Abstract

We present theoretical results that demonstrate a new technique that can be used to improve the sensitivity of thermal noise measurements: intracavity intensity stabilization. It is demonstrated that electro-optic feedback can be used to reduce intracavity intensity fluctuations, and the consequent radiation pressure fluctuations, by a factor of 2 below the quantum-noise limit. We show that this reduction is achievable in the presence of large classic intensity fluctuations in the incident laser beam. The benefits of this scheme are a consequence of the sub-Poissonian intensity statistics of the field inside a feedback loop and the quantum nondemolition nature of radiation pressure noise as a readout system for the intracavity intensity fluctuations.

© 1999 Optical Society of America

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References

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  1. P. R. Saulson, Fundamentals of Interferometric Gravi-tational Wave Detectors (World Scientific, Singapore, 1994).
  2. 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]
  3. D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, New York, 1994).
    [CrossRef]
  4. T. C. Ralph, C. C. Harb, and H.-A. Bachor, Phys. Rev. A 54, 4359 (1996).
    [CrossRef] [PubMed]
  5. C. W. Gardiner and M. J. Collett, Phys. Rev. A 31, 3761 (1985).
    [CrossRef] [PubMed]
  6. M. S. Taubman, H. Wiseman, D. E. McClelland, and H.-A. Bachor, J. Opt. Soc. Am. B 12, 1792 (1995).
    [CrossRef]
  7. B. C. Buchler, E. H. Huntington, C. C. Harb, and T. C. Ralph, Phys. Rev. A 57, 1286 (1998).
    [CrossRef]
  8. Lightwave Electronics Corporation, Lightwave Electronics 125-126 Series User Manual (Lightwave Electronics, Mountain View, Calif., 1995).
  9. J. H. Shapiro, G. Saplakoglu, S.-T. Ho, P. Kumar, B. E. A. Saleh, and M. C. Teich, J. Opt. Soc. Am. B 4, 1604 (1987).
    [CrossRef]
  10. H. A. Haus and Y. Yamamoto, Phys. Rev. A 34, 270 (1986).
    [CrossRef] [PubMed]
  11. H. M. Wiseman and G. J. Milburn, Phys. Rev. A 49, 1350 (1994).
    [CrossRef] [PubMed]
  12. K. Jacobs, P. Tombesi, M. J. Collett, and D. F. Walls, Phys. Rev. A 49, 1961 (1994).
    [CrossRef] [PubMed]
  13. H. M. Wiseman, Phys. Rev. A 49, 2133 (1994).
    [CrossRef] [PubMed]

1998 (1)

B. C. Buchler, E. H. Huntington, C. C. Harb, and T. C. Ralph, Phys. Rev. A 57, 1286 (1998).
[CrossRef]

1996 (1)

T. C. Ralph, C. C. Harb, and H.-A. Bachor, Phys. Rev. A 54, 4359 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (3)

H. M. Wiseman and G. J. Milburn, Phys. Rev. A 49, 1350 (1994).
[CrossRef] [PubMed]

K. Jacobs, P. Tombesi, M. J. Collett, and D. F. Walls, Phys. Rev. A 49, 1961 (1994).
[CrossRef] [PubMed]

H. M. Wiseman, Phys. Rev. A 49, 2133 (1994).
[CrossRef] [PubMed]

1987 (1)

1986 (1)

H. A. Haus and Y. Yamamoto, Phys. Rev. A 34, 270 (1986).
[CrossRef] [PubMed]

1985 (1)

C. W. Gardiner and M. J. Collett, Phys. Rev. A 31, 3761 (1985).
[CrossRef] [PubMed]

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]

Bachor, H.-A.

Buchler, B. C.

B. C. Buchler, E. H. Huntington, C. C. Harb, and T. C. Ralph, Phys. Rev. A 57, 1286 (1998).
[CrossRef]

Collett, M. J.

K. Jacobs, P. Tombesi, M. J. Collett, and D. F. Walls, Phys. Rev. A 49, 1961 (1994).
[CrossRef] [PubMed]

C. W. Gardiner and M. J. Collett, Phys. Rev. A 31, 3761 (1985).
[CrossRef] [PubMed]

Drever, R. W. P.

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]

Ford, G. M.

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]

Gardiner, C. W.

C. W. Gardiner and M. J. Collett, Phys. Rev. A 31, 3761 (1985).
[CrossRef] [PubMed]

Hall, J. L.

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]

Harb, C. C.

B. C. Buchler, E. H. Huntington, C. C. Harb, and T. C. Ralph, Phys. Rev. A 57, 1286 (1998).
[CrossRef]

T. C. Ralph, C. C. Harb, and H.-A. Bachor, Phys. Rev. A 54, 4359 (1996).
[CrossRef] [PubMed]

Haus, H. A.

H. A. Haus and Y. Yamamoto, Phys. Rev. A 34, 270 (1986).
[CrossRef] [PubMed]

Ho, S.-T.

