Abstract

The general problem of level crossing and optical double resonance line shapes is studied under different conditions of pulsed excitation. The theoretical effects of variable pulse shape and duration, of long and short observation periods, and the effects of positive and negative delay between the end of the pulse and the beginning of observation of the emitted fluorescence are investigated by means of a simple classical formulation. Agreement is obtained with line-shape expressions previously derived for more restricted assumptions. It is also shown that under appropriate conditions, pulse-excitation line shapes yield independent information on the mean life τ and <i>g</i> factor of the decaying state that has not been fully exploited in pulsed experiments carried out to date.

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  1. W. Hanle, Z. Physik 30, 93 (1924).
  2. For example, R. L. deZafra and W. Kirk, Am. J. Phys. 35, 573 (1967); B. Budick, in Advances in Atomic and Molecular Physics, 3, edited by D. R. Bates (Academic, New York, 1967), p. 73.
  3. I.-J. Ma, G. zuPutlitz, and G. Schütte, Physica 33, 282 (1967); and I.-J. Ma, J. Mertens, G. zuPutlitz, and G. Schütte, Z. Physik 208, 352 (1967).
  4. G. Copley, B. P. Kibble, and G. W. Series, J. Phys. B 1, 724 (1968).
  5. C. H. Liu, S. Bashkin, W. S. Bickel, and T. Hadeishi, Phys. Rev. Letters 26, 222 (1971).
  6. M. Carré, J. Désesquelles, M. Dufay, and M. L. Gaillard, Phys. Rev. Letters 27, 1407 (1971).
  7. D. A. Church, M. Druetta, and C. H. Liu, Phys. Rev. Letters 27, 1763 (1971).
  8. W. Happer and E. B. Saloman, Phys. Rev. 160, 23 (1967); P. P. Feofilov, The Physical Basis of Polarized Emission (Consultants Bureau, New York, 1961).
  9. C. G. Carrington, J. Phys. B 4, 1222 (1971).
  10. δ in Ref. 4 should have been 2δ (cf. Ref. 12). Hence all of the theoretical curves of Ref. 4 should be rescaled along the δ axis by a factor of ½.
  11. The magnetic-field value at which the lorentzian line shape in Figs. 2–6 reaches half its maximum amplitude is related to the natural lifetime τ by H½=ћ/(2µ0gτ), whereas the Larmor precession period is given by τL=2π/µ0gH. Hence at the field value H=H½, we have τL=4πnτ»τ.
  12. For example, A. Corney and G. W. Series, Proc. Phys. Soc. (London) 83, 207 (1964); J. N. Dodd, R. D. Kaul, and D. M. Warrington, Proc. Phys. Soc. (London) 84, 176 (1964); J. N. Dodd, W. J. Sandle, and D. Zissermann, Proc. Phys. Soc. (London) 92, 497 (1967) and references therein.
  13. S. Bashkin, W. S. Bickel, D. Fink, and R. K. Wangsness, Phys. Rev. Letters 15, 284 (1965); I. A. Sellin, C. D. Moak P. M. Griffin, and J. A. Biggerstaff, Phys. Rev. 184, 56 (1969) and references therein.
  14. For example, T. Hadeishi and W. A. Nierenberg, Phys. Rev. Letters 14, 891 (1965).
  15. G. zuPutlitz, Comments Mod. Phys. D 1, 74 (1969).

Bashkin, S.

C. H. Liu, S. Bashkin, W. S. Bickel, and T. Hadeishi, Phys. Rev. Letters 26, 222 (1971).

S. Bashkin, W. S. Bickel, D. Fink, and R. K. Wangsness, Phys. Rev. Letters 15, 284 (1965); I. A. Sellin, C. D. Moak P. M. Griffin, and J. A. Biggerstaff, Phys. Rev. 184, 56 (1969) and references therein.

Bickel, W. S.

S. Bashkin, W. S. Bickel, D. Fink, and R. K. Wangsness, Phys. Rev. Letters 15, 284 (1965); I. A. Sellin, C. D. Moak P. M. Griffin, and J. A. Biggerstaff, Phys. Rev. 184, 56 (1969) and references therein.

