Abstract

We have experimentally investigated the creation of spectrally ordered nuclear and electronic Zeeman coherences in a gas-phase sample. A Zeeman coherence is generated through the sequential excitation of two coupled optical transitions. In our experiment, one transition was excited by a data pulse and the other by a short reference pulse. Subsequent excitation of one of these transitions by a short reading pulse transforms the Zeeman coherence into an optical coherence and leads to the emission of a time-forward or time-reversed duplicate of the data pulse. Output signals up to 5% as intense as the original data pulse were observed. We present a general analysis that is applicable to both gases and solids and find that the solid-state analog of this process will exist only if the inhomogeneous broadening of the two optical transitions is highly correlated.

© 1985 Optical Society of America

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  1. S. Fernbach, W. G. Proctor, “Spin-echo memory device,” J. Appl. Phys. 26, 170 (1955).
    [CrossRef]
  2. A. G. Anderson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324 (1955).
    [CrossRef]
  3. S. O. Elyutin, S. M. Zakharov, E. A. Manykin, “Theoretical pulse-shapes for the photon (light) echo,” Zh. Eksp. Teor. Fiz. 76, 835 (1979) [Sov. Phys. JETP 49, 421 (1979)].
  4. V. A. Zuikov, V. V. Samartsev, R. G. Usmanov, “Correlation of the shape of the light echo signals with the shape of the excitation pulses,” Pisma Zh. Eksp. Teor. Fiz. 32, 293 (1980) [JETP Lett. 32, 270 (1980)];V. A. Zuikov, V. V. Samartsev, “Reverse photon echo method,” Phys. Status Solidi A 73, 683 (1982).
    [CrossRef]
  5. N. W. Carlson, L. J. Rothberg, A. G. Yodh, W. R. Babbitt, T. W. Mossberg, “Storage and time reversal of light pulses using photon echoes,” Opt. Lett. 8, 483 (1983).
    [CrossRef] [PubMed]
  6. N. W. Carlson, W. R. Babbitt, Y. S. Bai, T. W. Mossberg, “Field-inhibited optical dephasing and shape locking of photon echoes,” Opt. Lett. 9, 232 (1984).
    [CrossRef] [PubMed]
  7. T. 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 (1979).
    [CrossRef]
  8. 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 (1979).
    [CrossRef]
  9. J. B. W. Morsink, W. H. Hesselink, D. A. Wiersma, “Photon echo stimulated from optically induced nuclear spin polarization,” Chem. Phys. Lett. 64, 1 (1979).
    [CrossRef]
  10. J. B. W. Morsink, D. A. Wiersma, “Optical coherence storage in spin states,” in Proceedings of the Fourth International Conference on Laser Spectroscopy (Springer-Verlag, Berlin, 1979).
    [CrossRef]
  11. T. W. Mossberg, “Time-domain frequency-selective optical data storage,” Opt. Lett. 7, 77 (1982).
    [CrossRef] [PubMed]
  12. N. W. Carlson, Y. S. Bai, W. R. Babbitt, T. W. Mossberg, “Temporally programmed free-induction decay,” Phys. Rev. A 30, 1572 (1984).
    [CrossRef]
  13. A. Rebane, R. Kaarli, R. Saari, A. Anijalg, K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173 (1983).
    [CrossRef]
  14. W. Lange, J. Mlynek, “Quantum beats in transmission by time-resolved polarization spectroscopy,” Phys. Rev. Lett. 40, 1373 (1978).
    [CrossRef]
  15. J. Mlynek, W. Lange, H. Horde, H. Burggraf, “High-resolution coherence spectroscopy using pulse trains,” Phys. Rev. A 24, 1099 (1981).
    [CrossRef]
  16. Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, “Synchronized quantum beat spectroscopy using periodic impact excitations with cw mode-locking laser pulses,” Opt. Commun. 38, 357 (1981);R. G. Brewer, E. L. Hahn, “Coherent Raman beats,” Phys. Rev. A 8, 464 (1973).
    [CrossRef]
  17. See, for example, M. Levenson, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1982).For a detailed calculation of phase-matching in echoes, see T. W. Mossberg, E. Whittaker, R. Kachru, S. R. Hartmann, “Noble-gas-induced collisional broadening of the 3P1/2−3P3/2 transition of sodium measured by the tri-level-echo technique,”Phys. Rev. A 22, 1962 (1980).
    [CrossRef]

