Abstract

This is a brief account of recent results obtained in Paris by the development of optical-pumping techniques, and especially on the thesis of Cagnac and the thesis of Cohen-Tannoudji. Cagnac has used the optical-pumping technique to achieve nuclear orientation in the ground state of the odd mercury isotopes and has made an extensive study of the longitudinal relaxation time. Barrat and Cohen-Tannoudji have developed the quantum-mechanical theory of the optical-pumping cycle of an atom and Cohen-Tannoudji in his thesis has confirmed the theoretical predictions experimentally by applying Dehmelt’s cross-beam technique to Hg199: If a collection of atoms is irradiated permanently by light which can be absorbed and re-emitted, this pumping cycle has different effects on the ground-state properties of the atoms; these effects are experimentally detectable by observing the magnetic resonance of the atomic ground state. A broadening of the magnetic-resonance line proportional to the light intensity occurs. It is due to the shortening of the lifetime of the ground-state Zeeman levels by light absorptions. Other effects are displacements of the Zeeman levels of the ground state caused by irradiation resulting in a change of the magnetic-resonance frequency. Theory predicts displacements of 2 different kinds: (1) Displacements caused by real transitions—During an up-and-down transition of an atom, coherence is partly conserved. As a result, a certain amount of the g factor of the excited state is mixed with the g factor of the ground state. (2) Displacements caused by virtual transitions—These displacements are related to the dispersion of light. All these effects, predicted by the theory, have been qualitatively and quantitatively confirmed by Cohen’s experiments.

© 1963 Optical Society of America

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References

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  1. A. Kastler, J. Opt. Soc. Am. 47, 460 (1957). See also: Nuovo Cimento 6, No. 3, 1148 (1957).
    [Crossref]
  2. B. Cagnac, J. Brossel, and A. Kastler, Compt. Rend. 246, 1827 (1958); B. Cagnac and J. Brossel, ibid.  249, 77, 253 (1959); B. Cagnac and J. P. Barrat, ibid., p. 534; J. Brossel, Yearbook Phys. Soc. (London) 1960, 1.
  3. B. Cagnac, thesis, Paris1960, summarized in Ann. Phys. Paris 6, 467 (1961).
  4. W. Franzen, Phys. Rev. 115, 850 (1959).
    [Crossref]
  5. Another method of introducing coherence is optical excitation by modulated or periodically pulsed light.6
  6. W. E. Bell and A. L. Bloom, Phys. Rev. Letters 6, 280 (1961).
    [Crossref]
  7. H. G. Dehmelt, Phys. Rev. 105, 1924 (1957).
    [Crossref]
  8. W. E. Bell and A. L. Bloom, Phys. Rev. 107, 1559 (1957).
    [Crossref]
  9. C. Cohen-Tannoudji, thesis, Paris1962, Ann. Phys. Paris 7, 423 (1962). See also: C. Cohen-Tannoudji, Compt. Rend. 252, 384 (1961); Compt. Rend. 253, 2662, 2899 (1961).
  10. J. P. Barrat and C. Cohen-Tannoudji, J. Phys. Radium 22, 329, 443 (1961). See also: Compt. Rend. 252, 93, 255 (1961).
    [Crossref]
  11. In the theoretical paper of Barrat and Cohen-Tannoudji and in Cohen-Tannoudji’s thesis the symbols m and m′are used for the magnetic sublevels of the excited state and the symbols μ and μ′for the magnetic sublevels of the ground slate. In this review we have not to consider the m states of the excited state. We use m and m′ for the ground state.
  12. A. Abragam, The Principles of Nuclear Magnetism (Clarendon Press, Oxford, England, 1961), p. 24.

1961 (2)

W. E. Bell and A. L. Bloom, Phys. Rev. Letters 6, 280 (1961).
[Crossref]

J. P. Barrat and C. Cohen-Tannoudji, J. Phys. Radium 22, 329, 443 (1961). See also: Compt. Rend. 252, 93, 255 (1961).
[Crossref]

1959 (1)

W. Franzen, Phys. Rev. 115, 850 (1959).
[Crossref]

1958 (1)

B. Cagnac, J. Brossel, and A. Kastler, Compt. Rend. 246, 1827 (1958); B. Cagnac and J. Brossel, ibid.  249, 77, 253 (1959); B. Cagnac and J. P. Barrat, ibid., p. 534; J. Brossel, Yearbook Phys. Soc. (London) 1960, 1.

