Abstract

We describe experimentally accessible diagnostics for the excitation of optically dense frequency-selective media by linear frequency-chirped pulses using a sensitive pump–probe technique on the  7F0 to  5D0 transitions of 1.0% Eu3+:Y2SiO5. Distinct features within a transmitted cw probe pulse are used to identify the combination of linear chirp rate and optical power needed to produce an average Bloch-vector rotation of 90°. The resulting superposition state is thus an equal mixture of the ground and excited states on average. We find experimentally a linear relationship between the applied chirp-pulse intensity and chirp rate required to produce this half-inversion, a conclusion supported by both analytical calculations made using a Landau–Zener approach, and detailed computer simulations using the Maxwell–Bloch model. The numerical simulations predict experimentally observed phenomena such as the reshaping of probe pulses by stimulated emission or absorption. Finally, we quantify the relationship between chirp rate and optical power for half-inversion as a function of the optical density of the medium. The pump–probe experimental techniques and simulation analysis techniques developed here can be extended to produce an arbitrary mixture of ground and excited states, on average, in media spanning a wide range of optical density. Preparation of such media by chirped pulses for applications in quantum computing, photon-echo-based time-domain storage, and signal processing will be aided by these techniques.

© 2004 Optical Society of America

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  1. R. M. Macfarlane and R. M. Shelby, “Coherent transient and holeburning spectroscopy,” in Spectroscopy of Solids Containing Rare Earths, A. A. Kaplyanskii and R. M. Macfarlane, eds. (North-Holland, Amsterdam, 1987).
  2. M. D. Levenson, “Time domain optical information storage in systems capable of photochemical hole burning,” IBM Tech. Discl. Bull. 7, 2797 (1981).
  3. T. W. Mossberg, “Time-domain frequency-selective optical-data storage,” Opt. Lett. 7, 77–79 (1982).
    [CrossRef] [PubMed]
  4. J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39, 745 (1960).
    [CrossRef]
  5. Y. S. Bai and T. W. Mossberg, “Photon echo optical pulse compression,” Appl. Phys. Lett. 45, 1269–1272 (1984).
    [CrossRef]
  6. Y. S. Bai and T. W. Mossberg, “Experimental studies of photon-echo pulse compression,” Opt. Lett. 11, 30–32 (1986).
    [CrossRef]
  7. Y. S. Bai, W. R. Babbitt, and T. W. Mossberg, “Coherent transient optical pulse-shape storage recall using frequency-swept excitation pulses,” Opt. Lett. 11, 724–726 (1986).
    [CrossRef] [PubMed]
  8. T. Wang, H. Lin, and T. W. Mossberg, “Optical bit-rate conversion and bit-stream time-reversal by the use of swept-carrier frequency-selective optical-data storage techniques,” Opt. Lett. 20, 2033–2035 (1995).
    [CrossRef] [PubMed]
  9. K. D. Merkel and W. R. Babbitt, “Chirped-pulse programming of optical coherent transient true-time delays,” Opt. Lett. 23, 528–530 (1998).
    [CrossRef]
  10. R. W. Olson, H. W. H. Lee, F. G. Patterson, and M. D. Fayer, “Optical-density effects in photon-echo experiments,” J. Chem. Phys. 76, 31–39 (1982).
    [CrossRef]
  11. S. B. Altner, G. Zumofen, U. P. Wild, and M. Mitsunaga, “Photon-echo attenuation in rare-earth-ion-doped crystals,” Phys. Rev. B 54, 17493–17507 (1996).
    [CrossRef]
  12. M. Azadeh, C. S. Cornish, W. R. Babbitt, and L. Tsang, “Efficient photon echoes in optically thick media,” Phys. Rev. A 57, 4662–4668 (1998).
    [CrossRef]
  13. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1975).
  14. N. Ohlsson, R. K. Mohan, and S. Kroll, “Quantum computer hardware based on rare-earth-ion-doped inorganic crystals,” Opt. Commun. 201, 71–77 (2002).
    [CrossRef]