1984 (2)

N. W. Carlson, W. R. Babbitt, Y. S. Bai, T. W. Mossberg, “Field-inhibited optical dephasing and shape locking of photon echoes,” Opt. Lett. 9, 232 (1984).
[CrossRef] [PubMed]

N. W. Carlson, Y. S. Bai, W. R. Babbitt, T. W. Mossberg, “Temporally programmed free-induction decay,” Phys. Rev. A 30, 1572 (1984).
[CrossRef]

1983 (2)

A. Rebane, R. Kaarli, R. Saari, A. Anijalg, K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173 (1983).
[CrossRef]

N. W. Carlson, L. J. Rothberg, A. G. Yodh, W. R. Babbitt, T. W. Mossberg, “Storage and time reversal of light pulses using photon echoes,” Opt. Lett. 8, 483 (1983).
[CrossRef] [PubMed]

1982 (1)

1981 (2)

J. Mlynek, W. Lange, H. Horde, H. Burggraf, “High-resolution coherence spectroscopy using pulse trains,” Phys. Rev. A 24, 1099 (1981).
[CrossRef]

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, “Synchronized quantum beat spectroscopy using periodic impact excitations with cw mode-locking laser pulses,” Opt. Commun. 38, 357 (1981);R. G. Brewer, E. L. Hahn, “Coherent Raman beats,” Phys. Rev. A 8, 464 (1973).
[CrossRef]

1980 (1)

V. A. Zuikov, V. V. Samartsev, R. G. Usmanov, “Correlation of the shape of the light echo signals with the shape of the excitation pulses,” Pisma Zh. Eksp. Teor. Fiz. 32, 293 (1980) [JETP Lett. 32, 270 (1980)];V. A. Zuikov, V. V. Samartsev, “Reverse photon echo method,” Phys. Status Solidi A 73, 683 (1982).
[CrossRef]

1979 (4)

S. O. Elyutin, S. M. Zakharov, E. A. Manykin, “Theoretical pulse-shapes for the photon (light) echo,” Zh. Eksp. Teor. Fiz. 76, 835 (1979) [Sov. Phys. JETP 49, 421 (1979)].

T. 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 (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 (1979).
[CrossRef]

J. B. W. Morsink, W. H. Hesselink, D. A. Wiersma, “Photon echo stimulated from optically induced nuclear spin polarization,” Chem. Phys. Lett. 64, 1 (1979).
[CrossRef]

1978 (1)

W. Lange, J. Mlynek, “Quantum beats in transmission by time-resolved polarization spectroscopy,” Phys. Rev. Lett. 40, 1373 (1978).
[CrossRef]

1955 (2)

S. Fernbach, W. G. Proctor, “Spin-echo memory device,” J. Appl. Phys. 26, 170 (1955).
[CrossRef]

A. G. Anderson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324 (1955).
[CrossRef]

Anderson, A. G.

A. G. Anderson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324 (1955).
[CrossRef]

Anijalg, A.

A. Rebane, R. Kaarli, R. Saari, A. Anijalg, K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173 (1983).
[CrossRef]

Babbitt, W. R.

Bai, Y. S.

N. W. Carlson, W. R. Babbitt, Y. S. Bai, T. W. Mossberg, “Field-inhibited optical dephasing and shape locking of photon echoes,” Opt. Lett. 9, 232 (1984).
[CrossRef] [PubMed]

N. W. Carlson, Y. S. Bai, W. R. Babbitt, T. W. Mossberg, “Temporally programmed free-induction decay,” Phys. Rev. A 30, 1572 (1984).
[CrossRef]

Burggraf, H.

J. Mlynek, W. Lange, H. Horde, H. Burggraf, “High-resolution coherence spectroscopy using pulse trains,” Phys. Rev. A 24, 1099 (1981).
[CrossRef]

Carlson, N. W.

Elyutin, S. O.

S. O. Elyutin, S. M. Zakharov, E. A. Manykin, “Theoretical pulse-shapes for the photon (light) echo,” Zh. Eksp. Teor. Fiz. 76, 835 (1979) [Sov. Phys. JETP 49, 421 (1979)].

Fernbach, S.

