculating radiation of coherently or incoherently excited two-level atoms,” J. Phys. B 21, 683–712 (1988).
    [CrossRef]
  16. T. W. Mossberg, R. Kachru, S. R. Hartmann, A. M. Flusberg, “Echoes in gaseous media: a generalized theory of rephasing phenomena,” Phys. Rev. A 20, 1976–1996 (1979).
    [CrossRef]
  17. T. W. Mossberg, A. Flusberg, R. Kachru, S. R. Hartmann, “Total scattering cross section for Na on He measured by stimulated photon echoes,” Phys. Rev. Lett. 42, 1665–1669 (1979);R. Kachru, T. W. Mossberg, S. R. Hartmann, “Stimulated photon echo study of Na(32S1/2)–CO velocity changing collisions,” Opt. Commun. 30, 57–62 (1979).
    [CrossRef]
  18. H. Nakatsuka, J. Okada, M. Matsuoka, “Observation of coherence in two-photon excited Rb-vapor,” J. Phys. Soc. Jpn. 37, 1406–1412 (1974).
    [CrossRef]
  19. P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, M. D. Levenson, “Saturation effects in resonant three-photon ionisation of sodium with a non-monochromatic field,” J. Phys. B 11, 1733–1747 (1978).
    [CrossRef]
  20. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981), pp. 381–412.

1988 (1)

R. Friedberg, S. R. Hartmann, “A diagrammatic technique for calculating radiation of coherently or incoherently excited two-level atoms,” J. Phys. B 21, 683–712 (1988).
[CrossRef]

1987 (1)

M. Defour, J.-C. Keller, J.-L. Le Gouët, “Power effects in broadband optical transients,” Phys. Rev. A 36, 5226–5234 (1987).
[CrossRef] [PubMed]

1986 (4)

1985 (2)

1984 (3)

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, “Accumulated photon echoes with incoherent light in Nd3+ doped silicate glass,” Phys. Rev A 29, 2286–2289 (1984).
[CrossRef]

H. Nakatsuka, M. Tomita, M. Fujiwara, S. Asaka, “Subpicosecond photon echoes by using nanosecond laser pulses,” Opt. Commun. 52, 150–152 (1984).
[CrossRef]

N. Morita, T. Yajima, “Ultra-high-resolution coherent transient spectroscopy with incoherent light,” Phys. Rev. A 30, 2525–2536 (1984).
[CrossRef]

1979 (2)

T. W. Mossberg, R. Kachru, S. R. Hartmann, A. M. Flusberg, “Echoes in gaseous media: a generalized theory of rephasing phenomena,” Phys. Rev. A 20, 1976–1996 (1979).
[CrossRef]

T. W. Mossberg, A. Flusberg, R. Kachru, S. R. Hartmann, “Total scattering cross section for Na on He measured by stimulated photon echoes,” Phys. Rev. Lett. 42, 1665–1669 (1979);R. Kachru, T. W. Mossberg, S. R. Hartmann, “Stimulated photon echo study of Na(32S1/2)–CO velocity changing collisions,” Opt. Commun. 30, 57–62 (1979).
[CrossRef]

1978 (2)

A. Laubereau, W. Kaiser, “Vibrational dynamics of liquids and solids investigated by picosecond light pulses,” Rev. Mod. Phys. 50, 607–665 (1978);S. M. George, A. L. Harris, M. Berg, C. B. Harris, “Picosecond studies of the temperature dependence of homogeneous and inhomogeneous vibrational line width broadening in liquid acetonitrile,” J. Chem. Phys. 80, 83–94 (1984).
[CrossRef]

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, M. D. Levenson, “Saturation effects in resonant three-photon ionisation of sodium with a non-monochromatic field,” J. Phys. B 11, 1733–1747 (1978).
[CrossRef]

1977 (1)

P. F. Liao, N. P. Economou, R. R. Freeman, “Two-photon coherent transient measurements of Doppler-free linewidths with broad excitation,” Phys. Rev. Lett. 39, 1473–1476 (1977).
[CrossRef]

1974 (1)

H. Nakatsuka, J. Okada, M. Matsuoka, “Observation of coherence in two-photon excited Rb-vapor,” J. Phys. Soc. Jpn. 37, 1406–1412 (1974).
[CrossRef]

1972 (1)

R. G. Brewer, R. L. Shoemaker, “Optical free induction decay,” Phys. Rev. A 6, 2001–2007 (1972);R. G. de Voe, A. Szabo, S. C. Rand, R. G. Brewer, “Ultraslow optical dephasing of LaF3:Pr3+,” Phys. Rev. Lett. 42, 1560–1563 (1979).
[CrossRef]

1966 (1)

I. D. Abella, N. A. Kurnit, S. R. Hartmann, “Photon echoes,” Phys. Rev. 141, 391–406 (1966).
[CrossRef]

Abella, I. D.