C. H. Liu, S. Bashkin, W. S. Bickel, and T. Hadeishi, Phys. Rev. Letters 26, 222 (1971).

Carré, M.

M. Carré, J. Désesquelles, M. Dufay, and M. L. Gaillard, Phys. Rev. Letters 27, 1407 (1971).

Carrington, C. G.

C. G. Carrington, J. Phys. B 4, 1222 (1971).

Church, D. A.

D. A. Church, M. Druetta, and C. H. Liu, Phys. Rev. Letters 27, 1763 (1971).

Copley, G.

G. Copley, B. P. Kibble, and G. W. Series, J. Phys. B 1, 724 (1968).

Corney, A.

For example, A. Corney and G. W. Series, Proc. Phys. Soc. (London) 83, 207 (1964); J. N. Dodd, R. D. Kaul, and D. M. Warrington, Proc. Phys. Soc. (London) 84, 176 (1964); J. N. Dodd, W. J. Sandle, and D. Zissermann, Proc. Phys. Soc. (London) 92, 497 (1967) and references therein.

Désesquelles, J.

M. Carré, J. Désesquelles, M. Dufay, and M. L. Gaillard, Phys. Rev. Letters 27, 1407 (1971).

deZafra, R. L.

For example, R. L. deZafra and W. Kirk, Am. J. Phys. 35, 573 (1967); B. Budick, in Advances in Atomic and Molecular Physics, 3, edited by D. R. Bates (Academic, New York, 1967), p. 73.

Druetta, M.

D. A. Church, M. Druetta, and C. H. Liu, Phys. Rev. Letters 27, 1763 (1971).

Dufay, M.

M. Carré, J. Désesquelles, M. Dufay, and M. L. Gaillard, Phys. Rev. Letters 27, 1407 (1971).

Fink, D.

S. Bashkin, W. S. Bickel, D. Fink, and R. K. Wangsness, Phys. Rev. Letters 15, 284 (1965); I. A. Sellin, C. D. Moak P. M. Griffin, and J. A. Biggerstaff, Phys. Rev. 184, 56 (1969) and references therein.

Gaillard, M. L.

M. Carré, J. Désesquelles, M. Dufay, and M. L. Gaillard, Phys. Rev. Letters 27, 1407 (1971).

Hadeishi, T.

C. H. Liu, S. Bashkin, W. S. Bickel, and T. Hadeishi, Phys. Rev. Letters 26, 222 (1971).

For example, T. Hadeishi and W. A. Nierenberg, Phys. Rev. Letters 14, 891 (1965).

Hanle, W.

W. Hanle, Z. Physik 30, 93 (1924).

Happer, W.

W. Happer and E. B. Saloman, Phys. Rev. 160, 23 (1967); P. P. Feofilov, The Physical Basis of Polarized Emission (Consultants Bureau, New York, 1961).

Kibble, B. P.

G. Copley, B. P. Kibble, and G. W. Series, J. Phys. B 1, 724 (1968).

Kirk, W.

For example, R. L. deZafra and W. Kirk, Am. J. Phys. 35, 573 (1967); B. Budick, in Advances in Atomic and Molecular Physics, 3, edited by D. R. Bates (Academic, New York, 1967), p. 73.

Liu, C. H.

D. A. Church, M. Druetta, and C. H. Liu, Phys. Rev. Letters 27, 1763 (1971).

C. H. Liu, S. Bashkin, W. S. Bickel, and T. Hadeishi, Phys. Rev. Letters 26, 222 (1971).

Ma, I.-J.

I.-J. Ma, G. zuPutlitz, and G. Schütte, Physica 33, 282 (1967); and I.-J. Ma, J. Mertens, G. zuPutlitz, and G. Schütte, Z. Physik 208, 352 (1967).

Nierenberg, W. A.

For example, T. Hadeishi and W. A. Nierenberg, Phys. Rev. Letters 14, 891 (1965).

Saloman, E. B.

W. Happer and E. B. Saloman, Phys. Rev. 160, 23 (1967); P. P. Feofilov, The Physical Basis of Polarized Emission (Consultants Bureau, New York, 1961).