  15. M. Nilsson, L. Levin, N. Ohlsson, T. Christiansson, and S. Kroll, “Initial experiments concerning quantum information processing in rare-earth-ion doped crystals,” Phys. Scr. T102, 178–185 (2002).
    [CrossRef]
  16. L. D. Landau, “Zur Theorie der Energieübertragung II,” Phys. Z. Sowjetunion 2, 46 (1932).
  17. C. Zener, “Non-adiabatic crossing of energy levels,” Proc. R. Soc. London Ser. A 137, 696 (1932).
    [CrossRef]
  18. N. V. Vitanov and B. M. Garraway, “Landau–Zener model: effects of finite coupling duration,” Phys. Rev. A 53, 4288 (1996).
    [CrossRef] [PubMed]
  19. For mathematical convenience, Vitanov and Garraway (Ref. 18) chose to define Ω0 [rad/s ] as half of the laboratory Rabi frequency on resonance and β2 [rad/s 2 ] as half of the laboratory laser chirp rate, leading to a definition of the scaled dimensionless-coupling strength of ω=Ω0 /β. We have chosen quantities and units more convenient to the laboratory such that Ω0 [s −1 ] is the full laboratory Rabi frequency of the chirp, and Bcc [s −2 ] is the full laboratory chirp rate leading to definition of dimensionless-coupling strength given in Eq. (1). For comparisons with results in Ref. 26, it is easy to verify that Φ=ω/π.
  20. R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, “Geometrical representation of the Schrodinger equation for solving maser problems,” J. Appl. Phys. 28, 49–52 (1957).
    [CrossRef]
  21. R. Yano, M. Mitsunaga, and N. Uesugi, “Ultralong optical dephasing time in Eu3+:Y2SiO5,” Opt. Lett. 16, 1884–1886 (1991).
    [CrossRef] [PubMed]
  22. R. W. Equall, Y. Sun, R. L. Cone, and R. M. Macfarlane, “Ultraslow optical dephasing in Eu3+:Y2SiO5,” Phys. Rev. Lett. 72, 2179–2181 (1994).
    [CrossRef] [PubMed]
  23. R. Yano, M. Mitsunaga, and N. Uesugi, “Nonlinear laser spectroscopy of Eu3+:Y2SiO5 and its application to time-domain optical memory,” J. Opt. Soc. Am. B 9, 992–997 (1992).
    [CrossRef]
  24. F. Konz, Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, R. L. Hutcheson, and R. M. Macfarlane, “Temperature and concentration dependence of optical dephasing, spectral hole lifetime, and anisotropic absorption in Eu3+:Y2SiO5,” Phys. Rev. B 68, 085109 (2003).
    [CrossRef]
  25. Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. M. Leask, “Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystals,” Phys. Rev. B 62, 15443–15451 (2000).
    [CrossRef]
  26. B. A. Maximov, V. V. Illyukhin, Yu. A. Kharitonov, and N. V. Belov, “Crystal structure of yttrium oxyorthosilicate Y2O3⋅SiO2=Y2SiO5 dual function of yttrium,” Sov. Phys. Crystallogr. 15, 806–812 (1971).
  27. C. Li, C. Wyon, and R. Moncorge, “Spectroscopic properties and fluorescence dynamics of Er3+ and Yb3+ in Y2SiO5,” IEEE J. Quantum Electron. 28, 1209–1221 (1992).
    [CrossRef]
  28. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97–105 (1983).
    [CrossRef]
  29. R. L. Shoemaker, “Coherent transient infrared spectroscopy,” in Laser and Coherence Spectroscopy, J. I. Steinfield, ed. (Plenum, New York, 1978), pp. 197–317.
  30. Y. Sun, P. B. Sellin, C. M. Jefferson, and R. L. Cone, “Oscillator strength measurements on Eu 3+ :Y 2 SiO 5” (unpublished).
  31. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  32. G. W. Burr, T. L. Harris, W. R. Babbitt, and C. M. Jefferson, “Incorporating excitation-induced dephasing into the Maxwell–Bloch numerical modeling of photon echoes,” and references therein, J. Lumin. (to be published).

2003 (1)

F. Konz, Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, R. L. Hutcheson, and R. M. Macfarlane, “Temperature and concentration dependence of optical dephasing, spectral hole lifetime, and anisotropic absorption in Eu3+:Y2SiO5,” Phys. Rev. B 68, 085109 (2003).
[CrossRef]

2002 (2)

N. Ohlsson, R. K. Mohan, and S. Kroll, “Quantum computer hardware based on rare-earth-ion-doped inorganic crystals,” Opt. Commun. 201, 71–77 (2002).
[CrossRef]