I. D. Abella, N. A. Kurnit, S. R. Hartmann, “Photon echoes,” Phys. Rev. 141, 391–406 (1966).
[CrossRef]

Agostini, P.

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, M. D. Levenson, “Saturation effects in resonant three-photon ionisation of sodium with a non-monochromatic field,” J. Phys. B 11, 1733–1747 (1978).
[CrossRef]

Asaka, S.

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, “Accumulated photon echoes with incoherent light in Nd3+ doped silicate glass,” Phys. Rev A 29, 2286–2289 (1984).
[CrossRef]

H. Nakatsuka, M. Tomita, M. Fujiwara, S. Asaka, “Subpicosecond photon echoes by using nanosecond laser pulses,” Opt. Commun. 52, 150–152 (1984).
[CrossRef]

Beach, R.

R. Beach, D. De Beer, S. R. Hartmann, “Time-delayed fourwave mixing using intense incoherent light,” Phys. Rev. A 32, 3467–3474 (1985).
[CrossRef] [PubMed]

Brewer, R. G.

R. G. Brewer, R. L. Shoemaker, “Optical free induction decay,” Phys. Rev. A 6, 2001–2007 (1972);R. G. de Voe, A. Szabo, S. C. Rand, R. G. Brewer, “Ultraslow optical dephasing of LaF3:Pr3+,” Phys. Rev. Lett. 42, 1560–1563 (1979).
[CrossRef]

De Beer, D.

R. Beach, D. De Beer, S. R. Hartmann, “Time-delayed fourwave mixing using intense incoherent light,” Phys. Rev. A 32, 3467–3474 (1985).
[CrossRef] [PubMed]

Defour, M.

M. Defour, J.-C. Keller, J.-L. Le Gouët, “Power effects in broadband optical transients,” Phys. Rev. A 36, 5226–5234 (1987).
[CrossRef] [PubMed]

M. Defour, J.-C. Keller, J.-L. Le Gouët, “Broadband excitation and inhomogeneous broadening in photon-echo experiments,” J. Opt. Soc. Am. B 3, 544–547 (1986).
[CrossRef]

Economou, N. P.

P. F. Liao, N. P. Economou, R. R. Freeman, “Two-photon coherent transient measurements of Doppler-free linewidths with broad excitation,” Phys. Rev. Lett. 39, 1473–1476 (1977).
[CrossRef]

Flusberg, A.

T. W. Mossberg, A. Flusberg, R. Kachru, S. R. Hartmann, “Total scattering cross section for Na on He measured by stimulated photon echoes,” Phys. Rev. Lett. 42, 1665–1669 (1979);R. Kachru, T. W. Mossberg, S. R. Hartmann, “Stimulated photon echo study of Na(32S1/2)–CO velocity changing collisions,” Opt. Commun. 30, 57–62 (1979).
[CrossRef]

Flusberg, A. M.

T. W. Mossberg, R. Kachru, S. R. Hartmann, A. M. Flusberg, “Echoes in gaseous media: a generalized theory of rephasing phenomena,” Phys. Rev. A 20, 1976–1996 (1979).
[CrossRef]

Freeman, R. R.

P. F. Liao, N. P. Economou, R. R. Freeman, “Two-photon coherent transient measurements of Doppler-free linewidths with broad excitation,” Phys. Rev. Lett. 39, 1473–1476 (1977).
[CrossRef]

Friedberg, R.

R. Friedberg, S. R. Hartmann, “A diagrammatic technique for calculating radiation of coherently or incoherently excited two-level atoms,” J. Phys. B 21, 683–712 (1988).
[CrossRef]

Fujiwara, M.

M. Fujiwara, R. Kuroda, H. Nakatsuka, “Measurement of ultrafast dephasing time of cresyl fast violet in cellulose by photon echoes with incoherent light,” J. Opt. Soc. Am. B 2, 1634–1639 (1985).
[CrossRef]

H. Nakatsuka, M. Tomita, M. Fujiwara, S. Asaka, “Subpicosecond photon echoes by using nanosecond laser pulses,” Opt. Commun. 52, 150–152 (1984).
[CrossRef]

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, “Accumulated photon echoes with incoherent light in Nd3+ doped silicate glass,” Phys. Rev A 29, 2286–2289 (1984).
[CrossRef]

Georges, A. T.

