Abstract

The frequency shift of the light owing to a cavity length modulation has been observed with the spectroscopy of the 1S–3S two-photon transition in hydrogen. The excitation of this transition occurs at a wavelength of 205 nm. One produces this radiation by frequency doubling a 410-nm radiation in an enhancement ring cavity. The length modulation of this cavity induces frequency shifts and a splitting of the observed 1S–3S line. We obtain a good agreement between the experiment and the theoretical analysis.

© 2002 Optical Society of America

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References

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  1. T. W. Hänsch, B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 41, 441–444 (1980).
    [Crossref]
  2. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
    [Crossref]
  3. S. Bourzeix, B. de Beauvoir, F. Nez, M. D. Plimmer, F. de Tomasi, L. Julien, F. Biraben, D. N. Stacey, “High resolution spectroscopy of the hydrogen atom: determination of the 1S Lamb shift,” Phys. Rev. Lett. 76, 384–387 (1996).
    [Crossref] [PubMed]
  4. B. de Beauvoir, C. Schwob, O. Acef, J.-J. Zondy, L. Jozefowski, L. Hilico, F. Nez, L. Julien, A. Clairon, F. Biraben, “Metrology of the hydrogen and deuterium atoms: determination of the Rydberg constant and Lamb shifts,” Eur. Phys. J. D 12, 61–93 (2000).
    [Crossref]
  5. S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, F. Biraben, “Efficient frequency doubling of a continuous wave titanium-sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
    [Crossref]
  6. S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, F. Biraben, “Ultra-violet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
    [Crossref]
  7. F. Biraben, M. Bassini, B. Cagnac, “Line shapes in Doppler-free two-photon spectroscopy: the effect of finite transit time,” J. Phys. (Paris) 40, 445–455 (1979).
    [Crossref]

2000 (1)

B. de Beauvoir, C. Schwob, O. Acef, J.-J. Zondy, L. Jozefowski, L. Hilico, F. Nez, L. Julien, A. Clairon, F. Biraben, “Metrology of the hydrogen and deuterium atoms: determination of the Rydberg constant and Lamb shifts,” Eur. Phys. J. D 12, 61–93 (2000).
[Crossref]

1997 (1)

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, F. Biraben, “Ultra-violet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[Crossref]

1996 (1)

S. Bourzeix, B. de Beauvoir, F. Nez, M. D. Plimmer, F. de Tomasi, L. Julien, F. Biraben, D. N. Stacey, “High resolution spectroscopy of the hydrogen atom: determination of the 1S Lamb shift,” Phys. Rev. Lett. 76, 384–387 (1996).
[Crossref] [PubMed]

1993 (1)

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, F. Biraben, “Efficient frequency doubling of a continuous wave titanium-sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
[Crossref]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

1980 (1)

T. W. Hänsch, B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 41, 441–444 (1980).
[Crossref]

1979 (1)

F. Biraben, M. Bassini, B. Cagnac, “Line shapes in Doppler-free two-photon spectroscopy: the effect of finite transit time,” J. Phys. (Paris) 40, 445–455 (1979).
[Crossref]

Acef, O.

B. de Beauvoir, C. Schwob, O. Acef, J.-J. Zondy, L. Jozefowski, L. Hilico, F. Nez, L. Julien, A. Clairon, F. Biraben, “Metrology of the hydrogen and deuterium atoms: determination of the Rydberg constant and Lamb shifts,” Eur. Phys. J. D 12, 61–93 (2000).
[Crossref]

Bassini, M.

F. Biraben, M. Bassini, B. Cagnac, “Line shapes in Doppler-free two-photon spectroscopy: the effect of finite transit time,” J. Phys. (Paris) 40, 445–455 (1979).
[Crossref]

Biraben, F.

