Abstract

In molecular iodine, and most other gas-phase molecules as well, generation of a π/2 or π pulse is theoretically impossible. This result can be understood by analogy with microwave spectroscopy, since the rotational contribution to the transition dipole moment is an explicit function of the projection of the total angular momentum F = J + I along the electric-field axis. The only solution is the generation of phase-modulated pulses that inherently compensate for Rabi-frequency inhomogeneity. We present theoretical and experimental evidence that crafted phase- and amplitude-modulated pulse shapes can excite a uniform, localized, and nearly complete inversion in nuclear magnetic resonance and laser spectroscopy.

© 1986 Optical Society of America

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References

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  1. For a general review of work before 1982 see M. Burns, W. K. Liu, A. H. Zewail, in Spectroscopy and Excitation Dynamics of Condensed Matter Systems, V. M. Agranovich, R. M. Hochstrasser, eds. (North-Holland, Amsterdam, 1983), p. 301.
  2. W. S. Warren, A. H. Zewail, J. Chem. Phys. 75, 5986 (1981); J. Chem. Phys. 78, 2279, 78, 2298 (1983).
    [CrossRef]
  3. E. Sleva, A. H. Zewail, Chem. Phys. Lett. 110, 582 (1984).
    [CrossRef]
  4. W. S. Warren, M. A. Banash, in Coherence and Quantum Optics V, L. Mandel, E. Wolf, eds. (Plenum, New York, 1984) p. 959.
  5. M. A. Banash, J. Gutow, W. S. Warren, J. Luminescence 31–32, 855 (1984).
    [CrossRef]
  6. M. A. Banash, W. S. Warren, Laser Chem. (to be published).
  7. A. Z. Genack, in Proceedings of the International Laser Science Conference (American Institute of Physics, New York, 1985).
  8. R. G. Brewer, S. S. Kano, in Laser Induced Processes in Molecules, K. L. Kompa, S. D. Smith, eds. (Springer-Verlag, New York, 1979), p. 54.
    [CrossRef]
  9. J. Vigue, M. Broyer, J. C. Lehmann, J. Phys. (Paris) 42, 949 (1981).
    [CrossRef]
  10. L. Brewer, J. Tellinghuisen, J. Chem. Phys. 56, 3929 (1972).
    [CrossRef]
  11. C. H. Townes, A. L. Schawlow, Microwave Spectroscopy (McGraw-Hill, New York, 1955); G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand Reinhold, New York, 1950).
  12. W. S. Warren, A. H. Zewail, Laser Chem. 2, 37 (1983); E. Sleva, A. H. Zewail, J. Opt. Soc. Am. B 3, 483–487 (1986); Y. S. Bai, A. G. Yoth, T. W. Mossberg, Phys. Rev. Lett 55, 1277 (1985).
    [CrossRef] [PubMed]
  13. C. P. Slichter, Principles of Magnetic Resonance (Springer-Verlag, Berlin, 1980).
  14. R. Beach, S. R. Hartmann, Phys. Rev. Lett. 53, 663 (1984).
    [CrossRef]
  15. N. W. Carlson, W. R. Babbitt, Y. S. Bai, T. W. Mossberg, J. Opt. Soc. Am. B 2908 (1985); Y. S. Bai, T. W. Mossberg, Appl. Phys. Lett. 45, 1269 (1984).
    [CrossRef]
  16. D. Hoult, M. Silver, J. Magn. Reson. 59, 347 (1985); M. Silver, R. I. Joseph, Phys. Rev. A 312753 (1984).
    [CrossRef]
  17. M. H. Levitt, Progress in NMR Spectroscopy (Pergamon, New York, to be published); R. Freeman, S. P. Kempsall, M. H. Levitt, J. Mag. Reson. 38, 453 (1980).
  18. W. S. Warren, J. Chem. Phys. 81, 5437 (1984).
    [CrossRef]
  19. M. McCoy, W. S. Warren, J. Mag. Reson. 65, 178 (1985).