M. Nilsson, L. Levin, N. Ohlsson, T. Christiansson, and S. Kroll, “Initial experiments concerning quantum information processing in rare-earth-ion doped crystals,” Phys. Scr. T102, 178–185 (2002).
[CrossRef]

2000 (1)

Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. M. Leask, “Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystals,” Phys. Rev. B 62, 15443–15451 (2000).
[CrossRef]

1998 (2)

M. Azadeh, C. S. Cornish, W. R. Babbitt, and L. Tsang, “Efficient photon echoes in optically thick media,” Phys. Rev. A 57, 4662–4668 (1998).
[CrossRef]

K. D. Merkel and W. R. Babbitt, “Chirped-pulse programming of optical coherent transient true-time delays,” Opt. Lett. 23, 528–530 (1998).
[CrossRef]

1996 (2)

S. B. Altner, G. Zumofen, U. P. Wild, and M. Mitsunaga, “Photon-echo attenuation in rare-earth-ion-doped crystals,” Phys. Rev. B 54, 17493–17507 (1996).
[CrossRef]

N. V. Vitanov and B. M. Garraway, “Landau–Zener model: effects of finite coupling duration,” Phys. Rev. A 53, 4288 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (1)

R. W. Equall, Y. Sun, R. L. Cone, and R. M. Macfarlane, “Ultraslow optical dephasing in Eu3+:Y2SiO5,” Phys. Rev. Lett. 72, 2179–2181 (1994).
[CrossRef] [PubMed]

1992 (2)

R. Yano, M. Mitsunaga, and N. Uesugi, “Nonlinear laser spectroscopy of Eu3+:Y2SiO5 and its application to time-domain optical memory,” J. Opt. Soc. Am. B 9, 992–997 (1992).
[CrossRef]

C. Li, C. Wyon, and R. Moncorge, “Spectroscopic properties and fluorescence dynamics of Er3+ and Yb3+ in Y2SiO5,” IEEE J. Quantum Electron. 28, 1209–1221 (1992).
[CrossRef]

1991 (1)

1986 (2)

1984 (1)

Y. S. Bai and T. W. Mossberg, “Photon echo optical pulse compression,” Appl. Phys. Lett. 45, 1269–1272 (1984).
[CrossRef]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

1982 (2)

T. W. Mossberg, “Time-domain frequency-selective optical-data storage,” Opt. Lett. 7, 77–79 (1982).
[CrossRef] [PubMed]

R. W. Olson, H. W. H. Lee, F. G. Patterson, and M. D. Fayer, “Optical-density effects in photon-echo experiments,” J. Chem. Phys. 76, 31–39 (1982).
[CrossRef]

1981 (1)

M. D. Levenson, “Time domain optical information storage in systems capable of photochemical hole burning,” IBM Tech. Discl. Bull. 7, 2797 (1981).

1971 (1)

B. A. Maximov, V. V. Illyukhin, Yu. A. Kharitonov, and N. V. Belov, “Crystal structure of yttrium oxyorthosilicate Y2O3⋅SiO2=Y2SiO5 dual function of yttrium,” Sov. Phys. Crystallogr. 15, 806–812 (1971).

1960 (1)

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39, 745 (1960).
[CrossRef]

1957 (1)

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, “Geometrical representation of the Schrodinger equation for solving maser problems,” J. Appl. Phys. 28, 49–52 (1957).
[CrossRef]

1932 (2)

L. D. Landau, “Zur Theorie der Energieübertragung II,” Phys. Z. Sowjetunion 2, 46 (1932).

C. Zener, “Non-adiabatic crossing of energy levels,” Proc. R. Soc. London Ser. A 137, 696 (1932).
[CrossRef]

Albersheim, W. J.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39, 745 (1960).
[CrossRef]

Altner, S. B.

S. B. Altner, G. Zumofen, U. P. Wild, and M. Mitsunaga, “Photon-echo attenuation in rare-earth-ion-doped crystals,” Phys. Rev. B 54, 17493–17507 (1996).
[CrossRef]

Azadeh, M.

M. Azadeh, C. S. Cornish, W. R. Babbitt, and L. Tsang, “Efficient photon echoes in optically thick media,” Phys. Rev. A 57, 4662–4668 (1998).
[CrossRef]

Babbitt, W. R.

Bai, Y. S.

Belov, N. V.

B. A. Maximov, V. V. Illyukhin, Yu. A. Kharitonov, and N. V. Belov, “Crystal structure of yttrium oxyorthosilicate Y2O3⋅SiO2=Y2SiO5 dual function of yttrium,” Sov. Phys. Crystallogr. 15, 806–812 (1971).