B. de Beauvoir, C. Schwob, O. Acef, J.-J. Zondy, L. Jozefowski, L. Hilico, F. Nez, L. Julien, A. Clairon, F. Biraben, “Metrology of the hydrogen and deuterium atoms: determination of the Rydberg constant and Lamb shifts,” Eur. Phys. J. D 12, 61–93 (2000).
[Crossref]

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, F. Biraben, “Ultra-violet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[Crossref]

S. Bourzeix, B. de Beauvoir, F. Nez, M. D. Plimmer, F. de Tomasi, L. Julien, F. Biraben, D. N. Stacey, “High resolution spectroscopy of the hydrogen atom: determination of the 1S Lamb shift,” Phys. Rev. Lett. 76, 384–387 (1996).
[Crossref] [PubMed]

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, F. Biraben, “Efficient frequency doubling of a continuous wave titanium-sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
[Crossref]

F. Biraben, M. Bassini, B. Cagnac, “Line shapes in Doppler-free two-photon spectroscopy: the effect of finite transit time,” J. Phys. (Paris) 40, 445–455 (1979).
[Crossref]

Bourzeix, S.

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, F. Biraben, “Ultra-violet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[Crossref]

S. Bourzeix, B. de Beauvoir, F. Nez, M. D. Plimmer, F. de Tomasi, L. Julien, F. Biraben, D. N. Stacey, “High resolution spectroscopy of the hydrogen atom: determination of the 1S Lamb shift,” Phys. Rev. Lett. 76, 384–387 (1996).
[Crossref] [PubMed]

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, F. Biraben, “Efficient frequency doubling of a continuous wave titanium-sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
[Crossref]

Cagnac, B.

F. Biraben, M. Bassini, B. Cagnac, “Line shapes in Doppler-free two-photon spectroscopy: the effect of finite transit time,” J. Phys. (Paris) 40, 445–455 (1979).
[Crossref]

Clairon, A.

B. de Beauvoir, C. Schwob, O. Acef, J.-J. Zondy, L. Jozefowski, L. Hilico, F. Nez, L. Julien, A. Clairon, F. Biraben, “Metrology of the hydrogen and deuterium atoms: determination of the Rydberg constant and Lamb shifts,” Eur. Phys. J. D 12, 61–93 (2000).
[Crossref]

Couillaud, B.

T. W. Hänsch, B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 41, 441–444 (1980).
[Crossref]

de Beauvoir, B.

B. de Beauvoir, C. Schwob, O. Acef, J.-J. Zondy, L. Jozefowski, L. Hilico, F. Nez, L. Julien, A. Clairon, F. Biraben, “Metrology of the hydrogen and deuterium atoms: determination of the Rydberg constant and Lamb shifts,” Eur. Phys. J. D 12, 61–93 (2000).
[Crossref]

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, F. Biraben, “Ultra-violet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[Crossref]

S. Bourzeix, B. de Beauvoir, F. Nez, M. D. Plimmer, F. de Tomasi, L. Julien, F. Biraben, D. N. Stacey, “High resolution spectroscopy of the hydrogen atom: determination of the 1S Lamb shift,” Phys. Rev. Lett. 76, 384–387 (1996).
[Crossref] [PubMed]

de Tomasi, F.

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, F. Biraben, “Ultra-violet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[Crossref]

S. Bourzeix, B. de Beauvoir, F. Nez, M. D. Plimmer, F. de Tomasi, L. Julien, F. Biraben, D. N. Stacey, “High resolution spectroscopy of the hydrogen atom: determination of the 1S Lamb shift,” Phys. Rev. Lett. 76, 384–387 (1996).
[Crossref] [PubMed]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Hänsch, T. W.

T. W. Hänsch, B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 41, 441–444 (1980).
[Crossref]

Hilico, L.

B. de Beauvoir, C. Schwob, O. Acef, J.-J. Zondy, L. Jozefowski, L. Hilico, F. Nez, L. Julien, A. Clairon, F. Biraben, “Metrology of the hydrogen and deuterium atoms: determination of the Rydberg constant and Lamb shifts,” Eur. Phys. J. D 12, 61–93 (2000).
[Crossref]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Jozefowski, L.

