Abstract

We report on a new type of sublevel echoes, synchronized-quantum-beat (SQB) echoes, generated by a successive application of two resonant light-pulse trains. The echoes are selectively generated for a sublevel pair whose frequency splitting is equal to an integral multiple of the repetition frequency of the light pulses. By using mode-locked laser pulses tuned to the D1 transition, we observed SQB echoes (and free induction decay) for all Zeeman and hyperfine transitions in the ground state of sodium atoms in low magnetic fields.

© 1983 Optical Society of America

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  1. Y. Fukuda, K. Yamada, T. Hashi, Opt. Commun. 44, 297 (1983).
    [CrossRef]
  2. Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, Opt. Commun. 38, 357 (1981); J. Mlyneck, W. Lange, H. Harde, H. Burgraff, Phys. Rev. A 24, 1099 (1981); H. Harde, H. Burgraff, Opt. Commun. 40, 441 (1982), and references therein.
    [CrossRef]
  3. Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, Opt. Commun. 38, 357 (1981).
    [CrossRef]
  4. Y. Fukuda, M. Tanigawa, T. Hashi, K. Kondo, Opt. Lett. 8, 301 (1983).
    [CrossRef] [PubMed]
  5. R. Kachru, T. W. Mossberg, S. R. Hartmann, J. Phys. B 13, L363 (1980).
    [CrossRef]
  6. W. Happer, Rev. Mod. Phys. 44, 169 (1972).
    [CrossRef]

1983 (2)

Y. Fukuda, K. Yamada, T. Hashi, Opt. Commun. 44, 297 (1983).
[CrossRef]

Y. Fukuda, M. Tanigawa, T. Hashi, K. Kondo, Opt. Lett. 8, 301 (1983).
[CrossRef] [PubMed]

1981 (2)

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, Opt. Commun. 38, 357 (1981); J. Mlyneck, W. Lange, H. Harde, H. Burgraff, Phys. Rev. A 24, 1099 (1981); H. Harde, H. Burgraff, Opt. Commun. 40, 441 (1982), and references therein.
[CrossRef]

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, Opt. Commun. 38, 357 (1981).
[CrossRef]

1980 (1)

R. Kachru, T. W. Mossberg, S. R. Hartmann, J. Phys. B 13, L363 (1980).
[CrossRef]

1972 (1)

W. Happer, Rev. Mod. Phys. 44, 169 (1972).
[CrossRef]

Fukuda, Y.

Y. Fukuda, K. Yamada, T. Hashi, Opt. Commun. 44, 297 (1983).
[CrossRef]

Y. Fukuda, M. Tanigawa, T. Hashi, K. Kondo, Opt. Lett. 8, 301 (1983).
[CrossRef] [PubMed]

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, Opt. Commun. 38, 357 (1981); J. Mlyneck, W. Lange, H. Harde, H. Burgraff, Phys. Rev. A 24, 1099 (1981); H. Harde, H. Burgraff, Opt. Commun. 40, 441 (1982), and references therein.
[CrossRef]

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, Opt. Commun. 38, 357 (1981).
[CrossRef]

Happer, W.

W. Happer, Rev. Mod. Phys. 44, 169 (1972).
[CrossRef]

Hartmann, S. R.

R. Kachru, T. W. Mossberg, S. R. Hartmann, J. Phys. B 13, L363 (1980).
[CrossRef]

Hashi, T.

Y. Fukuda, M. Tanigawa, T. Hashi, K. Kondo, Opt. Lett. 8, 301 (1983).
[CrossRef] [PubMed]

Y. Fukuda, K. Yamada, T. Hashi, Opt. Commun. 44, 297 (1983).
[CrossRef]

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, Opt. Commun. 38, 357 (1981); J. Mlyneck, W. Lange, H. Harde, H. Burgraff, Phys. Rev. A 24, 1099 (1981); H. Harde, H. Burgraff, Opt. Commun. 40, 441 (1982), and references therein.
[CrossRef]

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, Opt. Commun. 38, 357 (1981).
[CrossRef]

Hayashi, J.

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, Opt. Commun. 38, 357 (1981).
[CrossRef]

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, Opt. Commun. 38, 357 (1981); J. Mlyneck, W. Lange, H. Harde, H. Burgraff, Phys. Rev. A 24, 1099 (1981); H. Harde, H. Burgraff, Opt. Commun. 40, 441 (1982), and references therein.
[CrossRef]

Kachru, R.

