Abstract

We demonstrate quantum-noise correlations between the spatial frequencies of a parametrically amplified signal image and the generated conjugate (idler) image. Test images were amplified by an optical parametric amplifier that can be operated either as a low-pass or a band-pass amplifier for spatial frequencies. Direct difference detection of the signal and idler spatial frequencies at ±16 mm-1 resulted in noise that fell below the shot-noise level by ≃5 dB. Parametric-gain and phase-mismatch dependence of the observed quantum-noise reduction is in good agreement with the theory of a spatially-broadband optical parametric amplifier.

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  1. M. Xiao, L.-A. Wu, H. J. Kimble, "Precision measurement beyond the shot-noise limit," Phys. Rev. Lett. 59, 278-281 (1987).
    [CrossRef] [PubMed]
  2. P. Grangier, R. E. Slusher, B. Yurke, A. LaPorta, "Squeezed-light-enhanced polarization interferometer," Phys. Rev. Lett. 59, 2153-2156 (1987).
    [CrossRef] [PubMed]
  3. M. Xiao, L.-A. Wu, H. J. Kimble, "Detection of amplitude modulation with squeezed light for sensitivity beyond the shot-noise limit," Opt. Lett. 13, 476-478 (1988).
    [CrossRef] [PubMed]
  4. E. S. Polzik, J. Carri, H. J. Kimble, "Spectroscopy with squeezed light," Phys. Rev. Lett. 68, 3020-3023 (1992).
    [CrossRef] [PubMed]
  5. D. C. Kilper, A. C. Schaefer, J. Erland, D. G. Steel, "Coherent nonlinear optical spectroscopy using photon-number squeezed light," Phys. Rev. A 54, R1785-R1788 (1996).
    [CrossRef] [PubMed]
  6. S. Kasapi, S. Lathi, Y. Yamamoto, "Amplitude-squeezed, frequency-modulated, tunable, diode-laser-based source for sub-shot-noise FM spectroscopy," Opt. Lett. 22, 478-480 (1997).
    [CrossRef] [PubMed]
  7. F. Marin, A. Bramati, V. Jost, E. Giacobino, "Demonstration of high sensitivity spectroscopy with squeezed semiconductor lasers," Opt. Commun. 140, 146-157 (1997).
    [CrossRef]
  8. Y.-Q. Li, P. Lynam, M. Xiao, P. J. Edwards, "Sub-shot-noise laser Doppler anemometry with amplitude-squeezed light," Phys. Rev. Lett. 78, 3105-3108 (1997).
    [CrossRef]
  9. M. I. Kolobov and P. Kumar, "Sub-shot-noise microscopy: imaging of faint phase objects with squeezed light," Opt. Lett. 18, 849-851 (1993).
    [CrossRef] [PubMed]
  10. M. I. Kolobov and I. V. Sokolov, "Multimode squeezing, antibunching in space and noise-free optical images," Europhys. Lett. 15, 271-276 (1991).
    [CrossRef]
  11. M. I. Kolobov and I. V. Sokolov, "Spatial behavior of squeezed states of light and quantum noise in optical images," Sov. Phys. JETP 69, 1097-1104 (1989).
  12. P. Kumar, M. L. Marable, and S.-K. Choi, "Quantum properties of the traveling-wave (2) process: theory, experiments, and applications," in Quantum Communication, Computing, and Measurement, O. Hirota, A. S. Holevo, and C. M. Caves, Eds., (Plenum, New York, 1997), pp. 531-544.
    [CrossRef]
  13. J. E. Midwinter, "Parametric infrared image converters," IEEE J. Quantum Electron. 4, 716-720 (1968).
    [CrossRef]
  14. A. H. Firester, "Parametric image conversion: Part I," J. Appl. Phys. 40, 4842-4849 (1969).
    [CrossRef]
  15. R. A. Andrews, "IR image parametric up-conversion," IEEE J. Quantum Electron. 6, 68-80 (1970).
    [CrossRef]
  16. Y. Fainman, E. Klancnik, S. H. Lee, "Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3," Opt. Eng. 25, 228-234 (1986).
  17. P. A. Laferriere, C. J. Wetterer, L. P. Schelonka, M. A. Kramer, "Spatial-frequency selection using downconversion optical parametric amplification," J. Appl. Phys. 65, 3347-3350 (1989).
    [CrossRef]
  18. F. Devaux, E. Lantz, A. Lacourt, D. Gindre, H. Maillotte, P. A. Doreau, T. Laurent, "Picosecond parametric amplification of a monochromatic image," Nonlinear Opt. 11, 25-37 (1995).
  19. F. Devaux and E. Lantz, "Parametric amplification of a polychromatic image," J. Opt. Soc. Am. B 12, 2245-2252 (1995).
    [CrossRef]
  20. F. Devaux and E. Lantz, "Ultrahigh-speed imaging by parametric image amplification," Opt. Commun. 118, 25-27 (1995).
    [CrossRef]
  21. J. Watson, P. Georges, T. Lepine, B. Alonzi, A. Brun, "Imaging in diffuse media with ultrafast degenerate optical parametric amplification," Opt. Lett. 20, 231-233 (1995).
    [CrossRef] [PubMed]
  22. S. M. Cameron, D. E. Bliss, M. W. Kimmel, "Gated frequency-resolved optical imaging with an optical parametric amplifier for medical applications," Proc. SPIE 2679, 195-203 (1996).
    [CrossRef]
  23. E. Lantz and F. Devaux, "Parametric amplification of images," Quantum Semiclassic. Opt. 9, 279-286 (1997).
    [CrossRef]
  24. S.-K. Choi, M. L. Marable, and P. Kumar, "Observation of quantum noise correlations in parametric image amplification," in Quantum Electronics and Laser Science, Vol. 12 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C. 1997), pp. 94-95.
  25. O. Aytuer and P. Kumar, "Pulsed twin beams of light," Phys. Rev. Lett. 65, 1551-1554 (1990).
    [CrossRef] [PubMed]
  26. A. Gavrielides, P. Peterson, D. Cardimona, "Diffractive imaging in three-wave interactions," J. Appl. Phys. 62, 2640-2645 (1987).
    [CrossRef]

