Abstract

The cascade Hanle-effect technique has been described in detail. It has been used to measure the radiative lifetimes of several excited S states in heavy alkali metal atoms. We obtained the following measurements (in nanoseconds): τ(K, 6 2S1/2) = 68 ± 9, τ(Rb, 7 2S1/2) = 91 ± 11, τ(Cs, 8 2S1/2) = 96 ± 14, and τ(Cs, 9 2S1/2) = 231 ± 35.

© 1976 Optical Society of America

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References

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  1. T. F. Gallagher, S. A. Edelstein, and R. M. Hill, Phys. Rev. A 11, 1504 (1975).
    [CrossRef]
  2. J. S. Deech, R. Luypaert, and G. W. Series, J. Phys. B 8, 1406 (1975).
    [CrossRef]
  3. R. Gupta, S. Chang, and W. Happer, Phys. Rev. A 6, 529 (1972).
    [CrossRef]
  4. P. A. Franken, Phys. Rev. 121, 508 (1961).
    [CrossRef]
  5. N. Bhaskar and A. Lurio, Phys. Rev. A (to be published).
  6. W. Happer and B. S. Mathur, Phys. Rev. 163, 12 (1967).
    [CrossRef]
  7. E. B. Saloman and W. Happer, Phys. Rev. 144, 7 (1966); J. P. Barrat, J. Phys. Radium 20, 541 (1959); J. Phys. Radium 20, 663 (1959).
    [CrossRef]
  8. C. Tai, W. Happer, and R. Gupta, Phys. Rev. A 12, 736 (1975).
    [CrossRef]
  9. B. Warner, Man. Nat. R. Astrol. Soc. 139, 115 (1968).
  10. P. Tsekeris, Columbia University (private communication).
  11. D. R. Bates and A. Damgaard, Philos. Trans. 242, 101 (1949).
    [CrossRef]

1975 (3)

T. F. Gallagher, S. A. Edelstein, and R. M. Hill, Phys. Rev. A 11, 1504 (1975).
[CrossRef]

J. S. Deech, R. Luypaert, and G. W. Series, J. Phys. B 8, 1406 (1975).
[CrossRef]

C. Tai, W. Happer, and R. Gupta, Phys. Rev. A 12, 736 (1975).
[CrossRef]

1972 (1)

R. Gupta, S. Chang, and W. Happer, Phys. Rev. A 6, 529 (1972).
[CrossRef]

1968 (1)

B. Warner, Man. Nat. R. Astrol. Soc. 139, 115 (1968).

1967 (1)

W. Happer and B. S. Mathur, Phys. Rev. 163, 12 (1967).
[CrossRef]

1966 (1)

E. B. Saloman and W. Happer, Phys. Rev. 144, 7 (1966); J. P. Barrat, J. Phys. Radium 20, 541 (1959); J. Phys. Radium 20, 663 (1959).
[CrossRef]

1961 (1)

P. A. Franken, Phys. Rev. 121, 508 (1961).
[CrossRef]

1949 (1)

D. R. Bates and A. Damgaard, Philos. Trans. 242, 101 (1949).
[CrossRef]

Bates, D. R.

D. R. Bates and A. Damgaard, Philos. Trans. 242, 101 (1949).
[CrossRef]

Bhaskar, N.

N. Bhaskar and A. Lurio, Phys. Rev. A (to be published).

Chang, S.

R. Gupta, S. Chang, and W. Happer, Phys. Rev. A 6, 529 (1972).
[CrossRef]

Damgaard, A.

D. R. Bates and A. Damgaard, Philos. Trans. 242, 101 (1949).
[CrossRef]

Deech, J. S.

J. S. Deech, R. Luypaert, and G. W. Series, J. Phys. B 8, 1406 (1975).
[CrossRef]

Edelstein, S. A.

T. F. Gallagher, S. A. Edelstein, and R. M. Hill, Phys. Rev. A 11, 1504 (1975).
[CrossRef]

Franken, P. A.