R. Kachru, T. W. Mossberg, S. R. Hartmann, J. Phys. B 13, L363 (1980).
[CrossRef]

Kondo, K.

Y. Fukuda, M. Tanigawa, T. Hashi, K. Kondo, Opt. Lett. 8, 301 (1983).
[CrossRef] [PubMed]

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, Opt. Commun. 38, 357 (1981); J. Mlyneck, W. Lange, H. Harde, H. Burgraff, Phys. Rev. A 24, 1099 (1981); H. Harde, H. Burgraff, Opt. Commun. 40, 441 (1982), and references therein.
[CrossRef]

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, Opt. Commun. 38, 357 (1981).
[CrossRef]

Mossberg, T. W.

R. Kachru, T. W. Mossberg, S. R. Hartmann, J. Phys. B 13, L363 (1980).
[CrossRef]

Tanigawa, M.

Y. Fukuda, M. Tanigawa, T. Hashi, K. Kondo, Opt. Lett. 8, 301 (1983).
[CrossRef] [PubMed]

Yamada, K.

Y. Fukuda, K. Yamada, T. Hashi, Opt. Commun. 44, 297 (1983).
[CrossRef]

J. Phys. B (1)

R. Kachru, T. W. Mossberg, S. R. Hartmann, J. Phys. B 13, L363 (1980).
[CrossRef]

Mod. Phys. (1)

W. Happer, Rev. Mod. Phys. 44, 169 (1972).
[CrossRef]

Opt. Commun. (3)

Y. Fukuda, K. Yamada, T. Hashi, Opt. Commun. 44, 297 (1983).
[CrossRef]

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, Opt. Commun. 38, 357 (1981); J. Mlyneck, W. Lange, H. Harde, H. Burgraff, Phys. Rev. A 24, 1099 (1981); H. Harde, H. Burgraff, Opt. Commun. 40, 441 (1982), and references therein.
[CrossRef]

Y. Fukuda, J. Hayashi, K. Kondo, T. Hashi, Opt. Commun. 38, 357 (1981).
[CrossRef]

Opt. Lett. (1)

Y. Fukuda, M. Tanigawa, T. Hashi, K. Kondo, Opt. Lett. 8, 301 (1983).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

(a) Energy-level diagram and allowed transitions for the σ+ light. (b) Geometrical arrangement of the experiment. (c) Trains of light pulses used for the generation of SQB echoes. (d) Timing of the pulse sequence.

Fig. 2
Fig. 2

Block diagram of the experimental apparatus.

Fig. 3
Fig. 3

Energy-level diagram of the ground state of sodium atoms in low magnetic fields: a–d indicate the transitions relevant to the signals in Figs. 4 and 5.

Fig. 4
Fig. 4

SQB FID signals obtained by applying a pulse train with a duration of 10 μsec: (a) is for the transition a in Fig. 3; (b) shows a superposition of FID signals for the transitions b and c in Fig. 3. Beat patterns of the signals are due to the detuning.

Fig. 5
Fig. 5

SQB-echo signals obtained by applying two pulse trains with durations Δ1 = 40 μsec and Δ2 = 4.5 μsec. Signals (a)–(c) are for transition b at H0 = 153 Oe, and (d)–(f) for a at H0 = 13 Oe in Fig. 3. The separations τ of the pulse trains are 40–120 μsec.

Equations (3)

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d ρ 12 d t = ( i Ω 12 γ ) ρ 12 + n = + δ ( t n T ) × ( P 2 P ρ 12 + P 2 4 ρ 21 ) ,
( P / 2 T ) { 1 exp [ ( i Ω γ P / T ) Δ 1 ] } γ + P / T i Ω × exp [ ( i Ω γ ) ( t Δ 1 ) ] exp ( i m ω 0 t )
ρ 12 ( echo ) = ( P 3 / 8 T 2 ) exp [ ( γ P / T ) Δ 2 ] sin ( Ω Δ 2 ) { 1 exp [ ( i Ω γ P / T ) Δ 1 ] } Ω ( γ + P / T + i Ω ) × exp [ γ ( t t 2 + τ ) ] exp [ i Ω ( t t 2 τ ) ] exp ( i m ω 0 t ) ,

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