Abstract

We present a frequency modulation scheme to detect atoms dispersively in a high-finesse optical cavity at low-light levels with immunity to cavity length fluctuations. We use multiple cavity resonances to provide common mode noise rejection, keeping the high intensity carrier off-resonant from all cavity modes. The method has applications in atomic squeezed state generation and quantum metrology.

© 2007 Optical Society of America

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References

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  1. A. Kuzmich, N. Bigelow, and L. Mandel, Europhys. Lett. 42, 481 (1998).
    [CrossRef]
  2. D. Wineland, J. Bollinger, F. L. Moore, and D. J. Heinzen, Phys. Rev. A 50, 67 (1994).
    [CrossRef] [PubMed]
  3. J. E. Lye, J. J. Hope, and J. D. Close, Phys. Rev. A 67, 043609 (2003).
    [CrossRef]
  4. A. K. Tuchman, R. Long, G. Vrijsen, J. Boudet, J. Lee, and M. A. Kasevich, Phys. Rev. A 74, 053821 (2006).
    [CrossRef]
  5. H. Mabuchi, J. Ye, and H. J. Kimble, Appl. Phys. B 68, 1095 (1999).
    [CrossRef]
  6. R. G. DeVoe and R. G. Brewer, Phys. Rev. A 30, 2827 (1984).
    [CrossRef]
  7. J. Ye, L. Ma, and J. L. Hall, J. Opt. Soc. Am. B 15, 6 (1998).
    [CrossRef]
  8. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
    [CrossRef]
  9. Cavity FSR and microwave fluctuations have each been measured at <10Hz rms, whereas atomic shot noise for 105 atoms and Δ=1GHz, is ∼600Hz rms.
  10. Since the difference in rf frequencies is likely to be in the audiofrequency range, this essentially eliminates rf noise from the equation.
  11. A. Schoof, J. Grunert, S. Ritter, and A. Hemmerich, Opt. Lett. 26, 1562 (2001).
    [CrossRef]

2006 (1)

A. K. Tuchman, R. Long, G. Vrijsen, J. Boudet, J. Lee, and M. A. Kasevich, Phys. Rev. A 74, 053821 (2006).
[CrossRef]

2003 (1)

J. E. Lye, J. J. Hope, and J. D. Close, Phys. Rev. A 67, 043609 (2003).
[CrossRef]

2001 (1)

1999 (1)

H. Mabuchi, J. Ye, and H. J. Kimble, Appl. Phys. B 68, 1095 (1999).
[CrossRef]

1998 (2)

A. Kuzmich, N. Bigelow, and L. Mandel, Europhys. Lett. 42, 481 (1998).
[CrossRef]

J. Ye, L. Ma, and J. L. Hall, J. Opt. Soc. Am. B 15, 6 (1998).
[CrossRef]

1994 (1)

D. Wineland, J. Bollinger, F. L. Moore, and D. J. Heinzen, Phys. Rev. A 50, 67 (1994).
[CrossRef] [PubMed]

1984 (1)

R. G. DeVoe and R. G. Brewer, Phys. Rev. A 30, 2827 (1984).
[CrossRef]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Appl. Phys. B (2)

H. Mabuchi, J. Ye, and H. J. Kimble, Appl. Phys. B 68, 1095 (1999).
[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Europhys. Lett. (1)

A. Kuzmich, N. Bigelow, and L. Mandel, Europhys. Lett. 42, 481 (1998).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Phys. Rev. A (4)

D. Wineland, J. Bollinger, F. L. Moore, and D. J. Heinzen, Phys. Rev. A 50, 67 (1994).
[CrossRef] [PubMed]

J. E. Lye, J. J. Hope, and J. D. Close, Phys. Rev. A 67, 043609 (2003).
[CrossRef]

A. K. Tuchman, R. Long, G. Vrijsen, J. Boudet, J. Lee, and M. A. Kasevich, Phys. Rev. A 74, 053821 (2006).
[CrossRef]

R. G. DeVoe and R. G. Brewer, Phys. Rev. A 30, 2827 (1984).
[CrossRef]

Other (2)

Cavity FSR and microwave fluctuations have each been measured at <10Hz rms, whereas atomic shot noise for 105 atoms and Δ=1GHz, is ∼600Hz rms.

Since the difference in rf frequencies is likely to be in the audiofrequency range, this essentially eliminates rf noise from the equation.

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Figures (4)

Fig. 1
Fig. 1

Frequency modulation methods.

Fig. 2
Fig. 2

Double frequency modulation setup.

Fig. 3
Fig. 3

Self-heterodyne characterization of the laser.

Fig. 4
Fig. 4

Measured dispersive cavity shifts.

Equations (6)

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Φ 1 = ν 1 cav ν 1 κ + ϕ 1 at ,
Φ 2 = ν 2 cav ν 2 κ + ϕ 2 at ,
Φ 2 = n ν FSR κ + ν mod ν 2 rf κ + Φ 1 + ϕ 2 at ϕ 1 at ,
Δ Φ = Φ 2 Φ 1 = n ν FSR κ + ν mod ν 2 rf κ + ϕ 2 at ϕ 1 at ,
Φ 3 = ν 3 cav ν 3 κ + ϕ 3 at = n ν FSR κ + ν mod + ν 3 rf κ + Φ 1 + ϕ 3 at ϕ 1 at .
Δ Φ = Φ 2 + Φ 3 2 Φ 1 = ν 3 rf ν 2 rf + 2 ν mod κ + ϕ 3 at + ϕ 2 at 2 ϕ 1 at ,

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