1985 (3)

D. Hoult, M. Silver, J. Magn. Reson. 59, 347 (1985); M. Silver, R. I. Joseph, Phys. Rev. A 312753 (1984).
[CrossRef]

M. McCoy, W. S. Warren, J. Mag. Reson. 65, 178 (1985).

N. W. Carlson, W. R. Babbitt, Y. S. Bai, T. W. Mossberg, J. Opt. Soc. Am. B 2908 (1985); Y. S. Bai, T. W. Mossberg, Appl. Phys. Lett. 45, 1269 (1984).
[CrossRef]

1984 (4)

R. Beach, S. R. Hartmann, Phys. Rev. Lett. 53, 663 (1984).
[CrossRef]

W. S. Warren, J. Chem. Phys. 81, 5437 (1984).
[CrossRef]

E. Sleva, A. H. Zewail, Chem. Phys. Lett. 110, 582 (1984).
[CrossRef]

M. A. Banash, J. Gutow, W. S. Warren, J. Luminescence 31–32, 855 (1984).
[CrossRef]

1983 (1)

W. S. Warren, A. H. Zewail, Laser Chem. 2, 37 (1983); E. Sleva, A. H. Zewail, J. Opt. Soc. Am. B 3, 483–487 (1986); Y. S. Bai, A. G. Yoth, T. W. Mossberg, Phys. Rev. Lett 55, 1277 (1985).
[CrossRef] [PubMed]

1981 (2)

W. S. Warren, A. H. Zewail, J. Chem. Phys. 75, 5986 (1981); J. Chem. Phys. 78, 2279, 78, 2298 (1983).
[CrossRef]

J. Vigue, M. Broyer, J. C. Lehmann, J. Phys. (Paris) 42, 949 (1981).
[CrossRef]

1972 (1)

L. Brewer, J. Tellinghuisen, J. Chem. Phys. 56, 3929 (1972).
[CrossRef]

Babbitt, W. R.

Bai, Y. S.

Banash, M. A.

M. A. Banash, J. Gutow, W. S. Warren, J. Luminescence 31–32, 855 (1984).
[CrossRef]

W. S. Warren, M. A. Banash, in Coherence and Quantum Optics V, L. Mandel, E. Wolf, eds. (Plenum, New York, 1984) p. 959.

M. A. Banash, W. S. Warren, Laser Chem. (to be published).

Beach, R.

R. Beach, S. R. Hartmann, Phys. Rev. Lett. 53, 663 (1984).
[CrossRef]

Brewer, L.

L. Brewer, J. Tellinghuisen, J. Chem. Phys. 56, 3929 (1972).
[CrossRef]

Brewer, R. G.

R. G. Brewer, S. S. Kano, in Laser Induced Processes in Molecules, K. L. Kompa, S. D. Smith, eds. (Springer-Verlag, New York, 1979), p. 54.
[CrossRef]

Broyer, M.

J. Vigue, M. Broyer, J. C. Lehmann, J. Phys. (Paris) 42, 949 (1981).
[CrossRef]

Burns, M.

For a general review of work before 1982 see M. Burns, W. K. Liu, A. H. Zewail, in Spectroscopy and Excitation Dynamics of Condensed Matter Systems, V. M. Agranovich, R. M. Hochstrasser, eds. (North-Holland, Amsterdam, 1983), p. 301.

Carlson, N. W.

Genack, A. Z.

A. Z. Genack, in Proceedings of the International Laser Science Conference (American Institute of Physics, New York, 1985).

Gutow, J.

M. A. Banash, J. Gutow, W. S. Warren, J. Luminescence 31–32, 855 (1984).
[CrossRef]

Hartmann, S. R.

R. Beach, S. R. Hartmann, Phys. Rev. Lett. 53, 663 (1984).
[CrossRef]

Hoult, D.

D. Hoult, M. Silver, J. Magn. Reson. 59, 347 (1985); M. Silver, R. I. Joseph, Phys. Rev. A 312753 (1984).
[CrossRef]

Kano, S. S.

R. G. Brewer, S. S. Kano, in Laser Induced Processes in Molecules, K. L. Kompa, S. D. Smith, eds. (Springer-Verlag, New York, 1979), p. 54.
[CrossRef]

Lehmann, J. C.

J. Vigue, M. Broyer, J. C. Lehmann, J. Phys. (Paris) 42, 949 (1981).
[CrossRef]

Levitt, M. H.

M. H. Levitt, Progress in NMR Spectroscopy (Pergamon, New York, to be published); R. Freeman, S. P. Kempsall, M. H. Levitt, J. Mag. Reson. 38, 453 (1980).

Liu, W. K.

For a general review of work before 1982 see M. Burns, W. K. Liu, A. H. Zewail, in Spectroscopy and Excitation Dynamics of Condensed Matter Systems, V. M. Agranovich, R. M. Hochstrasser, eds. (North-Holland, Amsterdam, 1983), p. 301.

McCoy, M.