S. Fernbach, W. G. Proctor, “Spin-echo memory device,” J. Appl. Phys. 26, 170 (1955).
[CrossRef]

Flusberg, A.

T. 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 (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 (1979).
[CrossRef]

Fukuda, Y.

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, “Synchronized quantum beat spectroscopy using periodic impact excitations with cw mode-locking laser pulses,” Opt. Commun. 38, 357 (1981);R. G. Brewer, E. L. Hahn, “Coherent Raman beats,” Phys. Rev. A 8, 464 (1973).
[CrossRef]

Garwin, R. L.

A. G. Anderson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324 (1955).
[CrossRef]

Hahn, E. L.

A. G. Anderson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324 (1955).
[CrossRef]

Hartmann, S. R.

T. 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 (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 (1979).
[CrossRef]

Hashi, T.

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, “Synchronized quantum beat spectroscopy using periodic impact excitations with cw mode-locking laser pulses,” Opt. Commun. 38, 357 (1981);R. G. Brewer, E. L. Hahn, “Coherent Raman beats,” Phys. Rev. A 8, 464 (1973).
[CrossRef]

Hayashi, J.

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, “Synchronized quantum beat spectroscopy using periodic impact excitations with cw mode-locking laser pulses,” Opt. Commun. 38, 357 (1981);R. G. Brewer, E. L. Hahn, “Coherent Raman beats,” Phys. Rev. A 8, 464 (1973).
[CrossRef]

Hesselink, W. H.

J. B. W. Morsink, W. H. Hesselink, D. A. Wiersma, “Photon echo stimulated from optically induced nuclear spin polarization,” Chem. Phys. Lett. 64, 1 (1979).
[CrossRef]

Horde, H.

J. Mlynek, W. Lange, H. Horde, H. Burggraf, “High-resolution coherence spectroscopy using pulse trains,” Phys. Rev. A 24, 1099 (1981).
[CrossRef]

Horton, J. W.

A. G. Anderson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324 (1955).
[CrossRef]

Kaarli, R.

A. Rebane, R. Kaarli, R. Saari, A. Anijalg, K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173 (1983).
[CrossRef]

Kachru, R.

T. 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 (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 (1979).
[CrossRef]

Kondo, K.

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, “Synchronized quantum beat spectroscopy using periodic impact excitations with cw mode-locking laser pulses,” Opt. Commun. 38, 357 (1981);R. G. Brewer, E. L. Hahn, “Coherent Raman beats,” Phys. Rev. A 8, 464 (1973).
[CrossRef]

Lange, W.

J. Mlynek, W. Lange, H. Horde, H. Burggraf, “High-resolution coherence spectroscopy using pulse trains,” Phys. Rev. A 24, 1099 (1981).
[CrossRef]

W. Lange, J. Mlynek, “Quantum beats in transmission by time-resolved polarization spectroscopy,” Phys. Rev. Lett. 40, 1373 (1978).
[CrossRef]

Levenson, M.

See, for example, M. Levenson, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1982).For a detailed calculation of phase-matching in echoes, see T. W. Mossberg, E. Whittaker, R. Kachru, S. R. Hartmann, “Noble-gas-induced collisional broadening of the 3P1/2−3P3/2 transition of sodium measured by the tri-level-echo technique,”Phys. Rev. A 22, 1962 (1980).
[CrossRef]

Manykin, E. A.

S. O. Elyutin, S. M. Zakharov, E. A. Manykin, “Theoretical pulse-shapes for the photon (light) echo,” Zh. Eksp. Teor. Fiz. 76, 835 (1979) [Sov. Phys. JETP 49, 421 (1979)].

Mlynek, J.

J. Mlynek, W. Lange, H. Horde, H. Burggraf, “High-resolution coherence spectroscopy using pulse trains,” Phys. Rev. A 24, 1099 (1981).
[CrossRef]

W. Lange, J. Mlynek, “Quantum beats in transmission by time-resolved polarization spectroscopy,” Phys. Rev. Lett. 40, 1373 (1978).
[CrossRef]

Morsink, J. B. W.

J. B. W. Morsink, W. H. Hesselink, D. A. Wiersma, “Photon echo stimulated from optically induced nuclear spin polarization,” Chem. Phys. Lett. 64, 1 (1979).
[CrossRef]

J. B. W. Morsink, D. A. Wiersma, “Optical coherence storage in spin states,” in Proceedings of the Fourth International Conference on Laser Spectroscopy (Springer-Verlag, Berlin, 1979).
[CrossRef]

Mossberg, T.