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, M. D. Levenson, “Saturation effects in resonant three-photon ionisation of sodium with a non-monochromatic field,” J. Phys. B 11, 1733–1747 (1978).
[CrossRef]

Golub, J. E.

Hartmann, S. R.

R. Friedberg, S. R. Hartmann, “A diagrammatic technique for calculating radiation of coherently or incoherently excited two-level atoms,” J. Phys. B 21, 683–712 (1988).
[CrossRef]

R. Beach, D. De Beer, S. R. Hartmann, “Time-delayed fourwave mixing using intense incoherent light,” Phys. Rev. A 32, 3467–3474 (1985).
[CrossRef] [PubMed]

T. W. Mossberg, R. Kachru, S. R. Hartmann, A. M. Flusberg, “Echoes in gaseous media: a generalized theory of rephasing phenomena,” Phys. Rev. A 20, 1976–1996 (1979).
[CrossRef]

T. W. Mossberg, A. Flusberg, R. Kachru, S. R. Hartmann, “Total scattering cross section for Na on He measured by stimulated photon echoes,” Phys. Rev. Lett. 42, 1665–1669 (1979);R. Kachru, T. W. Mossberg, S. R. Hartmann, “Stimulated photon echo study of Na(32S1/2)–CO velocity changing collisions,” Opt. Commun. 30, 57–62 (1979).
[CrossRef]

I. D. Abella, N. A. Kurnit, S. R. Hartmann, “Photon echoes,” Phys. Rev. 141, 391–406 (1966).
[CrossRef]

Kachru, R.

T. W. Mossberg, R. Kachru, S. R. Hartmann, A. M. Flusberg, “Echoes in gaseous media: a generalized theory of rephasing phenomena,” Phys. Rev. A 20, 1976–1996 (1979).
[CrossRef]

T. W. Mossberg, A. Flusberg, R. Kachru, S. R. Hartmann, “Total scattering cross section for Na on He measured by stimulated photon echoes,” Phys. Rev. Lett. 42, 1665–1669 (1979);R. Kachru, T. W. Mossberg, S. R. Hartmann, “Stimulated photon echo study of Na(32S1/2)–CO velocity changing collisions,” Opt. Commun. 30, 57–62 (1979).
[CrossRef]

Kaiser, W.

A. Laubereau, W. Kaiser, “Vibrational dynamics of liquids and solids investigated by picosecond light pulses,” Rev. Mod. Phys. 50, 607–665 (1978);S. M. George, A. L. Harris, M. Berg, C. B. Harris, “Picosecond studies of the temperature dependence of homogeneous and inhomogeneous vibrational line width broadening in liquid acetonitrile,” J. Chem. Phys. 80, 83–94 (1984).
[CrossRef]

Keller, J.-C.

M. Defour, J.-C. Keller, J.-L. Le Gouët, “Power effects in broadband optical transients,” Phys. Rev. A 36, 5226–5234 (1987).
[CrossRef] [PubMed]

M. Defour, J.-C. Keller, J.-L. Le Gouët, “Broadband excitation and inhomogeneous broadening in photon-echo experiments,” J. Opt. Soc. Am. B 3, 544–547 (1986).
[CrossRef]

Kurnit, N. A.

I. D. Abella, N. A. Kurnit, S. R. Hartmann, “Photon echoes,” Phys. Rev. 141, 391–406 (1966).
[CrossRef]

Kuroda, R.

Lambropoulos, P.

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, M. D. Levenson, “Saturation effects in resonant three-photon ionisation of sodium with a non-monochromatic field,” J. Phys. B 11, 1733–1747 (1978).
[CrossRef]

Laubereau, A.

A. Laubereau, W. Kaiser, “Vibrational dynamics of liquids and solids investigated by picosecond light pulses,” Rev. Mod. Phys. 50, 607–665 (1978);S. M. George, A. L. Harris, M. Berg, C. B. Harris, “Picosecond studies of the temperature dependence of homogeneous and inhomogeneous vibrational line width broadening in liquid acetonitrile,” J. Chem. Phys. 80, 83–94 (1984).
[CrossRef]

Le Gouët, J.-L.

M. Defour, J.-C. Keller, J.-L. Le Gouët, “Power effects in broadband optical transients,” Phys. Rev. A 36, 5226–5234 (1987).
[CrossRef] [PubMed]

M. Defour, J.-C. Keller, J.-L. Le Gouët, “Broadband excitation and inhomogeneous broadening in photon-echo experiments,” J. Opt. Soc. Am. B 3, 544–547 (1986).
[CrossRef]

Levenson, M. D.