Christiansson, T.

M. Nilsson, L. Levin, N. Ohlsson, T. Christiansson, and S. Kroll, “Initial experiments concerning quantum information processing in rare-earth-ion doped crystals,” Phys. Scr. T102, 178–185 (2002).
[CrossRef]

Cone, R. L.

F. Konz, Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, R. L. Hutcheson, and R. M. Macfarlane, “Temperature and concentration dependence of optical dephasing, spectral hole lifetime, and anisotropic absorption in Eu3+:Y2SiO5,” Phys. Rev. B 68, 085109 (2003).
[CrossRef]

Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. M. Leask, “Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystals,” Phys. Rev. B 62, 15443–15451 (2000).
[CrossRef]

R. W. Equall, Y. Sun, R. L. Cone, and R. M. Macfarlane, “Ultraslow optical dephasing in Eu3+:Y2SiO5,” Phys. Rev. Lett. 72, 2179–2181 (1994).
[CrossRef] [PubMed]

Cornish, C. S.

M. Azadeh, C. S. Cornish, W. R. Babbitt, and L. Tsang, “Efficient photon echoes in optically thick media,” Phys. Rev. A 57, 4662–4668 (1998).
[CrossRef]

Darlington, S.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39, 745 (1960).
[CrossRef]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Equall, R. W.

F. Konz, Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, R. L. Hutcheson, and R. M. Macfarlane, “Temperature and concentration dependence of optical dephasing, spectral hole lifetime, and anisotropic absorption in Eu3+:Y2SiO5,” Phys. Rev. B 68, 085109 (2003).
[CrossRef]

Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. M. Leask, “Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystals,” Phys. Rev. B 62, 15443–15451 (2000).
[CrossRef]

R. W. Equall, Y. Sun, R. L. Cone, and R. M. Macfarlane, “Ultraslow optical dephasing in Eu3+:Y2SiO5,” Phys. Rev. Lett. 72, 2179–2181 (1994).
[CrossRef] [PubMed]

Fayer, M. D.

R. W. Olson, H. W. H. Lee, F. G. Patterson, and M. D. Fayer, “Optical-density effects in photon-echo experiments,” J. Chem. Phys. 76, 31–39 (1982).
[CrossRef]

Feynman, R. P.

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, “Geometrical representation of the Schrodinger equation for solving maser problems,” J. Appl. Phys. 28, 49–52 (1957).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Garraway, B. M.

N. V. Vitanov and B. M. Garraway, “Landau–Zener model: effects of finite coupling duration,” Phys. Rev. A 53, 4288 (1996).
[CrossRef] [PubMed]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Hellwarth, R. W.

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, “Geometrical representation of the Schrodinger equation for solving maser problems,” J. Appl. Phys. 28, 49–52 (1957).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Hutcheson, R. L.

F. Konz, Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, R. L. Hutcheson, and R. M. Macfarlane, “Temperature and concentration dependence of optical dephasing, spectral hole lifetime, and anisotropic absorption in Eu3+:Y2SiO5,” Phys. Rev. B 68, 085109 (2003).
[CrossRef]

Illyukhin, V. V.

B. A. Maximov, V. V. Illyukhin, Yu. A. Kharitonov, and N. V. Belov, “Crystal structure of yttrium oxyorthosilicate Y2O3⋅SiO2=Y2SiO5 dual function of yttrium,” Sov. Phys. Crystallogr. 15, 806–812 (1971).

Kharitonov, Yu. A.

B. A. Maximov, V. V. Illyukhin, Yu. A. Kharitonov, and N. V. Belov, “Crystal structure of yttrium oxyorthosilicate Y2O3⋅SiO2=Y2SiO5 dual function of yttrium,” Sov. Phys. Crystallogr. 15, 806–812 (1971).

Klauder, J. R.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39, 745 (1960).
[CrossRef]

Konz, F.

F. Konz, Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, R. L. Hutcheson, and R. M. Macfarlane, “Temperature and concentration dependence of optical dephasing, spectral hole lifetime, and anisotropic absorption in Eu3+:Y2SiO5,” Phys. Rev. B 68, 085109 (2003).
[CrossRef]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Kroll, S.

