Abstract

We have checked whether the frequency ratio between fundamental and second-harmonic optical frequencies is exactly 1:2 by measuring the frequency difference between the second harmonics of two diode lasers and comparing it with the frequency difference of the fundamentals. We have improved the 30-year-old experimental limit on the accuracy of the 1:2 frequency ratio by 7 orders of magnitude for frequency-dependent shifts to 2.3 parts in 1013 for a KNbO3 crystal.

© 1995 Optical Society of America

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References

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  1. I. D. Abella, Proc. IRE 50, 1824 (1962).
  2. H. S. Boyne, W. C. Martin, J. Opt. Soc. Am. 52, 880 (1962).
    [CrossRef]
  3. T. Andreae, W. König, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, T. W. Hänsch, Phys. Rev. Lett. 69, 1923 (1992).
    [CrossRef] [PubMed]
  4. F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
    [CrossRef] [PubMed]
  5. M. S. Fee, K. Danzmann, S. Chu, Phys. Rev. A 45, 4911 (1992).
    [CrossRef] [PubMed]

1992 (3)

T. Andreae, W. König, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, T. W. Hänsch, Phys. Rev. Lett. 69, 1923 (1992).
[CrossRef] [PubMed]

F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
[CrossRef] [PubMed]

M. S. Fee, K. Danzmann, S. Chu, Phys. Rev. A 45, 4911 (1992).
[CrossRef] [PubMed]

1962 (2)

Abed, M.

F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
[CrossRef] [PubMed]

Abella, I. D.

I. D. Abella, Proc. IRE 50, 1824 (1962).

Acef, O.

F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
[CrossRef] [PubMed]

Andreae, T.

T. Andreae, W. König, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, T. W. Hänsch, Phys. Rev. Lett. 69, 1923 (1992).
[CrossRef] [PubMed]

Biraben, F.

F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
[CrossRef] [PubMed]

Bourzeix, S.

F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
[CrossRef] [PubMed]

Boyne, H. S.

Chu, S.

M. S. Fee, K. Danzmann, S. Chu, Phys. Rev. A 45, 4911 (1992).
[CrossRef] [PubMed]

Clairon, A.

F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
[CrossRef] [PubMed]

Danzmann, K.

M. S. Fee, K. Danzmann, S. Chu, Phys. Rev. A 45, 4911 (1992).
[CrossRef] [PubMed]

Fee, M. S.

M. S. Fee, K. Danzmann, S. Chu, Phys. Rev. A 45, 4911 (1992).
[CrossRef] [PubMed]

Felder, R.

F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
[CrossRef] [PubMed]

Hänsch, T. W.

T. Andreae, W. König, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, T. W. Hänsch, Phys. Rev. Lett. 69, 1923 (1992).
[CrossRef] [PubMed]

Julien, L.

F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
[CrossRef] [PubMed]

Juncar, P.

F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
[CrossRef] [PubMed]

König, W.

T. Andreae, W. König, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, T. W. Hänsch, Phys. Rev. Lett. 69, 1923 (1992).
[CrossRef] [PubMed]

Laurent, P.

F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
[CrossRef] [PubMed]

Leibfried, D.

T. Andreae, W. König, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, T. W. Hänsch, Phys. Rev. Lett. 69, 1923 (1992).
[CrossRef] [PubMed]

Martin, W. C.

Meschede, D.

T. Andreae, W. König, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, T. W. Hänsch, Phys. Rev. Lett. 69, 1923 (1992).
[CrossRef] [PubMed]

Millerioux, Y.

F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
[CrossRef] [PubMed]

Nez, F.

F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
[CrossRef] [PubMed]

Plimmer, M. D.

F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
[CrossRef] [PubMed]

Schmidt-Kaler, F.

T. Andreae, W. König, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, T. W. Hänsch, Phys. Rev. Lett. 69, 1923 (1992).
[CrossRef] [PubMed]

Wynands, R.

T. Andreae, W. König, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, T. W. Hänsch, Phys. Rev. Lett. 69, 1923 (1992).
[CrossRef] [PubMed]

Zimmermann, C.

T. Andreae, W. König, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, T. W. Hänsch, Phys. Rev. Lett. 69, 1923 (1992).
[CrossRef] [PubMed]

Zondy, J. J.

F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

Phys. Rev. A (1)

M. S. Fee, K. Danzmann, S. Chu, Phys. Rev. A 45, 4911 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

T. Andreae, W. König, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, T. W. Hänsch, Phys. Rev. Lett. 69, 1923 (1992).
[CrossRef] [PubMed]

F. Nez, M. D. Plimmer, S. Bourzeix, L. Julien, F. Biraben, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, P. Juncar, Phys. Rev. Lett. 69, 2326 (1992).
[CrossRef] [PubMed]

Proc. IRE (1)

I. D. Abella, Proc. IRE 50, 1824 (1962).

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Figures (2)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Logarithmic plot of the power spectral density of the down converted beat note between the sum frequency and the second harmonics. The width is limited entirely by the window function of the Fourier-transform spectrum analyzer (the Blackman–Harris window).

Equations (6)

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P i = ɛ 0 ( χ i j E j + 2 d i j k E j E k + ) ,
SH1 : f 11 = 2 f 1 + δ ( f 1 , f 1 ) , SH2 : f 22 = 2 f 2 + δ ( f 2 , f 2 ) , SUM : f 12 = f 1 + f 2 + δ ( f 1 , f 2 ) .
f 2211 = f 22 - f 11 = 2 Δ f + δ ( f 2 , f 2 ) - δ ( f 1 , f 1 ) , f 1211 = f 12 - f 11 = Δ f + δ ( f 1 , f 2 ) - δ ( f 1 , f 1 ) , f 2212 = f 22 - f 12 = Δ f + δ ( f 2 , f 2 ) - δ ( f 1 , f 2 ) ,
ɛ : = f a δ ( f a , f b ) | f x , f y = f b δ ( f a , f b ) | f y , f x ,
f 2211 = 2 Δ f ( 1 + ɛ ) , f 1211 = f 2212 = Δ f ( 1 + ɛ ) .
ɛ < 192 μ Hz Δ f = 2.3 × 10 - 13 .

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