Abstract

An improvement in precision beyond the limit set by the vacuum-state or zero-point fluctuations of the electromagnetic field is reported for the detection of amplitude modulation encoded on a weak signal beam. The improvement is achieved by employing the squeezed light from an optical parametric oscillator to reduce the level of fluctuations below the shot-noise limit. An increase in signal-to-noise ratio of 2.5 dB relative to the shot-noise limit is demonstrated.

© 1988 Optical Society of America

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References

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  1. J. S. Snyder, R. A. Keller, eds., Ultrasensitive Laser Spectroscopy, J. Opt. Soc. Am. B 2, 1428–1593 (1985).
  2. H. J. Kimble, D. F. Walls, eds., Squeezed States of the Electromagnetic Field, J. Opt. Soc. Am. B 4, 1450–1741 (1987).
  3. M. Xiao, L.-A. Wu, H. J. Kimble, Phys. Rev. Lett. 59, 278 (1987).
    [CrossRef] [PubMed]
  4. P. Grangier, R. E. Slusher, B. Yurke, A. LaPorta, Phys. Rev. Lett. 59, 2153 (1987).
    [CrossRef] [PubMed]
  5. L.-A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
    [CrossRef] [PubMed]
  6. L.-A. Wu, M. Xiao, H. J. Kimble, J. Opt. Soc. Am. B 4, 1465 (1987).
    [CrossRef]
  7. We denote Hilbert-space operators with a caret (ˆ).
  8. A. Yariv, Optical Electronics (Holt, Rinehart, and Winston, New York, 1985), Chap. 12.
  9. H. P. Yuen, V. W. S. Chan, Opt. Lett. 8, 177 (1983).
    [CrossRef] [PubMed]
  10. M. J. Collett, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984).
    [CrossRef]

1987 (4)

H. J. Kimble, D. F. Walls, eds., Squeezed States of the Electromagnetic Field, J. Opt. Soc. Am. B 4, 1450–1741 (1987).

M. Xiao, L.-A. Wu, H. J. Kimble, Phys. Rev. Lett. 59, 278 (1987).
[CrossRef] [PubMed]

P. Grangier, R. E. Slusher, B. Yurke, A. LaPorta, Phys. Rev. Lett. 59, 2153 (1987).
[CrossRef] [PubMed]

L.-A. Wu, M. Xiao, H. J. Kimble, J. Opt. Soc. Am. B 4, 1465 (1987).
[CrossRef]

1986 (1)

L.-A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

1985 (1)

1984 (1)

M. J. Collett, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984).
[CrossRef]

1983 (1)

Chan, V. W. S.

Collett, M. J.

M. J. Collett, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984).
[CrossRef]

Gardiner, C. W.

M. J. Collett, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984).
[CrossRef]

Grangier, P.

P. Grangier, R. E. Slusher, B. Yurke, A. LaPorta, Phys. Rev. Lett. 59, 2153 (1987).
[CrossRef] [PubMed]

Hall, J. L.

L.-A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Kimble, H. J.

L.-A. Wu, M. Xiao, H. J. Kimble, J. Opt. Soc. Am. B 4, 1465 (1987).
[CrossRef]

M. Xiao, L.-A. Wu, H. J. Kimble, Phys. Rev. Lett. 59, 278 (1987).
[CrossRef] [PubMed]

L.-A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

LaPorta, A.

P. Grangier, R. E. Slusher, B. Yurke, A. LaPorta, Phys. Rev. Lett. 59, 2153 (1987).
[CrossRef] [PubMed]

Slusher, R. E.

P. Grangier, R. E. Slusher, B. Yurke, A. LaPorta, Phys. Rev. Lett. 59, 2153 (1987).
[CrossRef] [PubMed]

Wu, H.

L.-A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Wu, L.-A.

L.-A. Wu, M. Xiao, H. J. Kimble, J. Opt. Soc. Am. B 4, 1465 (1987).
[CrossRef]

M. Xiao, L.-A. Wu, H. J. Kimble, Phys. Rev. Lett. 59, 278 (1987).
[CrossRef] [PubMed]

L.-A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Xiao, M.

M. Xiao, L.-A. Wu, H. J. Kimble, Phys. Rev. Lett. 59, 278 (1987).
[CrossRef] [PubMed]

L.-A. Wu, M. Xiao, H. J. Kimble, J. Opt. Soc. Am. B 4, 1465 (1987).
[CrossRef]

Yariv, A.

A. Yariv, Optical Electronics (Holt, Rinehart, and Winston, New York, 1985), Chap. 12.

Yuen, H. P.

Yurke, B.

P. Grangier, R. E. Slusher, B. Yurke, A. LaPorta, Phys. Rev. Lett. 59, 2153 (1987).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (3)

Opt. Lett. (1)

Phys. Rev. A (1)

M. J. Collett, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984).
[CrossRef]

Phys. Rev. Lett. (3)

M. Xiao, L.-A. Wu, H. J. Kimble, Phys. Rev. Lett. 59, 278 (1987).
[CrossRef] [PubMed]

P. Grangier, R. E. Slusher, B. Yurke, A. LaPorta, Phys. Rev. Lett. 59, 2153 (1987).
[CrossRef] [PubMed]

L.-A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Other (2)

We denote Hilbert-space operators with a caret (ˆ).

A. Yariv, Optical Electronics (Holt, Rinehart, and Winston, New York, 1985), Chap. 12.

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Figures (2)

Fig. 1
Fig. 1

Schematic of the apparatus for detection of amplitude modulation with squeezed states. The reflectivity of m1 is close to unity; m2 is a beam splitter with R = T = 0.5.

Fig. 2
Fig. 2

Spectral density Φ of photocurrent fluctuations versus signal phase β for fixed analysis frequency Ω0/2π = 1.6 MHz. The phase β between 〈E2〉 and 〈ELO〉 is swept in a sawtooth fashion to produce the periodic variation in Φ with the sharp features corresponding to the flyback to restart the scan. The dashed line gives the vacuum level obtained with inputs E0 and Es blocked. The gap in (a) is caused by a trigger event that interrupts the local-oscillator beam, (a) Vacuum-state input for Es, (b) squeezed-state input for Es. The slow variation of Φ over the scan in (b) results from a variation in ϕ to adjust for minimum noise level. An improvement of 2.5 dB in signal-to-noise ratio is achieved in (b) relative to (a) near the noise minimum. The time for the entire trace is 0.2 sec.

Equations (6)

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E ˆ 2 = E ˆ 1 T cos θ ( t ) ,
E ˆ 2 E ˆ 1 T ( 1 δ cos Ω 0 t ) ,
i s ( Ω 0 ) = 2 T e α η E ˆ LO E ˆ 1 δ cos β ,
i n = ( 2 e i B ) 1 / 2 = ( 2 e 2 α E ˆ LO E ˆ LO B ) 1 / 2 .
Ψ υ i s 2 i n 2 = α P 2 cos 2 β B δ 2 ,
Ψ ( Ω 0 , ϕ ) = Ψ υ / [ 1 + ζ S ( Ω 0 , ϕ ) ] = α P 2 δ 2 cos 2 β B [ 1 + ζ S ( Ω 0 , ϕ ) ] ,

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