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, M. D. Levenson, “Saturation effects in resonant three-photon ionisation of sodium with a non-monochromatic field,” J. Phys. B 11, 1733–1747 (1978).
[CrossRef]

Liao, P. F.

P. F. Liao, N. P. Economou, R. R. Freeman, “Two-photon coherent transient measurements of Doppler-free linewidths with broad excitation,” Phys. Rev. Lett. 39, 1473–1476 (1977).
[CrossRef]

Matsuoka, M.

M. Tomita, M. Matsuoka, “Ultrafast pump–probe measurement using intensity correlation of incoherent light,” J. Opt. Soc. Am. B 3, 560–563 (1986).
[CrossRef]

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, “Accumulated photon echoes with incoherent light in Nd3+ doped silicate glass,” Phys. Rev A 29, 2286–2289 (1984).
[CrossRef]

H. Nakatsuka, J. Okada, M. Matsuoka, “Observation of coherence in two-photon excited Rb-vapor,” J. Phys. Soc. Jpn. 37, 1406–1412 (1974).
[CrossRef]

Morita, N.

N. Morita, T. Yajima, “Ultra-high-resolution coherent transient spectroscopy with incoherent light,” Phys. Rev. A 30, 2525–2536 (1984).
[CrossRef]

Mossberg, T. W.

J. E. Golub, T. W. Mossberg, “Studies of picosecond collisional dephasing in atomic sodium vapor using broad-bandwidth transient four-wave mixing,” J. Opt. Soc. Am. B 3, 554–559 (1986).
[CrossRef]

J. E. Golub, T. W. Mossberg, “Ultra-high frequency interference beats in transient, incoherent-light four-wave mixing,” Opt. Lett. 11, 431–433 (1986).
[CrossRef] [PubMed]

T. W. Mossberg, A. Flusberg, R. Kachru, S. R. Hartmann, “Total scattering cross section for Na on He measured by stimulated photon echoes,” Phys. Rev. Lett. 42, 1665–1669 (1979);R. Kachru, T. W. Mossberg, S. R. Hartmann, “Stimulated photon echo study of Na(32S1/2)–CO velocity changing collisions,” Opt. Commun. 30, 57–62 (1979).
[CrossRef]

T. W. Mossberg, R. Kachru, S. R. Hartmann, A. M. Flusberg, “Echoes in gaseous media: a generalized theory of rephasing phenomena,” Phys. Rev. A 20, 1976–1996 (1979).
[CrossRef]

Nakatsuka, H.

M. Fujiwara, R. Kuroda, H. Nakatsuka, “Measurement of ultrafast dephasing time of cresyl fast violet in cellulose by photon echoes with incoherent light,” J. Opt. Soc. Am. B 2, 1634–1639 (1985).
[CrossRef]

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, “Accumulated photon echoes with incoherent light in Nd3+ doped silicate glass,” Phys. Rev A 29, 2286–2289 (1984).
[CrossRef]

H. Nakatsuka, M. Tomita, M. Fujiwara, S. Asaka, “Subpicosecond photon echoes by using nanosecond laser pulses,” Opt. Commun. 52, 150–152 (1984).
[CrossRef]

H. Nakatsuka, J. Okada, M. Matsuoka, “Observation of coherence in two-photon excited Rb-vapor,” J. Phys. Soc. Jpn. 37, 1406–1412 (1974).
[CrossRef]

Okada, J.

H. Nakatsuka, J. Okada, M. Matsuoka, “Observation of coherence in two-photon excited Rb-vapor,” J. Phys. Soc. Jpn. 37, 1406–1412 (1974).
[CrossRef]

Shoemaker, R. L.

R. G. Brewer, R. L. Shoemaker, “Optical free induction decay,” Phys. Rev. A 6, 2001–2007 (1972);R. G. de Voe, A. Szabo, S. C. Rand, R. G. Brewer, “Ultraslow optical dephasing of LaF3:Pr3+,” Phys. Rev. Lett. 42, 1560–1563 (1979).
[CrossRef]

Tomita, M.

M. Tomita, M. Matsuoka, “Ultrafast pump–probe measurement using intensity correlation of incoherent light,” J. Opt. Soc. Am. B 3, 560–563 (1986).
[CrossRef]

H. Nakatsuka, M. Tomita, M. Fujiwara, S. Asaka, “Subpicosecond photon echoes by using nanosecond laser pulses,” Opt. Commun. 52, 150–152 (1984).
[CrossRef]

Van Kampen, N. G.