1957 (3)

A. Kastler, J. Opt. Soc. Am. 47, 460 (1957). See also: Nuovo Cimento 6, No. 3, 1148 (1957).
[Crossref]

H. G. Dehmelt, Phys. Rev. 105, 1924 (1957).
[Crossref]

W. E. Bell and A. L. Bloom, Phys. Rev. 107, 1559 (1957).
[Crossref]

Abragam, A.

A. Abragam, The Principles of Nuclear Magnetism (Clarendon Press, Oxford, England, 1961), p. 24.

Barrat, J. P.

J. P. Barrat and C. Cohen-Tannoudji, J. Phys. Radium 22, 329, 443 (1961). See also: Compt. Rend. 252, 93, 255 (1961).
[Crossref]

Bell, W. E.

W. E. Bell and A. L. Bloom, Phys. Rev. Letters 6, 280 (1961).
[Crossref]

W. E. Bell and A. L. Bloom, Phys. Rev. 107, 1559 (1957).
[Crossref]

Bloom, A. L.

W. E. Bell and A. L. Bloom, Phys. Rev. Letters 6, 280 (1961).
[Crossref]

W. E. Bell and A. L. Bloom, Phys. Rev. 107, 1559 (1957).
[Crossref]

Brossel, J.

B. Cagnac, J. Brossel, and A. Kastler, Compt. Rend. 246, 1827 (1958); B. Cagnac and J. Brossel, ibid.  249, 77, 253 (1959); B. Cagnac and J. P. Barrat, ibid., p. 534; J. Brossel, Yearbook Phys. Soc. (London) 1960, 1.

Cagnac, B.

B. Cagnac, J. Brossel, and A. Kastler, Compt. Rend. 246, 1827 (1958); B. Cagnac and J. Brossel, ibid.  249, 77, 253 (1959); B. Cagnac and J. P. Barrat, ibid., p. 534; J. Brossel, Yearbook Phys. Soc. (London) 1960, 1.

B. Cagnac, thesis, Paris1960, summarized in Ann. Phys. Paris 6, 467 (1961).

Cohen-Tannoudji, C.

J. P. Barrat and C. Cohen-Tannoudji, J. Phys. Radium 22, 329, 443 (1961). See also: Compt. Rend. 252, 93, 255 (1961).
[Crossref]

C. Cohen-Tannoudji, thesis, Paris1962, Ann. Phys. Paris 7, 423 (1962). See also: C. Cohen-Tannoudji, Compt. Rend. 252, 384 (1961); Compt. Rend. 253, 2662, 2899 (1961).

Dehmelt, H. G.

H. G. Dehmelt, Phys. Rev. 105, 1924 (1957).
[Crossref]

Franzen, W.

W. Franzen, Phys. Rev. 115, 850 (1959).
[Crossref]

Kastler, A.

B. Cagnac, J. Brossel, and A. Kastler, Compt. Rend. 246, 1827 (1958); B. Cagnac and J. Brossel, ibid.  249, 77, 253 (1959); B. Cagnac and J. P. Barrat, ibid., p. 534; J. Brossel, Yearbook Phys. Soc. (London) 1960, 1.

A. Kastler, J. Opt. Soc. Am. 47, 460 (1957). See also: Nuovo Cimento 6, No. 3, 1148 (1957).
[Crossref]

Compt. Rend. (1)

B. Cagnac, J. Brossel, and A. Kastler, Compt. Rend. 246, 1827 (1958); B. Cagnac and J. Brossel, ibid.  249, 77, 253 (1959); B. Cagnac and J. P. Barrat, ibid., p. 534; J. Brossel, Yearbook Phys. Soc. (London) 1960, 1.

J. Opt. Soc. Am. (1)

J. Phys. Radium (1)

J. P. Barrat and C. Cohen-Tannoudji, J. Phys. Radium 22, 329, 443 (1961). See also: Compt. Rend. 252, 93, 255 (1961).
[Crossref]

Phys. Rev. (3)

H. G. Dehmelt, Phys. Rev. 105, 1924 (1957).
[Crossref]

W. E. Bell and A. L. Bloom, Phys. Rev. 107, 1559 (1957).
[Crossref]

W. Franzen, Phys. Rev. 115, 850 (1959).
[Crossref]

Phys. Rev. Letters (1)

W. E. Bell and A. L. Bloom, Phys. Rev. Letters 6, 280 (1961).
[Crossref]

Other (5)

C. Cohen-Tannoudji, thesis, Paris1962, Ann. Phys. Paris 7, 423 (1962). See also: C. Cohen-Tannoudji, Compt. Rend. 252, 384 (1961); Compt. Rend. 253, 2662, 2899 (1961).