M. McCoy, W. S. Warren, J. Mag. Reson. 65, 178 (1985).

Mossberg, T. W.

Schawlow, A. L.

C. H. Townes, A. L. Schawlow, Microwave Spectroscopy (McGraw-Hill, New York, 1955); G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand Reinhold, New York, 1950).

Silver, M.

D. Hoult, M. Silver, J. Magn. Reson. 59, 347 (1985); M. Silver, R. I. Joseph, Phys. Rev. A 312753 (1984).
[CrossRef]

Sleva, E.

E. Sleva, A. H. Zewail, Chem. Phys. Lett. 110, 582 (1984).
[CrossRef]

Slichter, C. P.

C. P. Slichter, Principles of Magnetic Resonance (Springer-Verlag, Berlin, 1980).

Tellinghuisen, J.

L. Brewer, J. Tellinghuisen, J. Chem. Phys. 56, 3929 (1972).
[CrossRef]

Townes, C. H.

C. H. Townes, A. L. Schawlow, Microwave Spectroscopy (McGraw-Hill, New York, 1955); G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand Reinhold, New York, 1950).

Vigue, J.

J. Vigue, M. Broyer, J. C. Lehmann, J. Phys. (Paris) 42, 949 (1981).
[CrossRef]

Warren, W. S.

M. McCoy, W. S. Warren, J. Mag. Reson. 65, 178 (1985).

M. A. Banash, J. Gutow, W. S. Warren, J. Luminescence 31–32, 855 (1984).
[CrossRef]

W. S. Warren, J. Chem. Phys. 81, 5437 (1984).
[CrossRef]

W. S. Warren, A. H. Zewail, Laser Chem. 2, 37 (1983); E. Sleva, A. H. Zewail, J. Opt. Soc. Am. B 3, 483–487 (1986); Y. S. Bai, A. G. Yoth, T. W. Mossberg, Phys. Rev. Lett 55, 1277 (1985).
[CrossRef] [PubMed]

W. S. Warren, A. H. Zewail, J. Chem. Phys. 75, 5986 (1981); J. Chem. Phys. 78, 2279, 78, 2298 (1983).
[CrossRef]

M. A. Banash, W. S. Warren, Laser Chem. (to be published).

W. S. Warren, M. A. Banash, in Coherence and Quantum Optics V, L. Mandel, E. Wolf, eds. (Plenum, New York, 1984) p. 959.

Zewail, A. H.

E. Sleva, A. H. Zewail, Chem. Phys. Lett. 110, 582 (1984).
[CrossRef]

W. S. Warren, A. H. Zewail, Laser Chem. 2, 37 (1983); E. Sleva, A. H. Zewail, J. Opt. Soc. Am. B 3, 483–487 (1986); Y. S. Bai, A. G. Yoth, T. W. Mossberg, Phys. Rev. Lett 55, 1277 (1985).
[CrossRef] [PubMed]

W. S. Warren, A. H. Zewail, J. Chem. Phys. 75, 5986 (1981); J. Chem. Phys. 78, 2279, 78, 2298 (1983).
[CrossRef]

For a general review of work before 1982 see M. Burns, W. K. Liu, A. H. Zewail, in Spectroscopy and Excitation Dynamics of Condensed Matter Systems, V. M. Agranovich, R. M. Hochstrasser, eds. (North-Holland, Amsterdam, 1983), p. 301.

Chem. Phys. Lett. (1)

E. Sleva, A. H. Zewail, Chem. Phys. Lett. 110, 582 (1984).
[CrossRef]

J. Chem. Phys. (3)

W. S. Warren, A. H. Zewail, J. Chem. Phys. 75, 5986 (1981); J. Chem. Phys. 78, 2279, 78, 2298 (1983).
[CrossRef]

L. Brewer, J. Tellinghuisen, J. Chem. Phys. 56, 3929 (1972).
[CrossRef]

W. S. Warren, J. Chem. Phys. 81, 5437 (1984).
[CrossRef]

J. Luminescence (1)

M. A. Banash, J. Gutow, W. S. Warren, J. Luminescence 31–32, 855 (1984).
[CrossRef]

J. Mag. Reson. (1)

M. McCoy, W. S. Warren, J. Mag. Reson. 65, 178 (1985).

J. Magn. Reson. (1)

D. Hoult, M. Silver, J. Magn. Reson. 59, 347 (1985); M. Silver, R. I. Joseph, Phys. Rev. A 312753 (1984).
[CrossRef]

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

J. Phys. (Paris) (1)

J. Vigue, M. Broyer, J. C. Lehmann, J. Phys. (Paris) 42, 949 (1981).
[CrossRef]

Laser Chem. (1)