P. A. Franken, Phys. Rev. 121, 508 (1961).
[CrossRef]

Gallagher, T. F.

T. F. Gallagher, S. A. Edelstein, and R. M. Hill, Phys. Rev. A 11, 1504 (1975).
[CrossRef]

Gupta, R.

C. Tai, W. Happer, and R. Gupta, Phys. Rev. A 12, 736 (1975).
[CrossRef]

R. Gupta, S. Chang, and W. Happer, Phys. Rev. A 6, 529 (1972).
[CrossRef]

Happer, W.

C. Tai, W. Happer, and R. Gupta, Phys. Rev. A 12, 736 (1975).
[CrossRef]

R. Gupta, S. Chang, and W. Happer, Phys. Rev. A 6, 529 (1972).
[CrossRef]

W. Happer and B. S. Mathur, Phys. Rev. 163, 12 (1967).
[CrossRef]

E. B. Saloman and W. Happer, Phys. Rev. 144, 7 (1966); J. P. Barrat, J. Phys. Radium 20, 541 (1959); J. Phys. Radium 20, 663 (1959).
[CrossRef]

Hill, R. M.

T. F. Gallagher, S. A. Edelstein, and R. M. Hill, Phys. Rev. A 11, 1504 (1975).
[CrossRef]

Lurio, A.

N. Bhaskar and A. Lurio, Phys. Rev. A (to be published).

Luypaert, R.

J. S. Deech, R. Luypaert, and G. W. Series, J. Phys. B 8, 1406 (1975).
[CrossRef]

Mathur, B. S.

W. Happer and B. S. Mathur, Phys. Rev. 163, 12 (1967).
[CrossRef]

Saloman, E. B.

E. B. Saloman and W. Happer, Phys. Rev. 144, 7 (1966); J. P. Barrat, J. Phys. Radium 20, 541 (1959); J. Phys. Radium 20, 663 (1959).
[CrossRef]

Series, G. W.

J. S. Deech, R. Luypaert, and G. W. Series, J. Phys. B 8, 1406 (1975).
[CrossRef]

Tai, C.

C. Tai, W. Happer, and R. Gupta, Phys. Rev. A 12, 736 (1975).
[CrossRef]

Tsekeris, P.

P. Tsekeris, Columbia University (private communication).

Warner, B.

B. Warner, Man. Nat. R. Astrol. Soc. 139, 115 (1968).

J. Phys. B (1)

J. S. Deech, R. Luypaert, and G. W. Series, J. Phys. B 8, 1406 (1975).
[CrossRef]

Man. Nat. R. Astrol. Soc. (1)

B. Warner, Man. Nat. R. Astrol. Soc. 139, 115 (1968).

Philos. Trans. (1)

D. R. Bates and A. Damgaard, Philos. Trans. 242, 101 (1949).
[CrossRef]

Phys. Rev. (3)

W. Happer and B. S. Mathur, Phys. Rev. 163, 12 (1967).
[CrossRef]

E. B. Saloman and W. Happer, Phys. Rev. 144, 7 (1966); J. P. Barrat, J. Phys. Radium 20, 541 (1959); J. Phys. Radium 20, 663 (1959).
[CrossRef]

P. A. Franken, Phys. Rev. 121, 508 (1961).
[CrossRef]

Phys. Rev. A (3)

R. Gupta, S. Chang, and W. Happer, Phys. Rev. A 6, 529 (1972).
[CrossRef]

C. Tai, W. Happer, and R. Gupta, Phys. Rev. A 12, 736 (1975).
[CrossRef]

T. F. Gallagher, S. A. Edelstein, and R. M. Hill, Phys. Rev. A 11, 1504 (1975).
[CrossRef]

Other (2)

P. Tsekeris, Columbia University (private communication).

N. Bhaskar and A. Lurio, Phys. Rev. A (to be published).

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Figures (9)

FIG. 1
FIG. 1

Schematic illustration of the atomic states involved in a cascade Hanle-effect experiment.