M. Nilsson, L. Levin, N. Ohlsson, T. Christiansson, and S. Kroll, “Initial experiments concerning quantum information processing in rare-earth-ion doped crystals,” Phys. Scr. T102, 178–185 (2002).
[CrossRef]

N. Ohlsson, R. K. Mohan, and S. Kroll, “Quantum computer hardware based on rare-earth-ion-doped inorganic crystals,” Opt. Commun. 201, 71–77 (2002).
[CrossRef]

Landau, L. D.

L. D. Landau, “Zur Theorie der Energieübertragung II,” Phys. Z. Sowjetunion 2, 46 (1932).

Leask, M. J. M.

Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. M. Leask, “Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystals,” Phys. Rev. B 62, 15443–15451 (2000).
[CrossRef]

Lee, H. W. H.

R. W. Olson, H. W. H. Lee, F. G. Patterson, and M. D. Fayer, “Optical-density effects in photon-echo experiments,” J. Chem. Phys. 76, 31–39 (1982).
[CrossRef]

Levenson, M. D.

M. D. Levenson, “Time domain optical information storage in systems capable of photochemical hole burning,” IBM Tech. Discl. Bull. 7, 2797 (1981).

Levin, L.

M. Nilsson, L. Levin, N. Ohlsson, T. Christiansson, and S. Kroll, “Initial experiments concerning quantum information processing in rare-earth-ion doped crystals,” Phys. Scr. T102, 178–185 (2002).
[CrossRef]

Li, C.

C. Li, C. Wyon, and R. Moncorge, “Spectroscopic properties and fluorescence dynamics of Er3+ and Yb3+ in Y2SiO5,” IEEE J. Quantum Electron. 28, 1209–1221 (1992).
[CrossRef]

Lin, H.

Macfarlane, R. M.

F. Konz, Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, R. L. Hutcheson, and R. M. Macfarlane, “Temperature and concentration dependence of optical dephasing, spectral hole lifetime, and anisotropic absorption in Eu3+:Y2SiO5,” Phys. Rev. B 68, 085109 (2003).
[CrossRef]

R. W. Equall, Y. Sun, R. L. Cone, and R. M. Macfarlane, “Ultraslow optical dephasing in Eu3+:Y2SiO5,” Phys. Rev. Lett. 72, 2179–2181 (1994).
[CrossRef] [PubMed]

Maximov, B. A.

B. A. Maximov, V. V. Illyukhin, Yu. A. Kharitonov, and N. V. Belov, “Crystal structure of yttrium oxyorthosilicate Y2O3⋅SiO2=Y2SiO5 dual function of yttrium,” Sov. Phys. Crystallogr. 15, 806–812 (1971).

Merkel, K. D.

Mitsunaga, M.

Mohan, R. K.

N. Ohlsson, R. K. Mohan, and S. Kroll, “Quantum computer hardware based on rare-earth-ion-doped inorganic crystals,” Opt. Commun. 201, 71–77 (2002).
[CrossRef]

Moncorge, R.

C. Li, C. Wyon, and R. Moncorge, “Spectroscopic properties and fluorescence dynamics of Er3+ and Yb3+ in Y2SiO5,” IEEE J. Quantum Electron. 28, 1209–1221 (1992).
[CrossRef]

Mossberg, T. W.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Nilsson, M.

M. Nilsson, L. Levin, N. Ohlsson, T. Christiansson, and S. Kroll, “Initial experiments concerning quantum information processing in rare-earth-ion doped crystals,” Phys. Scr. T102, 178–185 (2002).
[CrossRef]

Ohlsson, N.

N. Ohlsson, R. K. Mohan, and S. Kroll, “Quantum computer hardware based on rare-earth-ion-doped inorganic crystals,” Opt. Commun. 201, 71–77 (2002).
[CrossRef]

M. Nilsson, L. Levin, N. Ohlsson, T. Christiansson, and S. Kroll, “Initial experiments concerning quantum information processing in rare-earth-ion doped crystals,” Phys. Scr. T102, 178–185 (2002).
[CrossRef]

Olson, R. W.

R. W. Olson, H. W. H. Lee, F. G. Patterson, and M. D. Fayer, “Optical-density effects in photon-echo experiments,” J. Chem. Phys. 76, 31–39 (1982).
[CrossRef]

Patterson, F. G.

R. W. Olson, H. W. H. Lee, F. G. Patterson, and M. D. Fayer, “Optical-density effects in photon-echo experiments,” J. Chem. Phys. 76, 31–39 (1982).
[CrossRef]

Price, A. C.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39, 745 (1960).
[CrossRef]

Sun, Y.