Another method of introducing coherence is optical excitation by modulated or periodically pulsed light.6

B. Cagnac, thesis, Paris1960, summarized in Ann. Phys. Paris 6, 467 (1961).

In the theoretical paper of Barrat and Cohen-Tannoudji and in Cohen-Tannoudji’s thesis the symbols m and m′are used for the magnetic sublevels of the excited state and the symbols μ and μ′for the magnetic sublevels of the ground slate. In this review we have not to consider the m states of the excited state. We use m and m′ for the ground state.

A. Abragam, The Principles of Nuclear Magnetism (Clarendon Press, Oxford, England, 1961), p. 24.

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Figures (16)

Fig. 1
Fig. 1

Zeeman structure of the mercury line 2537 Å for the hyperfine component A of Hg199. (a) Energy-level scheme, (b) Polarization scheme.

Fig. 2
Fig. 2

Transient signal of optical pumping as a function of time.

Fig. 3
Fig. 3

Exponential of darkness relaxation.

Fig. 4
Fig. 4

Nuclear magnetic resonance curves of Hg199 at constant field H0. Variation of frequency of the applied H1 field. Each curve corresponds to a constant amplitude of H1.

Fig. 5
Fig. 5

Modulation signal of the cross beam.

Fig. 6
Fig. 6

1/τ2 as a function of the cross-beam light intensity.

Fig. 7
Fig. 7

Absorption-shape integral of Formula (18).

Fig. 8
Fig. 8

Dispersion-shape integral of Formula (19).

Fig. 9
Fig. 9

Coherent and incoherent excitation of Zeeman components.

Fig. 10
Fig. 10

Transverse relaxation rate as a function of (ωeω0).

Fig. 11
Fig. 11

The two effects of light relaxation by the cross beam: broadening and shift of the resonance curve for high light intensity.

Fig. 12
Fig. 12

Frequency shift as a function of cross-beam light intensity.

Fig. 13
Fig. 13

Frequency shift as a function of (ωeω0).

Fig. 14
Fig. 14

Level shift produced by virtual transitions.

Fig. 15
Fig. 15

Shifts produced by σ+ and by σ light.

Fig. 16
Fig. 16

Scanning experiment showing the dispersion shape of ΔE as a function of k1k0.

Equations (24)

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P = N + 1 2 N 1 2 N + 1 2 + N 1 2 = 1 2 N 1 2 N ,
T = C t e N 1 2 = C t e ( N / 2 ) ( 1 P ) .
M z = P N μ ,
T = C t e ( N / 2 ) [ 1 ( M z / N μ ) ] .
T 0 T = ( T 0 T ) e t / τ 1 .
1 / τ 1 = ( 1 / ϕ 1 ) + K I .
1 / τ 1 = ( 1 / ϕ 1 ) + ( 1 / T 1 ) .
1 / τ 2 = ( 1 / ϕ 2 ) + K 2 I 2 = ( 1 / ϕ 2 ) + ( 1 / T 2 ) .
ψ ( t ) = m a m ( t ) ψ m ,
m a m a m * = 1.
σ m m = a m ( t ) a m * ( t ) .
σ m m = a m ( t ) a m * ( t )
σ m m = a m ( t ) a m * ( t ) for m m ,
σ ¯ m m = 1 N N σ m m ,
1 / T 2 = a + b j .
σ m , m 1 ( t ) = | σ m , m 1 | e j ω 0 t e t / T 2 = | σ m , m 1 | e a t e j ( ω 0 + b ) t .
1 T 2 = Γ 2 ( A + + A ) Γ B Γ 2 Γ 2 + ( ω e ω 0 ) 2 + j [ Γ B Γ ( ω e ω 0 ) Γ 2 + ( ω e ω 0 ) 2 + Δ E ( A + A ) ] .
Γ 2 = 0 u ( k ) | A k | 2 d k Γ / 2 ( Γ / 2 ) 2 + ( k k 0 ) 2 ,
Δ E = 0 u ( k ) | A k | 2 d k k k 0 ( Γ / 2 ) 2 + ( k k 0 ) 2 .
Γ / 2 ( Γ / 2 ) 2 + ( k k 0 ) 2
1 1 3 [ Γ 2 / Γ 2 + ( ω e ω 0 ) 2 ] .
Δ φ = ( ω e ω 0 ) τ = ( ω e ω 0 ) / Γ .
1 / [ 1 + ( ω e ω 0 Γ ) 2 ]
( ω e ω 0 ) / Γ 1 + ( ω e ω 0 / Γ ) 2 .