B. de Beauvoir, C. Schwob, O. Acef, J.-J. Zondy, L. Jozefowski, L. Hilico, F. Nez, L. Julien, A. Clairon, F. Biraben, “Metrology of the hydrogen and deuterium atoms: determination of the Rydberg constant and Lamb shifts,” Eur. Phys. J. D 12, 61–93 (2000).
[Crossref]

Julien, L.

B. de Beauvoir, C. Schwob, O. Acef, J.-J. Zondy, L. Jozefowski, L. Hilico, F. Nez, L. Julien, A. Clairon, F. Biraben, “Metrology of the hydrogen and deuterium atoms: determination of the Rydberg constant and Lamb shifts,” Eur. Phys. J. D 12, 61–93 (2000).
[Crossref]

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, F. Biraben, “Ultra-violet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[Crossref]

S. Bourzeix, B. de Beauvoir, F. Nez, M. D. Plimmer, F. de Tomasi, L. Julien, F. Biraben, D. N. Stacey, “High resolution spectroscopy of the hydrogen atom: determination of the 1S Lamb shift,” Phys. Rev. Lett. 76, 384–387 (1996).
[Crossref] [PubMed]

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, F. Biraben, “Efficient frequency doubling of a continuous wave titanium-sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
[Crossref]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Nez, F.

B. de Beauvoir, C. Schwob, O. Acef, J.-J. Zondy, L. Jozefowski, L. Hilico, F. Nez, L. Julien, A. Clairon, F. Biraben, “Metrology of the hydrogen and deuterium atoms: determination of the Rydberg constant and Lamb shifts,” Eur. Phys. J. D 12, 61–93 (2000).
[Crossref]

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, F. Biraben, “Ultra-violet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[Crossref]

S. Bourzeix, B. de Beauvoir, F. Nez, M. D. Plimmer, F. de Tomasi, L. Julien, F. Biraben, D. N. Stacey, “High resolution spectroscopy of the hydrogen atom: determination of the 1S Lamb shift,” Phys. Rev. Lett. 76, 384–387 (1996).
[Crossref] [PubMed]

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, F. Biraben, “Efficient frequency doubling of a continuous wave titanium-sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
[Crossref]

Plimmer, M. D.

S. Bourzeix, B. de Beauvoir, F. Nez, M. D. Plimmer, F. de Tomasi, L. Julien, F. Biraben, D. N. Stacey, “High resolution spectroscopy of the hydrogen atom: determination of the 1S Lamb shift,” Phys. Rev. Lett. 76, 384–387 (1996).
[Crossref] [PubMed]

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, F. Biraben, “Efficient frequency doubling of a continuous wave titanium-sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
[Crossref]

Schwob, C.

B. de Beauvoir, C. Schwob, O. Acef, J.-J. Zondy, L. Jozefowski, L. Hilico, F. Nez, L. Julien, A. Clairon, F. Biraben, “Metrology of the hydrogen and deuterium atoms: determination of the Rydberg constant and Lamb shifts,” Eur. Phys. J. D 12, 61–93 (2000).
[Crossref]

Stacey, D. N.

S. Bourzeix, B. de Beauvoir, F. Nez, M. D. Plimmer, F. de Tomasi, L. Julien, F. Biraben, D. N. Stacey, “High resolution spectroscopy of the hydrogen atom: determination of the 1S Lamb shift,” Phys. Rev. Lett. 76, 384–387 (1996).
[Crossref] [PubMed]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Zondy, J.-J.

B. de Beauvoir, C. Schwob, O. Acef, J.-J. Zondy, L. Jozefowski, L. Hilico, F. Nez, L. Julien, A. Clairon, F. Biraben, “Metrology of the hydrogen and deuterium atoms: determination of the Rydberg constant and Lamb shifts,” Eur. Phys. J. D 12, 61–93 (2000).
[Crossref]

Appl. Phys. B (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Eur. Phys. J. D (1)

B. de Beauvoir, C. Schwob, O. Acef, J.-J. Zondy, L. Jozefowski, L. Hilico, F. Nez, L. Julien, A. Clairon, F. Biraben, “Metrology of the hydrogen and deuterium atoms: determination of the Rydberg constant and Lamb shifts,” Eur. Phys. J. D 12, 61–93 (2000).
[Crossref]