N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981), pp. 381–412.

Wheatley, S. E.

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, M. D. Levenson, “Saturation effects in resonant three-photon ionisation of sodium with a non-monochromatic field,” J. Phys. B 11, 1733–1747 (1978).
[CrossRef]

Yajima, T.

N. Morita, T. Yajima, “Ultra-high-resolution coherent transient spectroscopy with incoherent light,” Phys. Rev. A 30, 2525–2536 (1984).
[CrossRef]

J. Opt. Soc. Am. B (4)

J. Phys. B (2)

R. Friedberg, S. R. Hartmann, “A diagrammatic technique for calculating radiation of coherently or incoherently excited two-level atoms,” J. Phys. B 21, 683–712 (1988).
[CrossRef]

P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, M. D. Levenson, “Saturation effects in resonant three-photon ionisation of sodium with a non-monochromatic field,” J. Phys. B 11, 1733–1747 (1978).
[CrossRef]

J. Phys. Soc. Jpn. (1)

H. Nakatsuka, J. Okada, M. Matsuoka, “Observation of coherence in two-photon excited Rb-vapor,” J. Phys. Soc. Jpn. 37, 1406–1412 (1974).
[CrossRef]

Opt. Commun. (1)

H. Nakatsuka, M. Tomita, M. Fujiwara, S. Asaka, “Subpicosecond photon echoes by using nanosecond laser pulses,” Opt. Commun. 52, 150–152 (1984).
[CrossRef]

Opt. Lett. (1)

Phys. Rev A (1)

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, “Accumulated photon echoes with incoherent light in Nd3+ doped silicate glass,” Phys. Rev A 29, 2286–2289 (1984).
[CrossRef]

Phys. Rev. (1)

I. D. Abella, N. A. Kurnit, S. R. Hartmann, “Photon echoes,” Phys. Rev. 141, 391–406 (1966).
[CrossRef]

Phys. Rev. A (5)

N. Morita, T. Yajima, “Ultra-high-resolution coherent transient spectroscopy with incoherent light,” Phys. Rev. A 30, 2525–2536 (1984).
[CrossRef]

R. Beach, D. De Beer, S. R. Hartmann, “Time-delayed fourwave mixing using intense incoherent light,” Phys. Rev. A 32, 3467–3474 (1985).
[CrossRef] [PubMed]

M. Defour, J.-C. Keller, J.-L. Le Gouët, “Power effects in broadband optical transients,” Phys. Rev. A 36, 5226–5234 (1987).
[CrossRef] [PubMed]

R. G. Brewer, R. L. Shoemaker, “Optical free induction decay,” Phys. Rev. A 6, 2001–2007 (1972);R. G. de Voe, A. Szabo, S. C. Rand, R. G. Brewer, “Ultraslow optical dephasing of LaF3:Pr3+,” Phys. Rev. Lett. 42, 1560–1563 (1979).
[CrossRef]

T. W. Mossberg, R. Kachru, S. R. Hartmann, A. M. Flusberg, “Echoes in gaseous media: a generalized theory of rephasing phenomena,” Phys. Rev. A 20, 1976–1996 (1979).
[CrossRef]

Phys. Rev. Lett. (2)

T. W. Mossberg, A. Flusberg, R. Kachru, S. R. Hartmann, “Total scattering cross section for Na on He measured by stimulated photon echoes,” Phys. Rev. Lett. 42, 1665–1669 (1979);R. Kachru, T. W. Mossberg, S. R. Hartmann, “Stimulated photon echo study of Na(32S1/2)–CO velocity changing collisions,” Opt. Commun. 30, 57–62 (1979).
[CrossRef]

P. F. Liao, N. P. Economou, R. R. Freeman, “Two-photon coherent transient measurements of Doppler-free linewidths with broad excitation,” Phys. Rev. Lett. 39, 1473–1476 (1977).
[CrossRef]

Rev. Mod. Phys. (1)

A. Laubereau, W. Kaiser, “Vibrational dynamics of liquids and solids investigated by picosecond light pulses,” Rev. Mod. Phys. 50, 607–665 (1978);S. M. George, A. L. Harris, M. Berg, C. B. Harris, “Picosecond studies of the temperature dependence of homogeneous and inhomogeneous vibrational line width broadening in liquid acetonitrile,” J. Chem. Phys. 80, 83–94 (1984).
[CrossRef]

Other (1)

N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981), pp. 381–412.

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 (4)

Fig. 1
Fig. 1

Representation of the various correlation schemes involved in the expansion of the integrand in Eq. (11).

