Abstract

The precision of interferometry is directly linked to the fringe spacing of the recorded interferogram. Whereas all interferometric devices show a fringe spacing equal to a wavelength of the laser light we present a novel scheme of a two-beam interferometer exhibiting a fringe spacing reduced by a factor of 2; the direct detection of the beat signal is replaced with the monitoring of the fluorescence of a twofold degenerate atomic system resonant with the laser. The λ2 fringe spacing in the fluorescence signal is demonstrated with a hot sodium vapor excited by a broadband laser tuned to the D1 line. In the saturation regime, the dark fringes are expected to be extremely narrow, leading to the possibility of nanoscale displacement measurements or atom localization.

© 2009 Optical Society of America

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References

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  1. P. Hariharan, Optical Interferometry, 2nd ed. (Academic, 2003).
  2. J. C. Delagnes and M. A. Bouchene, Phys. Rev. Lett. 98, 053602 (2007).
    [CrossRef] [PubMed]
  3. R. Loudon, Quantum Theory of Light, 3rd ed. (Oxford U. Press, 2000), Chap. 1.
  4. G. S. Agarwal and K. T. Kapale, J. Phys. B 39, 3437 (2006).
    [CrossRef]
  5. J.-P. Pique and S. Farinotti, J. Opt. Soc. Am. B 20, 2093 (2003).
    [CrossRef]
  6. L. P. Yatsenko, B. W. Shore, and K. Bergmann, Opt. Commun. 236, 183 (2002).
    [CrossRef]
  7. W. Happer, Rev. Mod. Phys. 44, 169 (1972).
    [CrossRef]

2007

J. C. Delagnes and M. A. Bouchene, Phys. Rev. Lett. 98, 053602 (2007).
[CrossRef] [PubMed]

2006

G. S. Agarwal and K. T. Kapale, J. Phys. B 39, 3437 (2006).
[CrossRef]

2003

2002

L. P. Yatsenko, B. W. Shore, and K. Bergmann, Opt. Commun. 236, 183 (2002).
[CrossRef]

1972

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

Agarwal, G. S.

G. S. Agarwal and K. T. Kapale, J. Phys. B 39, 3437 (2006).
[CrossRef]

Bergmann, K.

L. P. Yatsenko, B. W. Shore, and K. Bergmann, Opt. Commun. 236, 183 (2002).
[CrossRef]

Bouchene, M. A.

J. C. Delagnes and M. A. Bouchene, Phys. Rev. Lett. 98, 053602 (2007).
[CrossRef] [PubMed]

Delagnes, J. C.

J. C. Delagnes and M. A. Bouchene, Phys. Rev. Lett. 98, 053602 (2007).
[CrossRef] [PubMed]

Farinotti, S.

Happer, W.

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

Hariharan, P.

P. Hariharan, Optical Interferometry, 2nd ed. (Academic, 2003).

Kapale, K. T.

G. S. Agarwal and K. T. Kapale, J. Phys. B 39, 3437 (2006).
[CrossRef]

Loudon, R.

R. Loudon, Quantum Theory of Light, 3rd ed. (Oxford U. Press, 2000), Chap. 1.

Pique, J.-P.

Shore, B. W.

L. P. Yatsenko, B. W. Shore, and K. Bergmann, Opt. Commun. 236, 183 (2002).
[CrossRef]

Yatsenko, L. P.

L. P. Yatsenko, B. W. Shore, and K. Bergmann, Opt. Commun. 236, 183 (2002).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

G. S. Agarwal and K. T. Kapale, J. Phys. B 39, 3437 (2006).
[CrossRef]

Opt. Commun.

L. P. Yatsenko, B. W. Shore, and K. Bergmann, Opt. Commun. 236, 183 (2002).
[CrossRef]

Phys. Rev. Lett.

J. C. Delagnes and M. A. Bouchene, Phys. Rev. Lett. 98, 053602 (2007).
[CrossRef] [PubMed]

Rev. Mod. Phys.

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

Other

R. Loudon, Quantum Theory of Light, 3rd ed. (Oxford U. Press, 2000), Chap. 1.

P. Hariharan, Optical Interferometry, 2nd ed. (Academic, 2003).

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Figures (5)

Fig. 1
Fig. 1

Top, generic two-beam interferometer; φ is the phase shift between both beams. Bottom, Mach–Zehnder interferometer using the monitoring of the resonant fluorescence as the beat signal (see text).

Fig. 2
Fig. 2

Fine structure of the sodium D 1 line. A is the rate of spontaneous emission (10 MHz), and B is the Einstein coefficient for the σ transition.

Fig. 3
Fig. 3

Variation of the fluorescence signal with the phase shift for different values of the saturation parameter.

Fig. 4
Fig. 4

Top, sketch of the Michelson interferometer. Bottom left, intensity transmitted across the analyzer at 45° during a scan of the translation stage. Bottom right, fluorescence signal recorded for the same scan.

Fig. 5
Fig. 5

Fluorescence pattern seen from the top of the sodium cell when both beams overlap with an angle of 1 mrad with (left) parallel and (right) perpendicular polarizations.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

N ̇ e = B I N ± g B I N e A N e ,
N ̇ g = B I ± N g + B I ± N ± e + ( A 3 ) N e + ( 2 A 3 ) N ± e .
N + g + N g = cos 2 φ + 2 I sat I 0 2 cos 2 φ + 2 I sat I 0 ,
N + e + N e = 2 N + e = cos 2 φ 2 cos 2 φ + 2 I sat I 0 ,

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