J. Phys. (Paris) (1)

F. Biraben, M. Bassini, B. Cagnac, “Line shapes in Doppler-free two-photon spectroscopy: the effect of finite transit time,” J. Phys. (Paris) 40, 445–455 (1979).
[Crossref]

Opt. Commun. (3)

T. W. Hänsch, B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 41, 441–444 (1980).
[Crossref]

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien, F. Biraben, “Efficient frequency doubling of a continuous wave titanium-sapphire laser in an external enhancement cavity,” Opt. Commun. 99, 89–94 (1993).
[Crossref]

S. Bourzeix, B. de Beauvoir, F. Nez, F. de Tomasi, L. Julien, F. Biraben, “Ultra-violet light generation at 205 nm by two frequency doubling steps of a cw titanium-sapphire laser,” Opt. Commun. 133, 239–244 (1997).
[Crossref]

Phys. Rev. Lett. (1)

S. Bourzeix, B. de Beauvoir, F. Nez, M. D. Plimmer, F. de Tomasi, L. Julien, F. Biraben, D. N. Stacey, “High resolution spectroscopy of the hydrogen atom: determination of the 1S Lamb shift,” Phys. Rev. Lett. 76, 384–387 (1996).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for the observation of the 1S–3S transition in hydrogen (PD, photodiode; PM, photomultiplier; DIS, discriminator). The 15-kHz modulation of the UV cavity is in quadrature with respect to the modulation of the BBO cavity. In the inset, design of the BBO cavity. A prism is used to extract the UV light at 205 nm.

Fig. 2
Fig. 2

Timing of the modulations of the BBO and UV cavities. (a) Length of the BBO cavity versus the time. The dashed line points out the length corresponding to the resonance condition with the 410-nm light. (b) Output of the BBO cavity at 205 nm. (c) Length of the UV cavity. The modulation of the UV cavity length is in quadrature with the modulation of the BBO cavity length. Therefore the UV pulses are produced when the length of the UV cavity is at an extremum. (d) Airy’s peak of the UV cavity (the figure is rotated by 90°). When the UV cavity is exactly in resonance with the UV light (solid curve), two successive UV pulses correspond to the same intensity of the UV cavity. If the cavity length is shifted with respect to the resonance (dashed curve), the intensity inside the UV cavity is not the same for two successive UV pulses.

Fig. 3
Fig. 3

Spectral densities (a) |E 410(ω)|2 and (b) |F(ω)|2 for the cases where the cavity length decreases (solid curves) or increases (dashed curves).

Fig. 4
Fig. 4

Spectrum analyzer recording of the beat note between the 410-nm light transmitted by the BBO cavity and a reference 410-nm laser beam. In the case of the curve (a), the modulation amplitude is ten times larger than for the curve (b), α = 8 and 0.8, respectively (see the text). The resolution bandwidth is 10 kHz.

Fig. 5
Fig. 5

Recording of the 1S–3S two-photon transition in hydrogen. The two curves correspond to the signal recorded when the cavity length increases (◆) or decreases (□). The modulation coefficient of the BBO cavity is α ≃ 5 and the pulse duration 4 µs at 410 nm.

Equations (9)

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Lt=L0±2πa0ν0t,
E410t=ReτE0expiωLt1+r expiδt+r expiδt2+=ReτE0 expiωLt1-r expiδt, 
δ=4πa0ν0ωLc.
E410ω=12π-+expiωtReτE0 expiωLt1-r expiδtdt.
|E410ω|2=0if ω<ωL,|E410ω|2=τ2E024r2δ2×exp-ω-ωLΔif ω>ωL,
E205tReτE0 expiωLt1-r expiδt2.
-+|Fω|21ω-ωat2+Γ2/4dω,
Fω=12π-+τ4E04 expiω-4ωLt41-r exp-iδt4dt.
|Fω|2=0if ω<4ωL,|Fω|2=τ4E0424r4δ42ω-4ωL6×exp-ω-4ωLΔ,if ω>4ωL.

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