Fig. 2
Fig. 2

Representation of the correlation schemes that are dominant in the interaction of an atomic sample with two time-delayed, correlated fields. Expansion is restricted to the first order in the field χ2. which is assumed to be weak.

Fig. 3
Fig. 3

Diagrammatic representation of an atomic sample interaction with two time-delayed correlated fields under the assumption that one field is weak.

Fig. 4
Fig. 4

Two-line diagrams that are involved in the calculation of the second-order statistical moments of atomic quantities when excitation is provided by a single broadband field.

Equations (51)

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

n a b ( r , v , t ) = p = + n ̂ a b ( p ; v , t ) exp i p K r .
E i ( r , t ) = i ( t ) cos [ ω t k i r + φ i ( t ) ] ,
χ i ( t ) = μ a b i ( t ) exp [ i φ i ( t ) ] / ,
χ i ( t ) = χ i 0 ( t ) i ( t ) ,
i ( t ) = 0 , i ( t ) i * ( t τ ) = g ( τ ) , i ( t ) i ( t τ ) = 0 ,
τ c = 0 g ( τ ) d τ .
( t 1 ) ( t n ) * ( t n + 1 ) * ( t 2 n ) = p j = 1 n ( t j ) * [ t p ( n + j ) ] ,
γ a b τ c 1 , γ a τ L 1 , γ b τ L 1 .
a b ( r , v , t ) = Re [ χ ( r , t ) t d t χ * ( r , t ) × n a b ( r , v , t ) exp ( i Δ + γ a b ) ( t t ) ] ,
n ̂ a b ( 1 ; v , t ) = m = 1 n = 1 m ( ) m A m n ( v , t ) n a b ( 0 ) ( v ) , n ̂ a b ( 1 ; v , t ) = n ̂ a b * ( 1 ; v , t ) ,
A m n ( v , t ) = t d t 1 t 1 d t 2 t 2 n 2 d t 2 n 1 t 2 n 1 d t 2 n × t 2 m 2 d t 2 m 1 t 2 m 1 d t 2 m × Re [ χ 1 ( t 1 ) χ 1 * ( t 2 ) exp ( i Δ + γ a b ) ( t 1 t 2 ) ] × [ ½ χ 2 ( t 2 n 1 ) χ 1 * ( t 2 n ) exp ( i Δ + γ a b ) × ( t 2 n 1 t 2 n ) + ½ χ 1 * ( t 2 n 1 ) χ 2 ( t 2 n ) × exp ( i Δ γ a b ) ( t 2 n 1 t 2 n ) ] × Re [ χ 1 ( t 2 m 1 ) × χ 1 * ( t 2 m ) exp ( i Δ + γ a b ) ( t 2 m 1 t 2 m ) ] .
B ( t ) = t d t 1 t 1 d t 2 t 2 d t 3 t 3 d t 4 × Re [ χ ( t 1 ) χ * ( t 2 ) ] Re [ χ ( t 3 ) χ * ( t 4 ) ] .
χ 2 ( t ) = β χ 1 ( t t 12 ) .
A m n ( v , t ) = p = n m A m n p ( v , t ) ,
A m n p ( v , t ) = t d t 1 t 1 d t 2 t 2 n 2 d t 2 n 1 t 2 n 1 d t 2 n × t 2 n d t 2 n + 1 t 2 p 1 d t 2 p t 2 m 2 d t 2 m 1 t 2 m 1 d t 2 m × Re [ χ 1 ( t 1 ) χ 1 * ( t 2 ) exp ( i Δ + γ a b ) ( t 1 t 2 ) ] × × ½ χ 2 ( t 2 n 1 ) χ 1 * ( t 2 p ) exp ( i Δ + γ a b ) ( t 2 n 1 t 2 p ) × ½ χ 1 * ( t 2 n ) χ 1 ( t 2 n + 1 ) exp ( i Δ + γ a b ) ( t 2 n + 1 t 2 n ) × × ½ χ 1 * ( t 2 p 2 ) χ 1 ( t 2 p 1 ) exp ( i Δ + γ a b ) × ( t 2 p 1 t 2 p 2 ) × Re [ χ 1 ( t 2 p + 1 ) χ 1 * ( t 2 p + 2 ) × exp ( i Δ + γ a b ) ( t 2 p + 1 t 2 p + 2 ) ] × Re [ χ 1 ( t 2 m 1 ) × χ 1 * ( t 2 m ) exp ( i Δ + γ a b ) ( t 2 m 1 t 2 m ) ] .