F. Konz, Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, R. L. Hutcheson, and R. M. Macfarlane, “Temperature and concentration dependence of optical dephasing, spectral hole lifetime, and anisotropic absorption in Eu3+:Y2SiO5,” Phys. Rev. B 68, 085109 (2003).
[CrossRef]

Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. M. Leask, “Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystals,” Phys. Rev. B 62, 15443–15451 (2000).
[CrossRef]

R. W. Equall, Y. Sun, R. L. Cone, and R. M. Macfarlane, “Ultraslow optical dephasing in Eu3+:Y2SiO5,” Phys. Rev. Lett. 72, 2179–2181 (1994).
[CrossRef] [PubMed]

Thiel, C. W.

F. Konz, Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, R. L. Hutcheson, and R. M. Macfarlane, “Temperature and concentration dependence of optical dephasing, spectral hole lifetime, and anisotropic absorption in Eu3+:Y2SiO5,” Phys. Rev. B 68, 085109 (2003).
[CrossRef]

Tsang, L.

M. Azadeh, C. S. Cornish, W. R. Babbitt, and L. Tsang, “Efficient photon echoes in optically thick media,” Phys. Rev. A 57, 4662–4668 (1998).
[CrossRef]

Uesugi, N.

Vernon, F. L.

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, “Geometrical representation of the Schrodinger equation for solving maser problems,” J. Appl. Phys. 28, 49–52 (1957).
[CrossRef]

Vitanov, N. V.

N. V. Vitanov and B. M. Garraway, “Landau–Zener model: effects of finite coupling duration,” Phys. Rev. A 53, 4288 (1996).
[CrossRef] [PubMed]

Wang, G. M.

Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. M. Leask, “Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystals,” Phys. Rev. B 62, 15443–15451 (2000).
[CrossRef]

Wang, T.

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Wild, U. P.

S. B. Altner, G. Zumofen, U. P. Wild, and M. Mitsunaga, “Photon-echo attenuation in rare-earth-ion-doped crystals,” Phys. Rev. B 54, 17493–17507 (1996).
[CrossRef]

Wyon, C.

C. Li, C. Wyon, and R. Moncorge, “Spectroscopic properties and fluorescence dynamics of Er3+ and Yb3+ in Y2SiO5,” IEEE J. Quantum Electron. 28, 1209–1221 (1992).
[CrossRef]

Yano, R.

Zener, C.

C. Zener, “Non-adiabatic crossing of energy levels,” Proc. R. Soc. London Ser. A 137, 696 (1932).
[CrossRef]

Zumofen, G.

S. B. Altner, G. Zumofen, U. P. Wild, and M. Mitsunaga, “Photon-echo attenuation in rare-earth-ion-doped crystals,” Phys. Rev. B 54, 17493–17507 (1996).
[CrossRef]

Appl. Phys. B (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Appl. Phys. Lett. (1)

Y. S. Bai and T. W. Mossberg, “Photon echo optical pulse compression,” Appl. Phys. Lett. 45, 1269–1272 (1984).
[CrossRef]

Bell Syst. Tech. J. (1)

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39, 745 (1960).
[CrossRef]

IBM Tech. Discl. Bull. (1)

M. D. Levenson, “Time domain optical information storage in systems capable of photochemical hole burning,” IBM Tech. Discl. Bull. 7, 2797 (1981).

IEEE J. Quantum Electron. (1)

C. Li, C. Wyon, and R. Moncorge, “Spectroscopic properties and fluorescence dynamics of Er3+ and Yb3+ in Y2SiO5,” IEEE J. Quantum Electron. 28, 1209–1221 (1992).
[CrossRef]

J. Appl. Phys. (1)

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, “Geometrical representation of the Schrodinger equation for solving maser problems,” J. Appl. Phys. 28, 49–52 (1957).
[CrossRef]

J. Chem. Phys. (1)

R. W. Olson, H. W. H. Lee, F. G. Patterson, and M. D. Fayer, “Optical-density effects in photon-echo experiments,” J. Chem. Phys. 76, 31–39 (1982).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

N. Ohlsson, R. K. Mohan, and S. Kroll, “Quantum computer hardware based on rare-earth-ion-doped inorganic crystals,” Opt. Commun. 201, 71–77 (2002).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. A (2)

