Abstract

We propose a scheme that uses spatially multimode squeezed light, generated by means of a traveling-wave optical parametric amplifier, with which a faint phase object can be imaged with sensitivity better than the shot-noise limit.

© 1993 Optical Society of America

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References

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  1. M. Xiao, L.-A. Wu, H. J. Kimble, Phys. Rev. Lett. 59, 278 (1987).
    [CrossRef] [PubMed]
  2. P. Grangier, R. E. Slusher, B. Yurke, A. LaPorta, Phys. Rev. Lett. 59, 2153 (1987).
    [CrossRef] [PubMed]
  3. M. Xiao, L.-A. Wu, H. J. Kimble, Opt. Lett. 13, 476 (1988).
    [CrossRef] [PubMed]
  4. E. S. Polzik, J. Carri, H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
    [CrossRef] [PubMed]
  5. H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-24, 657 (1978); H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980); J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979); J. H. Shapiro, IEEE J. Quantum Electron. QE-21, 237 (1985).
    [CrossRef]
  6. M. I. Kolobov, I. V. Sokolov, Sov. Phys. JETP 69, 1097 (1989); M. I. Kolobov, Phys. Rev. A 44, 1986 (1991); I. V. Sokolov, Sov. Phys. JETP 73, 421 (1991).
    [CrossRef] [PubMed]
  7. O. Aytür, P. Kumar, Opt. Lett. 17, 529 (1992); C. Kim, R.-D. Li, P. Kumar, in Quantum Electronics Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper QThF1.
    [CrossRef]
  8. C. M. Caves, Phys. Rev. D 23, 1693 (1981).
    [CrossRef]
  9. B. Yurke, S. L. McCall, J. R. Klauder, Phys. Rev. A 33, 4033 (1986).
    [CrossRef] [PubMed]
  10. C. M. Caves, B. L. Schumaker, Phys. Rev. A 31, 3068 (1985).
    [CrossRef] [PubMed]
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 1.

1992 (2)

1989 (1)

M. I. Kolobov, I. V. Sokolov, Sov. Phys. JETP 69, 1097 (1989); M. I. Kolobov, Phys. Rev. A 44, 1986 (1991); I. V. Sokolov, Sov. Phys. JETP 73, 421 (1991).
[CrossRef] [PubMed]

1988 (1)

1987 (2)

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]

1986 (1)

B. Yurke, S. L. McCall, J. R. Klauder, Phys. Rev. A 33, 4033 (1986).
[CrossRef] [PubMed]

1985 (1)

C. M. Caves, B. L. Schumaker, Phys. Rev. A 31, 3068 (1985).
[CrossRef] [PubMed]

1981 (1)

C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[CrossRef]

1978 (1)

H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-24, 657 (1978); H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980); J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979); J. H. Shapiro, IEEE J. Quantum Electron. QE-21, 237 (1985).
[CrossRef]

Aytür, O.

Carri, J.

E. S. Polzik, J. Carri, H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

Caves, C. M.

C. M. Caves, B. L. Schumaker, Phys. Rev. A 31, 3068 (1985).
[CrossRef] [PubMed]

C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 1.

Grangier, P.

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

Kimble, H. J.

E. S. Polzik, J. Carri, H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

M. Xiao, L.-A. Wu, H. J. Kimble, Opt. Lett. 13, 476 (1988).
[CrossRef] [PubMed]

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

Klauder, J. R.

B. Yurke, S. L. McCall, J. R. Klauder, Phys. Rev. A 33, 4033 (1986).
[CrossRef] [PubMed]

Kolobov, M. I.

M. I. Kolobov, I. V. Sokolov, Sov. Phys. JETP 69, 1097 (1989); M. I. Kolobov, Phys. Rev. A 44, 1986 (1991); I. V. Sokolov, Sov. Phys. JETP 73, 421 (1991).
[CrossRef] [PubMed]

Kumar, P.

LaPorta, A.

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

McCall, S. L.

B. Yurke, S. L. McCall, J. R. Klauder, Phys. Rev. A 33, 4033 (1986).
[CrossRef] [PubMed]

Polzik, E. S.

E. S. Polzik, J. Carri, H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

Schumaker, B. L.

C. M. Caves, B. L. Schumaker, Phys. Rev. A 31, 3068 (1985).
[CrossRef] [PubMed]

Shapiro, J. H.