T. 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 (1979).
[CrossRef]

Mossberg, T. W.

Proctor, W. G.

S. Fernbach, W. G. Proctor, “Spin-echo memory device,” J. Appl. Phys. 26, 170 (1955).
[CrossRef]

Rebane, A.

A. Rebane, R. Kaarli, R. Saari, A. Anijalg, K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173 (1983).
[CrossRef]

Rothberg, L. J.

Saari, R.

A. Rebane, R. Kaarli, R. Saari, A. Anijalg, K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173 (1983).
[CrossRef]

Samartsev, V. V.

V. A. Zuikov, V. V. Samartsev, R. G. Usmanov, “Correlation of the shape of the light echo signals with the shape of the excitation pulses,” Pisma Zh. Eksp. Teor. Fiz. 32, 293 (1980) [JETP Lett. 32, 270 (1980)];V. A. Zuikov, V. V. Samartsev, “Reverse photon echo method,” Phys. Status Solidi A 73, 683 (1982).
[CrossRef]

Timpmann, K.

A. Rebane, R. Kaarli, R. Saari, A. Anijalg, K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173 (1983).
[CrossRef]

Tucker, G. L.

A. G. Anderson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324 (1955).
[CrossRef]

Usmanov, R. G.

V. A. Zuikov, V. V. Samartsev, R. G. Usmanov, “Correlation of the shape of the light echo signals with the shape of the excitation pulses,” Pisma Zh. Eksp. Teor. Fiz. 32, 293 (1980) [JETP Lett. 32, 270 (1980)];V. A. Zuikov, V. V. Samartsev, “Reverse photon echo method,” Phys. Status Solidi A 73, 683 (1982).
[CrossRef]

Walker, R. M.

A. G. Anderson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324 (1955).
[CrossRef]

Wiersma, D. A.

J. B. W. Morsink, W. H. Hesselink, D. A. Wiersma, “Photon echo stimulated from optically induced nuclear spin polarization,” Chem. Phys. Lett. 64, 1 (1979).
[CrossRef]

J. B. W. Morsink, D. A. Wiersma, “Optical coherence storage in spin states,” in Proceedings of the Fourth International Conference on Laser Spectroscopy (Springer-Verlag, Berlin, 1979).
[CrossRef]

Yodh, A. G.

Zakharov, S. M.

S. O. Elyutin, S. M. Zakharov, E. A. Manykin, “Theoretical pulse-shapes for the photon (light) echo,” Zh. Eksp. Teor. Fiz. 76, 835 (1979) [Sov. Phys. JETP 49, 421 (1979)].

Zuikov, V. A.

V. A. Zuikov, V. V. Samartsev, R. G. Usmanov, “Correlation of the shape of the light echo signals with the shape of the excitation pulses,” Pisma Zh. Eksp. Teor. Fiz. 32, 293 (1980) [JETP Lett. 32, 270 (1980)];V. A. Zuikov, V. V. Samartsev, “Reverse photon echo method,” Phys. Status Solidi A 73, 683 (1982).
[CrossRef]

Chem. Phys. Lett. (1)

J. B. W. Morsink, W. H. Hesselink, D. A. Wiersma, “Photon echo stimulated from optically induced nuclear spin polarization,” Chem. Phys. Lett. 64, 1 (1979).
[CrossRef]

J. Appl. Phys. (2)

S. Fernbach, W. G. Proctor, “Spin-echo memory device,” J. Appl. Phys. 26, 170 (1955).
[CrossRef]

A. G. Anderson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324 (1955).
[CrossRef]

Opt. Commun. (2)

A. Rebane, R. Kaarli, R. Saari, A. Anijalg, K. Timpmann, “Photochemical time-domain holography of weak picosecond pulses,” Opt. Commun. 47, 173 (1983).
[CrossRef]

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, “Synchronized quantum beat spectroscopy using periodic impact excitations with cw mode-locking laser pulses,” Opt. Commun. 38, 357 (1981);R. G. Brewer, E. L. Hahn, “Coherent Raman beats,” Phys. Rev. A 8, 464 (1973).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (3)

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 (1979).
[CrossRef]