A m n p ( v , t ) = β t d t 2 t 2 n 4 d t 2 n 2 t 2 n 2 t 12 × d t 2 p t 2 p t 2 p + t 12 d t 2 n + 1 t 2 p t 2 n + 1 d t 2 n + 3 × t 2 p t 2 p 3 d t 2 p 1 t 2 p d t 2 p + 2 t 2 m 2 d t 2 m × { Re [ G ( Δ ) ] } n [ χ 0 ( t 2 ) χ 0 ( t 2 n 2 ) ] 2 × [ G * ( Δ ) / 2 ] p n [ χ 0 ( t 2 p ) χ 0 ( t 2 n + 1 ) × χ 0 ( t 2 p 1 ) ] 2 × { Re [ G ( Δ ) ] } m p [ χ 0 ( t 2 p + 2 ) χ 0 ( t 2 m ) ] 2 × exp ( i Δ + γ a b ) t 12 ,
G ( Δ ) = 0 d τ g ( τ ) exp i Δ τ .
A m n p ( v , t ) = β Re [ G ( Δ ) ] t t 12 d t [ χ 0 ( t ) ] 2 × { Re [ G ( Δ ) ] t + t 12 t d t [ χ 0 ( t ) ] 2 } n 1 / ( n 1 ) ! × { G * ( Δ ) t t + t 12 d t [ χ 0 ( t ) ] 2 / 2 } p n / ( p n ) ! × { Re [ G ( Δ ) ] t d t [ χ 0 ( t ) ] 2 } m p / ( m p ) ! × exp ( i Δ + γ a b ) t 12 .
m = 1 n = 1 m p = n m ( ) m A m n p ( v , t ) = β t t 12 d t Re [ G ( Δ ) ] [ χ 0 ( t ) ] 2 × exp { Re [ G ( Δ ) ] t d t [ χ 0 ( t ) ] 2 } × exp { G * ( Δ ) t t + t 12 d t [ χ 0 ( t ) ] 2 / 2 } × exp ( i Δ + γ a b ) t 12 × exp { Re [ G ( Δ ) ] t + t 12 t d t [ χ 0 ( t ) ] 2 } .
U p ( t , t ; Δ ) = exp { Re [ G ( Δ ) ] t t d t [ χ 0 ( t ) ] 2 } ;
U c ( t , t ; Δ ) = exp { G * ( Δ ) t t d t [ χ 0 ( t ) ] 2 / 2 } × exp ( i Δ + γ a b ) ( t t ) ;
n a b ( r , v , t ) = U p ( t , t ; Δ ) n a b ( r , v , t ) .
n ̂ a b ( 1 ; v , t ) = β exp { Re [ G ( Δ ) ] t d t [ χ 0 ( t ) ] 2 } × t t 12 d t Re [ G ( Δ ) ] [ χ 0 ( t ) ] 2 × exp { G ( Δ ) t t + t 12 d t [ χ 0 ( t ) ] 2 / 2 } × exp ( i Δ + γ a b ) t 12 n a b ( 0 ) ( v ) .
exp { G ( Δ ) t t + t 12 d t [ χ 0 ( t ) ] 2 } exp ( i Δ + γ a b ) t 12 ,
g ( τ ) = exp ( | τ | / τ c ) .
n ̂ a b ( 1 ; v , t ) = β exp { t d t [ χ 0 ( t ) ] 2 τ c ( Δ ) } × t t 12 d t [ χ 0 ( t ) ] 2 τ c ( Δ ) × exp ( { γ a b [ χ 0 ( t ) ] 2 τ c ( Δ ) / 2 } t 12 ) × exp ( i Δ t 12 { 1 + [ χ 0 ( t ) ] 2 τ c ( Δ ) / 2 } ) × n a b ( 0 ) ( v ) ,
( Δ ) = ( 1 + Δ 2 τ c 2 ) 1 .
Ω D 2 τ c 3 τ L [ χ 0 ( t ) ] 2 1 .
Ω D 2 τ c 3 t 12 [ χ 0 ( t ) ] 2 1 .
Ω D 3 τ c 4 t 12 [ χ 0 ( t ) ] 2 1 .
exp { γ a b [ χ 0 ( t ) ] 2 τ c / 2 + i Δ } t 12 .