H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-24, 657 (1978); H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980); J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979); J. H. Shapiro, IEEE J. Quantum Electron. QE-21, 237 (1985).
[CrossRef]

Slusher, R. E.

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

Sokolov, I. V.

M. I. Kolobov, I. V. Sokolov, Sov. Phys. JETP 69, 1097 (1989); M. I. Kolobov, Phys. Rev. A 44, 1986 (1991); I. V. Sokolov, Sov. Phys. JETP 73, 421 (1991).
[CrossRef] [PubMed]

Wu, L.-A.

M. Xiao, L.-A. Wu, H. J. Kimble, Opt. Lett. 13, 476 (1988).
[CrossRef] [PubMed]

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

Xiao, M.

M. Xiao, L.-A. Wu, H. J. Kimble, Opt. Lett. 13, 476 (1988).
[CrossRef] [PubMed]

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

Yuen, H. P.

H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-24, 657 (1978); H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980); J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979); J. H. Shapiro, IEEE J. Quantum Electron. QE-21, 237 (1985).
[CrossRef]

Yurke, B.

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

B. Yurke, S. L. McCall, J. R. Klauder, Phys. Rev. A 33, 4033 (1986).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (1)

H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-24, 657 (1978); H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980); J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979); J. H. Shapiro, IEEE J. Quantum Electron. QE-21, 237 (1985).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (2)

B. Yurke, S. L. McCall, J. R. Klauder, Phys. Rev. A 33, 4033 (1986).
[CrossRef] [PubMed]

C. M. Caves, B. L. Schumaker, Phys. Rev. A 31, 3068 (1985).
[CrossRef] [PubMed]

Phys. Rev. D (1)

C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[CrossRef]

Phys. Rev. Lett. (3)

E. S. Polzik, J. Carri, H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

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]

Sov. Phys. JETP (1)

M. I. Kolobov, I. V. Sokolov, Sov. Phys. JETP 69, 1097 (1989); M. I. Kolobov, Phys. Rev. A 44, 1986 (1991); I. V. Sokolov, Sov. Phys. JETP 73, 421 (1991).
[CrossRef] [PubMed]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 1.

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Figures (2)

Fig. 1
Fig. 1

Schematic of the proposed scheme to detect faint phase objects with sensitivity better than the shot-noise limit.

Fig. 2
Fig. 2

Normalized spatial-frequency spectra of the squeezing produced by a traveling-wave OPA.6 Curve (a) is for the desqueezed quadrature, and curve (b) is for the squeezed quadrature; the OPA phase-sensitive gain is exp(2rs) = 4 and η = 1. The homodyne-detection noise power Δi±2(q) (ordinate) is normalized relative to the shot-noise level, and the spatial frequency (abscissa) is in units of (kp/l)1/2.

Equations (9)

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i 0 ( ρ ) = η [ cos ϕ a ^ 1 ( ρ ) a ^ 1 ( ρ ) - a ^ 2 ( ρ ) a ^ 2 ( ρ ) - sin ϕ a ^ 1 ( ρ ) a ^ 2 ( ρ ) + a ^ 2 ( ρ ) a ^ 1 ( ρ ) ] ,
a ^ 1 ( ρ ) Ψ = α Ψ .
a ^ ( l , q ) = u ( q ) a ^ ( 0 , q ) + v ( q ) a ^ ( 0 , - q ) ,
Δ i 2 ( q , θ ) = i ( 1 - η + η { exp [ 2 r ( q ) ] cos 2 θ ( q ) + exp [ - 2 r ( q ) ] sin 2 θ ( q ) } ) ,
Δ i + 2 ( q s ) = i exp ( 2 r s ) ,             Δ i - 2 ( q s ) = i exp ( - 2 r s ) .
i 0 ( ρ ) = η α 2 cos ϕ ,
Δ i 0 2 ( q , θ , ϕ ) = η α 2 ( 1 - η + η { exp [ 2 r ( q ) ] cos 2 θ ( q ) + exp [ - 2 r ( q ) ] sin 2 θ ( q ) } sin 2 ϕ + η cos 2 ϕ ) .
Δ ϕ min 2 ( q , θ ) = ( 1 - η + η { cos 2 θ ( q ) exp [ 2 r ( q ) ] + sin 2 θ ( q ) exp [ - 2 r ( q ) ] } ) / η α 2 .
Δ ϕ min 2 ( q s ) = exp ( - 2 r s ) / α 2 .

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