N. W. Carlson, Y. S. Bai, W. R. Babbitt, T. W. Mossberg, “Temporally programmed free-induction decay,” Phys. Rev. A 30, 1572 (1984).
[CrossRef]

J. Mlynek, W. Lange, H. Horde, H. Burggraf, “High-resolution coherence spectroscopy using pulse trains,” Phys. Rev. A 24, 1099 (1981).
[CrossRef]

Phys. Rev. Lett. (2)

W. Lange, J. Mlynek, “Quantum beats in transmission by time-resolved polarization spectroscopy,” Phys. Rev. Lett. 40, 1373 (1978).
[CrossRef]

T. 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 (1979).
[CrossRef]

Pisma Zh. Eksp. Teor. Fiz. (1)

V. A. Zuikov, V. V. Samartsev, R. G. Usmanov, “Correlation of the shape of the light echo signals with the shape of the excitation pulses,” Pisma Zh. Eksp. Teor. Fiz. 32, 293 (1980) [JETP Lett. 32, 270 (1980)];V. A. Zuikov, V. V. Samartsev, “Reverse photon echo method,” Phys. Status Solidi A 73, 683 (1982).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

S. O. Elyutin, S. M. Zakharov, E. A. Manykin, “Theoretical pulse-shapes for the photon (light) echo,” Zh. Eksp. Teor. Fiz. 76, 835 (1979) [Sov. Phys. JETP 49, 421 (1979)].

Other (2)

J. B. W. Morsink, D. A. Wiersma, “Optical coherence storage in spin states,” in Proceedings of the Fourth International Conference on Laser Spectroscopy (Springer-Verlag, Berlin, 1979).
[CrossRef]

See, for example, M. Levenson, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1982).For a detailed calculation of phase-matching in echoes, see T. W. Mossberg, E. Whittaker, R. Kachru, S. R. Hartmann, “Noble-gas-induced collisional broadening of the 3P1/2−3P3/2 transition of sodium measured by the tri-level-echo technique,”Phys. Rev. A 22, 1962 (1980).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Energy-level schemes used in the discussion of (a) excited-state Zeeman coherences and (b) ground-state Zeeman coherences. Three excitation pulses, numbered according to their temporal order, excite the indicated transitions and lead to the emission of a FID signal.

Fig. 2
Fig. 2

Schematic of experimental setup. BS denotes a beam stop. PCBC denotes a polarizing cube beam combiner. λ/4 and λ/2 denote quarter- and half-wave plates. P1–P3 denote the path of excitation pulses. AOM1–AOM4 denote acousto-optic modulators. M1 is a moveable mirror. For creating excited-state coherences in the 3P1 state of 174Yb, AOM3 downshifted P2 (solid line). For creating ground-state coherences in nuclear spin levels of the 1S0 state of 173Yb, AOM3 upshifted P2 (dashed line), and M1 was moved to deflect P2 along the same path.

Fig. 3
Fig. 3

Excitation-pulse sequence and FID signal in excited-state Zeeman coherence experiment. Traces b)–e) have the same time scale. a) Excitation-pulse sequence and time-forward FID signal. Photon echo from pulses 1 and 3 is also shown. This scan was recorded by scattering excitation-pulse light into a photomultiplier tube, so the relative pulse intensities are not accurate. b) Reference (left) and read (right) pulses recorded on a photodiode. c) Data pulse recorded on photomultiplier. Laser tuned off resonance. d) Time-forward FID signal recorded on photomultiplier tube. e) Time-reversed FID signal recorded on photomultiplier tube.

Fig. 4
Fig. 4

Excitation pulses and FID signals from ground-state nuclear-spin coherences. a) Reference (left) and read (right) pulses recorded on photodiode. b) Data pulse recorded on photomultiplier tube. c) Time-reversed FID signal. The time interval between the reference and read pulses, τ23, was 400 nsec. d) Time-reversed FID signal with τ23 = 3000 nsec.

Fig. 5
Fig. 5

Ground-state nuclear Zeeman coherence FID as a function of data-pulse intensity. a) Data pulse recorded on photomultiplier tube. b) Time-reversed FID signal with data-pulse intensity of 0.17 W/cm2. c) Time-reversed FID signal showing severe distortion with a data-pulse intensity of 0.36 W/cm2.