2 γ a b [ χ 0 ( t ) ] 2 τ c .
n a b ( v , t ) = m C m ( v , t ) n a b ( 0 ) ( v ) ,
C m ( v , t ) = t d t 1 t 1 d t 2 t 2 m 2 d t 2 m 1 t 2 m 1 d t 2 m × Re { χ ( t 1 ) χ * ( t 2 ) exp ( i Δ + γ a b ) ( t 1 t 2 ) ] } × × Re [ χ ( t 2 m 1 ) χ * ( t 2 m ) exp ( i Δ + γ a b ) × ( t 2 m 1 t 2 m ) ] .
U b ( t , t ; Ω ) = t t d t G ( 0 ) [ χ 0 ( t ) ] 2 [ U p ( t , t ; 0 ) ] 2 × 2 Re [ U c ( t , t ; Δ ) U c * ( t , t ; Δ ) ] ,
χ 0 ( t ) = { 0 t < 0 or t > T χ 0 0 t T .
U b ( t , t ; Ω ) = Θ ( t ) U ( t t ; Ω ) ,
U ( τ ; Ω ) = 2 α Re { [ exp ( α + 2 γ a b + i Ω ) τ exp 2 α τ ] / ( α 2 γ a b i Ω ) } ,
n a b ( v , t ) n a b ( v , t ) = m = 0 D 2 m ( v , v ; t ) [ n a b ( 0 ) ( v ) ] 2 ,
D 2 m ( v , v ; t ) = α m t d t 2 t 2 d t 4 t 2 m 2 d t 2 m × [ U p ( 0 , t 2 m ; 0 ) ] 2 U b ( t 2 m , t 2 m 2 ; Ω ) × × U b ( t 2 , t ; Ω )
D 2 m ( v , v ; t ) = α m 0 d τ 1 0 d τ 2 0 d τ m × exp 2 α ( t τ 1 τ 2 τ m ) × U ( τ m ; Ω ) U ( τ 1 ; Ω ) × Θ ( t τ 1 ) Θ ( t τ 1 τ 2 ) × Θ ( t τ 1 τ 2 τ m ) .
Θ ( t τ 1 ) Θ ( t τ 1 τ 2 ) Θ ( t τ 1 τ 2 τ m ) Θ ( t τ 1 τ 2 τ m ) .
Θ ( t τ 1 τ 2 τ m ) exp [ 2 α ( t τ 1 τ 2 τ m ) ] = 0 d τ m + 1 δ ( t τ 1 τ m τ m + 1 ) exp ( 2 α τ m + 1 ) .
D 2 m ( v , v , t ) = ( 2 π ) 1 d Q { [ α Û ( Q ; Ω ) ] m exp ( iQt ) } / ( i Q + 2 α ) ,
Û ( Q ; Ω ) = 0 d τ U ( τ ; Ω ) exp ( i Q τ ) .
n a b ( v , t ) n a b ( v , t ) = n a b ( v , 0 ) n a b ( v , 0 ) ( 2 π ) 1 × d Q exp ( iQt ) / { ( i Q + 2 α ) × [ 1 α Û ( Q ; Ω ) ] } .
[ n a b ( v , t ) ] 2 = [ n a b ( v , 0 ) ] 2 { α + 2 γ a b + 2 α exp [ ( 3 α + 2 γ a b ) t ] } / ( 3 α + 2 γ a b ) .
ρ a b ( v , t ) ρ b a ( v , t ) = n a b ( v , 0 ) n a b ( v , 0 ) α ( 2 π ) 1 × d Q exp iQt / { ( i Q + 2 α ) [ α + 2 γ a b + i ( Ω + Q ) ] [ 1 α Û ( Q ; Ω ) ] } .
n a b ( v , t ) n a b ( v , t ) = ρ a b ( v , 0 ) ρ b a ( v , 0 ) α ( 2 π ) 1 × d Q exp ( iQt ) / { ( i Q + 2 α ) [ α + 2 γ a b + i ( Q Ω ) ] [ 1 α Û ( Q ; Ω ) ] } .
ρ a b ( v , t ) ρ b a ( v , t ) = ρ a b ( v , 0 ) ρ b a ( v , 0 ) α 2 ( 2 π ) 1 × d Q exp ( iQt ) ( { [ α + 2 γ a b + i ( Q Ω ) ] 2 ( 2 α + i Q ) × [ 1 α Û ( Q ; Ω ) ] } 1 + α 2 × [ α + 2 γ a b + i ( Q Ω ) ] 1 ) ,
ρ b a ( v , t ) ρ a b ( v , t ) = ρ a b ( v , 0 ) ρ b a ( v , 0 ) α 2 ( 2 π ) 1 × d Q exp ( iQt ) { [ ( α + 2 γ a b + i Q ) 2 + Ω 2 ] + ( 2 α + i Q ) ] [ 1 α Û ( Q ; Ω ) ] } 1 .

Metrics