Hough, J.

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]

Huntington, E. H.

B. C. Buchler, E. H. Huntington, C. C. Harb, and T. C. Ralph, Phys. Rev. A 57, 1286 (1998).
[CrossRef]

Jacobs, K.

K. Jacobs, P. Tombesi, M. J. Collett, and D. F. Walls, Phys. Rev. A 49, 1961 (1994).
[CrossRef] [PubMed]

Kowalski, F. V.

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]

Kumar, P.

McClelland, D. E.

Milburn, G. J.

H. M. Wiseman and G. J. Milburn, Phys. Rev. A 49, 1350 (1994).
[CrossRef] [PubMed]

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, New York, 1994).
[CrossRef]

Munley, A. J.

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]

Ralph, T. C.

B. C. Buchler, E. H. Huntington, C. C. Harb, and T. C. Ralph, Phys. Rev. A 57, 1286 (1998).
[CrossRef]

T. C. Ralph, C. C. Harb, and H.-A. Bachor, Phys. Rev. A 54, 4359 (1996).
[CrossRef] [PubMed]

Saleh, B. E. A.

Saplakoglu, G.

Saulson, P. R.

P. R. Saulson, Fundamentals of Interferometric Gravi-tational Wave Detectors (World Scientific, Singapore, 1994).

Shapiro, J. H.

Taubman, M. S.

Teich, M. C.

Tombesi, P.

K. Jacobs, P. Tombesi, M. J. Collett, and D. F. Walls, Phys. Rev. A 49, 1961 (1994).
[CrossRef] [PubMed]

Walls, D. F.

K. Jacobs, P. Tombesi, M. J. Collett, and D. F. Walls, Phys. Rev. A 49, 1961 (1994).
[CrossRef] [PubMed]

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, New York, 1994).
[CrossRef]

Ward, H.

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]

Wiseman, H.

Wiseman, H. M.

H. M. Wiseman, Phys. Rev. A 49, 2133 (1994).
[CrossRef] [PubMed]

H. M. Wiseman and G. J. Milburn, Phys. Rev. A 49, 1350 (1994).
[CrossRef] [PubMed]

Yamamoto, Y.

H. A. Haus and Y. Yamamoto, Phys. Rev. A 34, 270 (1986).
[CrossRef] [PubMed]

Appl. Phys. B (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]

J. Opt. Soc. Am. B (2)

Phys. Rev. A (7)

B. C. Buchler, E. H. Huntington, C. C. Harb, and T. C. Ralph, Phys. Rev. A 57, 1286 (1998).
[CrossRef]

H. A. Haus and Y. Yamamoto, Phys. Rev. A 34, 270 (1986).
[CrossRef] [PubMed]

H. M. Wiseman and G. J. Milburn, Phys. Rev. A 49, 1350 (1994).
[CrossRef] [PubMed]

K. Jacobs, P. Tombesi, M. J. Collett, and D. F. Walls, Phys. Rev. A 49, 1961 (1994).
[CrossRef] [PubMed]

H. M. Wiseman, Phys. Rev. A 49, 2133 (1994).
[CrossRef] [PubMed]

T. C. Ralph, C. C. Harb, and H.-A. Bachor, Phys. Rev. A 54, 4359 (1996).
[CrossRef] [PubMed]

C. W. Gardiner and M. J. Collett, Phys. Rev. A 31, 3761 (1985).
[CrossRef] [PubMed]

Other (3)

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, New York, 1994).
[CrossRef]

Lightwave Electronics Corporation, Lightwave Electronics 125-126 Series User Manual (Lightwave Electronics, Mountain View, Calif., 1995).

P. R. Saulson, Fundamentals of Interferometric Gravi-tational Wave Detectors (World Scientific, Singapore, 1994).

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Figures (1)

Fig. 1
Fig. 1

Experimental arrangement for a thermal noise measurement. The dashed part of the figure indicates the feedback loop: PZT, piezoelectric transducer.

Equations (12)

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

a^·=-κ+ιδX^ΔT+ιδX^ΔRa^+2κinA^in+2κoutδA^ν+2κLδA^L,
Vref-ω=1+8κinα2VΔRω+VΔTω+2κin-κ2+ω2]Vin-ω-1ω2+κ2.
VΔRω=FωVaω.
δX˜aω=2κinδX˜Ain+2κoutδX˜Aν+2κLδX˜ALκ+ιω.
Vaω=2κinVin+2κout+2κLκ2+ω2.
Va=2/κ.
δX˜AinδX˜Ain-δX˜R,
δX˜R=2κoutηKωδX˜a-KωηδX˜Aν+1-ηδX˜AD,
Vaf=2κinVin+2κin1-ηKω2+2ηκinKω+2κout2+2κLκ+ιω+2κoutκinηKω2.
Vaf=12ηκout.
VafVa=κ4ηκout.
VafVa=12η.

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