FIG. 2
FIG. 2

Theoretical cascade Hanle signal shape for an atom without hyperfine structure.

FIG. 3
FIG. 3

Shape of the cascade Hanle curve for the 6 2S1/2 state of K39 fed by 6 2P1/2 state.

FIG. 4
FIG. 4

Shape of the cascade Hanle curve for the 6 2S1/2 state of K fed by the 6 2P1/2 state if the nuclear spin were equal to 1 2.

FIG. 5
FIG. 5

Schematic illustration of the experimental arrangement.

FIG. 6
FIG. 6

Experimental cascade Hanle curve for the 8 2S1/2 state of Cs133.

FIG. 7
FIG. 7

Cascade Hanle curve for the 7 2S1/2 state of Rb85 at three different temperatures of the Rb vapor, showing that no noticeable broadening occurs in this temperature range.

FIG. 8
FIG. 8

Theoretical cascade Hanle curves assuming white-light (circles) and non-white-light (crosses) excitation.

FIG. 9
FIG. 9

Some of our experimental results. The solid lines are the least-squares-fitted theoretical curves. The theoretical shown here correspond to τb = 85 and 230 ns for the 8 2S1/2 and 9 2S1/2 states of Cs133, τb = 90 ns for the 7 2S1/2 state of Rb85, and τb = 70 ns for the 6 2S1/2 state of K39.

Tables (3)

Tables Icon

TABLE I List of relevant experimental parameters.

Tables Icon

TABLE II List of the excited state lifetimes that were used to analyze the data. η is the percentage change in the best-fitted value of the branch state lifetime if the excited state lifetime is increased by 5% (see text).

Tables Icon

TABLE III Theoretical and the experimental values of lifetimes.

Equations (7)

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Δ I Δ Ω = 4 3 ( e m c ) 6 u 4 ω e b ω b f ( ω g e ) 2 1 ( 2 J g + 1 ) ( 2 I + 1 ) × m n j k μ ν j p m · n p k k u ˆ · p f ν f ν u ˆ * · p j × m ê · p g μ g μ ê * · p n × ( Γ e + i ω m n ) - 1 ( Γ b + i ω j k ) - 1 .
S = L M ( - 1 ) M Γ e b Γ b f B L E L M U L - M ( Γ e + i M ω e ) ( Γ b + i M ω b ) ,
E L M = m e m ( e m - M ) * ( - 1 ) m - M - 1 C ( 11 L ; m , M - m ) ,
B L = K ( 2 J e + 1 ) ( 2 J b + 1 ) W ( J g J e 1 L ; 1 J e ) × W ( 1 J e J b L ; J b J e ) W ( L 1 J b J f ; 1 J b ) .
S = Γ e b Γ b f 3 Γ e Γ b ( B 0 + 1 2 B 2 ) + 1 2 B 2 ( Γ e b Γ b f ( Γ e Γ b - 4 ω e ω b ) ( Γ e 2 + 4 ω e 2 ) ( Γ b 2 + 4 ω b 2 ) ) .
1 2 ( Γ e b / Γ e ) B 2 [ Γ b f Γ b / ( Γ b 2 + 4 ω b 2 ) ] ,
S = S 0 + S 1 + S 2 = 1 3 Γ e b Γ b f Γ e Γ b B 0 + 1 2 B 1 ( Γ e b Γ b f ( Γ e Γ b - ω e ω b ) ( Γ e 2 + ω e 2 ) ( Γ b 2 + ω b 2 ) ) + 1 8 B 2 ( Γ e b Γ b f 3 Γ e Γ b + Γ e b Γ b f ( Γ e Γ b - 4 ω e ω b ) ( Γ e 2 + 4 ω e 2 ) ( Γ b 2 + 4 ω b 2 ) ) .