Equations (28)

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E p ( r , t ) = E p ( t η p ) cos [ ω p ( t η p ) ] ,
η p = k ̂ p ( r r 0 ) c + t p ,
p = ( 2 π τ p ) E p α * ( ω α j ) exp ( i ω α j t ) + c . c . ,
E p α ( ω α j ) = β p α exp ( i ω α j t p α ) E p 0 ( β p α ω α j ) ,
β p α = ( 1 k ̂ p v α c ) 1 ,
t p α = β p α { t p + k ̂ p [ ( r α r 0 ) v α t ] c } ,
E p 0 ( ω α j ) = 1 2 π E p ( t ) cos ( ω p t ) exp ( i ω α j t ) d t .
θ p α ( ω α j ) = 4 π d j | E p α ( ω α j ) | /
ρ a b α exp ( i ω α > t 1 α ) exp ( i ω α < t 2 α ) E 1 0 * ( β 1 α ω α > ) E 2 0 ( β 2 α ω α < ) | E 1 0 ( β 1 α ω α > ) | | E 2 0 ( β 2 α ω α < ) | × sin θ 1 α sin ( θ 2 α 2 ) exp [ i ( ω α > ω α < ) t ] f α exp [ i ( ω α > ω α < ) t ] .
ρ α FID f α * [ exp ( i ω α > t 3 α ) E 3 0 * ( β 3 α ω α > ) sin ( θ 3 α 2 ) exp ( i ω α < t ) | E 3 0 ( β 3 α ω α > ) | ] .
ρ α FID ( r α , v α , ω α < , ω α > , t ) exp [ i ω α < ( t t 2 α ) + i ω α > ( t 3 α t 1 α ) ] × E 1 0 ( β 1 α ω α > ) E 2 0 * ( β 2 α ω α < ) E 3 0 * ( β 3 α ω α > ) .
E FID α ( r , t ) ρ α FID ( r α , v α , ω α < , ω α > , t ) | r r α | + c . c . ,
E FID ( r , t ) = α E FID α ( r , t ) .
γ α = ω α > / ω α < .
ρ FID ( r α , ω l α < , γ α , t ) E 1 0 ( γ α ω l α < ) E 2 0 * ( ω l α < ) × E 3 0 * ( γ α ω l α < ) × exp [ i ω l α < q ( r α , γ α , t ) ] ,
q ( r α , γ α , t ) = t [ t 3 + ( t 2 t 1 ) + ( r α r 0 ) c + ( γ α 1 ) ( t 3 t 1 ) ]
ω l α < = ω α < ( 1 + υ z α c ) .
E FID ( r , t ) d r s d ω l < d γ g ( r s , ω l < , γ ) × ρ FID [ r s , ω l < , γ , t ( r s ) ] | r r s | + c . c . ,
E FID ( r , t ) d ω l < d γ g ( ω l < , γ ) E 1 0 * ( γ ω l < ) × E 2 0 ( ω l < ) E 3 0 ( γ ω l < ) × exp [ i ω l < q ( r , γ , t ) ] + c . c . ,
E FID I ( r , t ; γ ) E 1 [ q ( r , γ , t ) γ 1 ] cos [ ω 1 q ( r , γ , t ) γ 1 ] .
E FID II ( r , t ; γ ) E 2 [ q ( r , γ , t ) ] cos [ ω 2 q ( r , γ , t ) ] ,
t FID ( r ) center = t 3 + ( t 2 t 1 ) + ( r r 0 ) c + ( γ 1 ) ( t 3 t 1 ) .
E FID II ( r , t ) d γ E FID II ( r , t ; γ ) G ( γ ) d γ E 2 { t [ t s + ( γ 1 ) ( t 3 t 1 ) ] } × cos ( ω 2 { t [ t s + ( γ 1 ) ( t 3 t 1 ) ] } ) G ( γ ) ,
t s = t 3 + ( t 2 t 1 ) + ( r r 0 ) c .
Δ γ 1 ω 2 ( t 3 t 1 ) ,
γ α 1 + ( 3 × 10 7 rad sec 1 / G ) B s / ω α <
Δ γ = ( 3 × 10 7 rad sec 1 / G ) Δ B s ω α < .
Δ B s [ ( 3 × 10 7 rad sec 1 / G ) ( t 3 t 1 ) ] 1 .

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