N. V. Vitanov and B. M. Garraway, “Landau–Zener model: effects of finite coupling duration,” Phys. Rev. A 53, 4288 (1996).
[CrossRef] [PubMed]

M. Azadeh, C. S. Cornish, W. R. Babbitt, and L. Tsang, “Efficient photon echoes in optically thick media,” Phys. Rev. A 57, 4662–4668 (1998).
[CrossRef]

Phys. Rev. B (3)

S. B. Altner, G. Zumofen, U. P. Wild, and M. Mitsunaga, “Photon-echo attenuation in rare-earth-ion-doped crystals,” Phys. Rev. B 54, 17493–17507 (1996).
[CrossRef]

F. Konz, Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, R. L. Hutcheson, and R. M. Macfarlane, “Temperature and concentration dependence of optical dephasing, spectral hole lifetime, and anisotropic absorption in Eu3+:Y2SiO5,” Phys. Rev. B 68, 085109 (2003).
[CrossRef]

Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. M. Leask, “Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystals,” Phys. Rev. B 62, 15443–15451 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

R. W. Equall, Y. Sun, R. L. Cone, and R. M. Macfarlane, “Ultraslow optical dephasing in Eu3+:Y2SiO5,” Phys. Rev. Lett. 72, 2179–2181 (1994).
[CrossRef] [PubMed]

Phys. Scr. (1)

M. Nilsson, L. Levin, N. Ohlsson, T. Christiansson, and S. Kroll, “Initial experiments concerning quantum information processing in rare-earth-ion doped crystals,” Phys. Scr. T102, 178–185 (2002).
[CrossRef]

Phys. Z. Sowjetunion (1)

L. D. Landau, “Zur Theorie der Energieübertragung II,” Phys. Z. Sowjetunion 2, 46 (1932).

Proc. R. Soc. London Ser. A (1)

C. Zener, “Non-adiabatic crossing of energy levels,” Proc. R. Soc. London Ser. A 137, 696 (1932).
[CrossRef]

Sov. Phys. Crystallogr. (1)

B. A. Maximov, V. V. Illyukhin, Yu. A. Kharitonov, and N. V. Belov, “Crystal structure of yttrium oxyorthosilicate Y2O3⋅SiO2=Y2SiO5 dual function of yttrium,” Sov. Phys. Crystallogr. 15, 806–812 (1971).

Other (7)

For mathematical convenience, Vitanov and Garraway (Ref. 18) chose to define Ω0 [rad/s ] as half of the laboratory Rabi frequency on resonance and β2 [rad/s 2 ] as half of the laboratory laser chirp rate, leading to a definition of the scaled dimensionless-coupling strength of ω=Ω0 /β. We have chosen quantities and units more convenient to the laboratory such that Ω0 [s −1 ] is the full laboratory Rabi frequency of the chirp, and Bcc [s −2 ] is the full laboratory chirp rate leading to definition of dimensionless-coupling strength given in Eq. (1). For comparisons with results in Ref. 26, it is easy to verify that Φ=ω/π.

R. L. Shoemaker, “Coherent transient infrared spectroscopy,” in Laser and Coherence Spectroscopy, J. I. Steinfield, ed. (Plenum, New York, 1978), pp. 197–317.

Y. Sun, P. B. Sellin, C. M. Jefferson, and R. L. Cone, “Oscillator strength measurements on Eu 3+ :Y 2 SiO 5” (unpublished).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

G. W. Burr, T. L. Harris, W. R. Babbitt, and C. M. Jefferson, “Incorporating excitation-induced dephasing into the Maxwell–Bloch numerical modeling of photon echoes,” and references therein, J. Lumin. (to be published).

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1975).

R. M. Macfarlane and R. M. Shelby, “Coherent transient and holeburning spectroscopy,” in Spectroscopy of Solids Containing Rare Earths, A. A. Kaplyanskii and R. M. Macfarlane, eds. (North-Holland, Amsterdam, 1987).

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Figures (8)

Fig. 1
Fig. 1

Oscilloscope traces of transmitted chirped-pump/cw-probe pulse pairs and the resulting photon echo; each is an average of 32 shots. The chirp rate is fixed. The shape of the transmitted probe pulse indicates the degree of inversion created by the chirped pulse. “H” indicates the highest applied chirp power, and “L” is the lowest.

