Abstract

Optically induced resonance Raman transitions in atomic and molecular beams are proposed as a means of achieving ultrahigh resolution in the microwave and far-infrared regions. Line broadening that is due to laser jitter is eliminated by correlating the frequency jitter of the two optical fields inducing the Raman transition. A Raman-separated oscillatory-field technique for reducing transit-time broadening is considered.

© 1981 Optical Society of America

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References

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  1. R. P. Hackel, S. Ezekiel, Phys. Rev. Lett. 42, 1736 (1979), and references therein.
    [Crossref]
  2. M. S. Feld, M. M. Burns, T. V. Kuhl, P. G. Pappas, D. E. Murnick, Opt. Lett. 5, 79 (1980).
    [Crossref] [PubMed]
  3. Residual line broadening in the case in which the jitter in the two lasers is correlated depends on the jitter rate in relation to the interaction time for the Raman process. For the resonant Raman process considered here, the time scale is the short lifetime of the intermediate state.
  4. N. F. Ramsey, Molecular Beams (Oxford U. Press, London, 1963).
  5. Ye. V. Baklanov, V. P. Chebotayev, B. Ya. Dubetsky, Appl. Phys.11, 201 (1976).
    [Crossref]
  6. M. M. Salour, C. Cohen-Tannoudji, Phys. Rev. Lett. 38, 757 (1977).
    [Crossref]
  7. Ye. V. Baklanov, B. Ya. Dubetsky, V. P. Chebotayev, Appl. Phys. 9, 171 (1976).
    [Crossref]
  8. J. C. Bergquist, S. A. Lee, J. L. Hall, Phys. Rev. Lett. 38, 159 (1977); S. N. Bagayev, A. S. Dychkov, V. P. Chetotayev, Pis’ma Zh. Eksp. Teor. Fiz. 26, 591 (1977).
    [Crossref]
  9. V. P. Chebotayev, B. Ya. Dubetsky, Appl. Phys. 18, 217 (1979).
    [Crossref]
  10. The condition (Ωp − Ωs − ω31)τ ≪ 1 is taken for convenience and is not a serious restriction, since the velocity-averaged Ramsey resonance linewidth will be of order u/L ≪ 1/τ.
  11. For a similar calculation of the line shape for resonant Raman transitions in vapors, including the Gaussian laser field distribution, see J. E. Thomas, W. W. Quivers, Phys. Rev. A. 22, 2115 (1980).
    [Crossref]

1980 (2)

M. S. Feld, M. M. Burns, T. V. Kuhl, P. G. Pappas, D. E. Murnick, Opt. Lett. 5, 79 (1980).
[Crossref] [PubMed]

For a similar calculation of the line shape for resonant Raman transitions in vapors, including the Gaussian laser field distribution, see J. E. Thomas, W. W. Quivers, Phys. Rev. A. 22, 2115 (1980).
[Crossref]

1979 (2)

V. P. Chebotayev, B. Ya. Dubetsky, Appl. Phys. 18, 217 (1979).
[Crossref]

R. P. Hackel, S. Ezekiel, Phys. Rev. Lett. 42, 1736 (1979), and references therein.
[Crossref]

1977 (2)

J. C. Bergquist, S. A. Lee, J. L. Hall, Phys. Rev. Lett. 38, 159 (1977); S. N. Bagayev, A. S. Dychkov, V. P. Chetotayev, Pis’ma Zh. Eksp. Teor. Fiz. 26, 591 (1977).
[Crossref]

M. M. Salour, C. Cohen-Tannoudji, Phys. Rev. Lett. 38, 757 (1977).
[Crossref]

1976 (1)

Ye. V. Baklanov, B. Ya. Dubetsky, V. P. Chebotayev, Appl. Phys. 9, 171 (1976).
[Crossref]

Baklanov, Ye. V.

Ye. V. Baklanov, B. Ya. Dubetsky, V. P. Chebotayev, Appl. Phys. 9, 171 (1976).
[Crossref]

Ye. V. Baklanov, V. P. Chebotayev, B. Ya. Dubetsky, Appl. Phys.11, 201 (1976).
[Crossref]

Bergquist, J. C.

J. C. Bergquist, S. A. Lee, J. L. Hall, Phys. Rev. Lett. 38, 159 (1977); S. N. Bagayev, A. S. Dychkov, V. P. Chetotayev, Pis’ma Zh. Eksp. Teor. Fiz. 26, 591 (1977).
[Crossref]

Burns, M. M.

Chebotayev, V. P.

V. P. Chebotayev, B. Ya. Dubetsky, Appl. Phys. 18, 217 (1979).
[Crossref]

Ye. V. Baklanov, B. Ya. Dubetsky, V. P. Chebotayev, Appl. Phys. 9, 171 (1976).
[Crossref]

Ye. V. Baklanov, V. P. Chebotayev, B. Ya. Dubetsky, Appl. Phys.11, 201 (1976).
[Crossref]

Cohen-Tannoudji, C.

M. M. Salour, C. Cohen-Tannoudji, Phys. Rev. Lett. 38, 757 (1977).
[Crossref]

Dubetsky, B. Ya.

Ye. V. Baklanov, V. P. Chebotayev, B. Ya. Dubetsky, Appl. Phys.11, 201 (1976).
[Crossref]

Ezekiel, S.

R. P. Hackel, S. Ezekiel, Phys. Rev. Lett. 42, 1736 (1979), and references therein.
[Crossref]

Feld, M. S.