Schütte, G.

I.-J. Ma, G. zuPutlitz, and G. Schütte, Physica 33, 282 (1967); and I.-J. Ma, J. Mertens, G. zuPutlitz, and G. Schütte, Z. Physik 208, 352 (1967).

Series, G. W.

G. Copley, B. P. Kibble, and G. W. Series, J. Phys. B 1, 724 (1968).

For example, A. Corney and G. W. Series, Proc. Phys. Soc. (London) 83, 207 (1964); J. N. Dodd, R. D. Kaul, and D. M. Warrington, Proc. Phys. Soc. (London) 84, 176 (1964); J. N. Dodd, W. J. Sandle, and D. Zissermann, Proc. Phys. Soc. (London) 92, 497 (1967) and references therein.

Wangsness, R. K.

S. Bashkin, W. S. Bickel, D. Fink, and R. K. Wangsness, Phys. Rev. Letters 15, 284 (1965); I. A. Sellin, C. D. Moak P. M. Griffin, and J. A. Biggerstaff, Phys. Rev. 184, 56 (1969) and references therein.

zuPutlitz, G.

G. zuPutlitz, Comments Mod. Phys. D 1, 74 (1969).

I.-J. Ma, G. zuPutlitz, and G. Schütte, Physica 33, 282 (1967); and I.-J. Ma, J. Mertens, G. zuPutlitz, and G. Schütte, Z. Physik 208, 352 (1967).

Other (15)

W. Hanle, Z. Physik 30, 93 (1924).

For example, R. L. deZafra and W. Kirk, Am. J. Phys. 35, 573 (1967); B. Budick, in Advances in Atomic and Molecular Physics, 3, edited by D. R. Bates (Academic, New York, 1967), p. 73.

I.-J. Ma, G. zuPutlitz, and G. Schütte, Physica 33, 282 (1967); and I.-J. Ma, J. Mertens, G. zuPutlitz, and G. Schütte, Z. Physik 208, 352 (1967).

G. Copley, B. P. Kibble, and G. W. Series, J. Phys. B 1, 724 (1968).

C. H. Liu, S. Bashkin, W. S. Bickel, and T. Hadeishi, Phys. Rev. Letters 26, 222 (1971).

M. Carré, J. Désesquelles, M. Dufay, and M. L. Gaillard, Phys. Rev. Letters 27, 1407 (1971).

D. A. Church, M. Druetta, and C. H. Liu, Phys. Rev. Letters 27, 1763 (1971).

W. Happer and E. B. Saloman, Phys. Rev. 160, 23 (1967); P. P. Feofilov, The Physical Basis of Polarized Emission (Consultants Bureau, New York, 1961).

C. G. Carrington, J. Phys. B 4, 1222 (1971).

δ in Ref. 4 should have been 2δ (cf. Ref. 12). Hence all of the theoretical curves of Ref. 4 should be rescaled along the δ axis by a factor of ½.

The magnetic-field value at which the lorentzian line shape in Figs. 2–6 reaches half its maximum amplitude is related to the natural lifetime τ by H½=ћ/(2µ0gτ), whereas the Larmor precession period is given by τL=2π/µ0gH. Hence at the field value H=H½, we have τL=4πnτ»τ.

For example, A. Corney and G. W. Series, Proc. Phys. Soc. (London) 83, 207 (1964); J. N. Dodd, R. D. Kaul, and D. M. Warrington, Proc. Phys. Soc. (London) 84, 176 (1964); J. N. Dodd, W. J. Sandle, and D. Zissermann, Proc. Phys. Soc. (London) 92, 497 (1967) and references therein.

S. Bashkin, W. S. Bickel, D. Fink, and R. K. Wangsness, Phys. Rev. Letters 15, 284 (1965); I. A. Sellin, C. D. Moak P. M. Griffin, and J. A. Biggerstaff, Phys. Rev. 184, 56 (1969) and references therein.

For example, T. Hadeishi and W. A. Nierenberg, Phys. Rev. Letters 14, 891 (1965).

G. zuPutlitz, Comments Mod. Phys. D 1, 74 (1969).

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