Fig. 2
Fig. 2

Combinations of chirp Rabi frequency and root chirp rate that created a half-inversion in experiment (open circles) and in simulation (solid triangles). The dotted line is a linear fit to the simulation results. The solid line is the low optical-density limit predicted by Landau–Zener theory. The slopes of lines on this graph are dimensionless-coupling strengths, Φ.

Fig. 3
Fig. 3

Schematic of the experimental apparatus. The dye laser was stabilized both in intensity and frequency. An acousto-optic modulator, AOM 1, was used to gate the laser beam. AOM 2 was used in a double-pass configuration to impress linear frequency chirps and arbitrary frequency offsets on the pulses from AOM 1. The laser was then focused into the Eu3+:Y2SiO5 crystal residing in the cryostat. The laser pulses before and after the cryostat were recorded with fast silicon photodiodes (PD). A photomultiplier tube (PMT), protected from overload by a Pockels cell optical gate, measured the photon echoes. In the figure, M labels mirrors, L labels lenses, CCM indicates the concave mirror, BS labels beam splitters, λ/2 labels half-wave plates, PBS labels polarizing beam splitters, and AMP labels radio-frequency amplifiers used to drive the acousto-optic modulators.

Fig. 4
Fig. 4

Effect of compensating the transfer function of AOM2. The upper trace is the intensity of an unequalized chirp of 120-MHz optical bandwidth generated by AOM2, as measured by PD3. The intensity rolloff is due to the modulator transfer function. The lower trace is the result of predistorting the RF drive signal amplitude to compensate for the modulator transfer function, which produces a constant-intensity chirped pulse. The residual intensity ripple that is symmetric about the center of the chirp is an artifact caused by low digital sampling resolution in the construction of the RF chirp waveform. This artifact is evident in the transmitted chirps in Fig. 1.

Fig. 5
Fig. 5

Maxwell–Bloch simulation of a pump–probe experiments with αL=1.20, analogous to those in Fig. 1. The dotted trace in the upper panel is the incident intensity, and the solid trace is the intensity after transmission. The bottom panel shows the average inversion, r3, as a function of detuning following the chirp. The transmitted chirp exhibited nutation and created slightly less than a half-inversion, as indicated by both the transmitted probe-pulse slope and r3.

Fig. 6
Fig. 6

Graphical representation of the analysis associating the probe-pulse shape with media inversion. Subplot (a) shows several simulated probe pulses for experimental conditions of Fig. 1. Each pulse has been fit with a straight line between its rising and falling edges. Subplot (b) shows the inversion, averaged over optical density, through which each probe pulse was transmitted. Vertical lines at Δ=±0.5 MHz indicate the detuning range over which the inversion was averaged. The slopes of the lines fit to the probe pulses are plotted versus the corresponding average inversion in subplot (c); the dimensionless coupling strength, Φ, used to generate each inversion labels the points. The curve fit to these data shows that the probe slope is zero at r3=0.

Fig. 7
Fig. 7

Calculated media inversion as a function of dimensionless-coupling strength, Φ, for a wide range of absorption lengths. The uppermost curve is the Landau–Zener prediction, valid for αL=0. The predictions of the Maxwell–Bloch simulations are shown as a family of curves. Each represents the inversion, r3, averaged over αL and over a bandwidth, Δ=±0.5 MHz, about the center of the chirp. The uppermost of these is from the first slice of media, representing αL=0.08. The remaining simulation curves are for αL ranging from 0.40 to 10.0 in increments of 0.40. The curve for αL=1.2 predicts the average inversion for the same optical density as the experimentally studied sample. The intersection of each curve with the dotted horizontal line at r3=0 indicates the dimensionless-coupling strength required to create a half-inversion.

Fig. 8
Fig. 8

Dimensionless-coupling strength s required to create a half-inversion are plotted as a function of absorption length. The solid line is a polynomial fit to these results. The solid diamond represents the dimensionless-coupling strength experimentally found to create a half-inversion in αL=1.2, which was calculated from the slope of the line in Fig. 4 as described in the text.

Equations (8)

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ΦΩ0(Bc/τc)1/2.
P=1-exp[-(πΦ)2].
r3(Φ)=1-2 exp[-(πΦ)2].
Φ(r3)=1π ln21-r3.
Φ(0)=0.265.
I=pATH=cn8πΩ0μ212,
Ω0=8πμ212cn21/2pATH1/2CRabiI.
Φ1/2EX=Ωc(Bc/τc)1/2=0.32±0.01,

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