Hackel, R. P.

R. P. Hackel, S. Ezekiel, Phys. Rev. Lett. 42, 1736 (1979), and references therein.
[Crossref]

Hall, J. L.

J. C. Bergquist, S. A. Lee, J. L. Hall, Phys. Rev. Lett. 38, 159 (1977); S. N. Bagayev, A. S. Dychkov, V. P. Chetotayev, Pis’ma Zh. Eksp. Teor. Fiz. 26, 591 (1977).
[Crossref]

Kuhl, T. V.

Lee, S. A.

J. C. Bergquist, S. A. Lee, J. L. Hall, Phys. Rev. Lett. 38, 159 (1977); S. N. Bagayev, A. S. Dychkov, V. P. Chetotayev, Pis’ma Zh. Eksp. Teor. Fiz. 26, 591 (1977).
[Crossref]

Murnick, D. E.

Pappas, P. G.

Quivers, W. W.

For a similar calculation of the line shape for resonant Raman transitions in vapors, including the Gaussian laser field distribution, see J. E. Thomas, W. W. Quivers, Phys. Rev. A. 22, 2115 (1980).
[Crossref]

Ramsey, N. F.

N. F. Ramsey, Molecular Beams (Oxford U. Press, London, 1963).

Salour, M. M.

M. M. Salour, C. Cohen-Tannoudji, Phys. Rev. Lett. 38, 757 (1977).
[Crossref]

Thomas, J. E.

For a similar calculation of the line shape for resonant Raman transitions in vapors, including the Gaussian laser field distribution, see J. E. Thomas, W. W. Quivers, Phys. Rev. A. 22, 2115 (1980).
[Crossref]

Ya. Dubetsky, B.

V. P. Chebotayev, B. Ya. Dubetsky, Appl. Phys. 18, 217 (1979).
[Crossref]

Ye. V. Baklanov, B. Ya. Dubetsky, V. P. Chebotayev, Appl. Phys. 9, 171 (1976).
[Crossref]

Appl. Phys. (2)

Ye. V. Baklanov, B. Ya. Dubetsky, V. P. Chebotayev, Appl. Phys. 9, 171 (1976).
[Crossref]

V. P. Chebotayev, B. Ya. Dubetsky, Appl. Phys. 18, 217 (1979).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A. (1)

For a similar calculation of the line shape for resonant Raman transitions in vapors, including the Gaussian laser field distribution, see J. E. Thomas, W. W. Quivers, Phys. Rev. A. 22, 2115 (1980).
[Crossref]

Phys. Rev. Lett. (3)

J. C. Bergquist, S. A. Lee, J. L. Hall, Phys. Rev. Lett. 38, 159 (1977); S. N. Bagayev, A. S. Dychkov, V. P. Chetotayev, Pis’ma Zh. Eksp. Teor. Fiz. 26, 591 (1977).
[Crossref]

R. P. Hackel, S. Ezekiel, Phys. Rev. Lett. 42, 1736 (1979), and references therein.
[Crossref]

M. M. Salour, C. Cohen-Tannoudji, Phys. Rev. Lett. 38, 757 (1977).
[Crossref]

Other (4)

Residual line broadening in the case in which the jitter in the two lasers is correlated depends on the jitter rate in relation to the interaction time for the Raman process. For the resonant Raman process considered here, the time scale is the short lifetime of the intermediate state.

N. F. Ramsey, Molecular Beams (Oxford U. Press, London, 1963).

Ye. V. Baklanov, V. P. Chebotayev, B. Ya. Dubetsky, Appl. Phys.11, 201 (1976).
[Crossref]

The condition (Ωp − Ωs − ω31)τ ≪ 1 is taken for convenience and is not a serious restriction, since the velocity-averaged Ramsey resonance linewidth will be of order u/L ≪ 1/τ.

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Figures (1)

Fig. 1
Fig. 1

Scheme for Raman-induced Ramsey resonance in an atomic beam.

Equations (12)

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E p ( t ) = E 0 p 2 exp ( i Ω p t + ) + c . c . ,
E s ( t ) = E 0 s * 2 exp ( i Ω s t + ) + c . c .
a ˙ m ( t ) = i n V mn ( t ) exp ( i ω mn t ) a n ( t ) γ m 2 a m ( t ) ,
V mn ( t ) = μ mn [ E p ( t ) + E s ( t ) ] ,
a 3 ( 1 ) β 32 β 21 τ 2 γ 2 exp [ i ( φ 1 ψ 1 ) ] ,
β 32 = i μ 32 E 0 s * ; β 21 = i μ 21 E 0 p .
a 3 ( 2 ) β 32 β 21 τ 2 γ 2 exp ( i Δ T ) exp [ i ( φ 2 ψ 2 ) ] ,
| a 3 ( 1 ) + a 3 ( 2 ) 2 | = 1 / 2 | β 32 β 21 τ γ 2 | 2 × { 1 + cos [ Δ T + ( φ 1 ψ 1 ) ( φ 2 ψ 2 ) ] } .
Δ P s ( υ ) = δ N ˙ s cos [ Δ T + ( φ 1 ψ 1 ) ( φ 2 ψ 2 ) ] ,
s ω 23 2 | β 32 β 21 τ γ 2 | 2 .
Δ p s = N ˙ 0 ω 23 2 I s I p I SAT 2 ,
I SAT = c 8 π | h 2 γ 2 μ 32 e ˆ 2 * μ 21 e ˆ 1 u d | ,

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