W. S. Warren, A. H. Zewail, Laser Chem. 2, 37 (1983); E. Sleva, A. H. Zewail, J. Opt. Soc. Am. B 3, 483–487 (1986); Y. S. Bai, A. G. Yoth, T. W. Mossberg, Phys. Rev. Lett 55, 1277 (1985).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

R. Beach, S. R. Hartmann, Phys. Rev. Lett. 53, 663 (1984).
[CrossRef]

Other (8)

M. H. Levitt, Progress in NMR Spectroscopy (Pergamon, New York, to be published); R. Freeman, S. P. Kempsall, M. H. Levitt, J. Mag. Reson. 38, 453 (1980).

C. P. Slichter, Principles of Magnetic Resonance (Springer-Verlag, Berlin, 1980).

C. H. Townes, A. L. Schawlow, Microwave Spectroscopy (McGraw-Hill, New York, 1955); G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand Reinhold, New York, 1950).

M. A. Banash, W. S. Warren, Laser Chem. (to be published).

A. Z. Genack, in Proceedings of the International Laser Science Conference (American Institute of Physics, New York, 1985).

R. G. Brewer, S. S. Kano, in Laser Induced Processes in Molecules, K. L. Kompa, S. D. Smith, eds. (Springer-Verlag, New York, 1979), p. 54.
[CrossRef]

For a general review of work before 1982 see M. Burns, W. K. Liu, A. H. Zewail, in Spectroscopy and Excitation Dynamics of Condensed Matter Systems, V. M. Agranovich, R. M. Hochstrasser, eds. (North-Holland, Amsterdam, 1983), p. 301.

W. S. Warren, M. A. Banash, in Coherence and Quantum Optics V, L. Mandel, E. Wolf, eds. (Plenum, New York, 1984) p. 959.

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Figures (4)

Fig. 1
Fig. 1

Schematic illustration of the variation in Rabi frequency for the various (J, MJ) or (F, MF) components of an electronic transition in a diatomic molecule. For this illustration we chose an R-branch transition with ΔF = ΔJ. The linearly polarized case gives transitions that are fairly well bunched, but there is still a large total range. The circularly polarized case is even less uniform. These distributions make π pulses impossible in I2.

Fig. 2
Fig. 2

NMR spectra showing the effects of pulse shaping. The magnet (500-MHz proton frequency) was intentionally detuned to create a broad line (first spectrum) analogous to Doppler broadening. The inversion profile from a rectangular π pulse (second spectrum) is not uniform because of high-frequency components in the pulse shape. The inversion profile from our pulse shapes is much better.

Fig. 3
Fig. 3

Schematic of laser apparatus to create shaped pulses. This circuitry uses a video digital-to-analog converter, ECL logic, and ultrafast operational amplifiers to give a minimum step resolution of roughly 7 nsec. This shape is imposed as a modulation on a rectangular radio-frequency pulse and then transmitted to an acousto-optic modulator. The actual laser output intensity (square of the electric field) is also shown. We use shaped pulses to select a single-velocity component (a narrow, well-defined frequency range) from a Doppler-broadened gas to probe collisional dynamics.

Fig. 4
Fig. 4

Theoretical and experimental demonstration of shaped composite pulses. In each figure the sequence is (π/2)xπy − (π/2)x. The theoretical figures have resonance offset expressed in terms of the peak pulse amplitude; in those units, the Hermite pulses give a narrower distribution than do rectangular pulses because the pulse shape is near its maximum amplitude only for a small fraction of the time. In the experimental figures the band-widths are equalized by using more intense Hermite pulses. If the exciting field intensity (or, equivalently, the transition dipole moment) is decreased by 25%, the rectangular pulse excitation decreases by only about 2% directly on resonance, but slightly off resonance the excitation decreases substantially. In addition, spurious inversion is generated off resonance, and the distribution becomes less uniform. The Hermite composite performs similarly on resonance but generates no spurious inversion and keeps a nearly rectangular excitation profile.

Equations (3)

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ω 1 ( t ) = B [ sech ( a t ) ] 1 + μ i
ω 1 ( t ) = C [ 1.0 - 0.957 ( t / T ) 2 ] exp [ - ( t / T ) 2 ] ,
( π / 2 ) x - ( π ) y - ( π / 2 ) x

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