Other (26)

M. Xiao, L.-A. Wu, H. J. Kimble, "Precision measurement beyond the shot-noise limit," Phys. Rev. Lett. 59, 278-281 (1987).
[CrossRef] [PubMed]

P. Grangier, R. E. Slusher, B. Yurke, A. LaPorta, "Squeezed-light-enhanced polarization interferometer," Phys. Rev. Lett. 59, 2153-2156 (1987).
[CrossRef] [PubMed]

M. Xiao, L.-A. Wu, H. J. Kimble, "Detection of amplitude modulation with squeezed light for sensitivity beyond the shot-noise limit," Opt. Lett. 13, 476-478 (1988).
[CrossRef] [PubMed]

E. S. Polzik, J. Carri, H. J. Kimble, "Spectroscopy with squeezed light," Phys. Rev. Lett. 68, 3020-3023 (1992).
[CrossRef] [PubMed]

D. C. Kilper, A. C. Schaefer, J. Erland, D. G. Steel, "Coherent nonlinear optical spectroscopy using photon-number squeezed light," Phys. Rev. A 54, R1785-R1788 (1996).
[CrossRef] [PubMed]

S. Kasapi, S. Lathi, Y. Yamamoto, "Amplitude-squeezed, frequency-modulated, tunable, diode-laser-based source for sub-shot-noise FM spectroscopy," Opt. Lett. 22, 478-480 (1997).
[CrossRef] [PubMed]

F. Marin, A. Bramati, V. Jost, E. Giacobino, "Demonstration of high sensitivity spectroscopy with squeezed semiconductor lasers," Opt. Commun. 140, 146-157 (1997).
[CrossRef]

Y.-Q. Li, P. Lynam, M. Xiao, P. J. Edwards, "Sub-shot-noise laser Doppler anemometry with amplitude-squeezed light," Phys. Rev. Lett. 78, 3105-3108 (1997).
[CrossRef]

M. I. Kolobov and P. Kumar, "Sub-shot-noise microscopy: imaging of faint phase objects with squeezed light," Opt. Lett. 18, 849-851 (1993).
[CrossRef] [PubMed]

M. I. Kolobov and I. V. Sokolov, "Multimode squeezing, antibunching in space and noise-free optical images," Europhys. Lett. 15, 271-276 (1991).
[CrossRef]

M. I. Kolobov and I. V. Sokolov, "Spatial behavior of squeezed states of light and quantum noise in optical images," Sov. Phys. JETP 69, 1097-1104 (1989).

P. Kumar, M. L. Marable, and S.-K. Choi, "Quantum properties of the traveling-wave (2) process: theory, experiments, and applications," in Quantum Communication, Computing, and Measurement, O. Hirota, A. S. Holevo, and C. M. Caves, Eds., (Plenum, New York, 1997), pp. 531-544.
[CrossRef]

J. E. Midwinter, "Parametric infrared image converters," IEEE J. Quantum Electron. 4, 716-720 (1968).
[CrossRef]

A. H. Firester, "Parametric image conversion: Part I," J. Appl. Phys. 40, 4842-4849 (1969).
[CrossRef]

R. A. Andrews, "IR image parametric up-conversion," IEEE J. Quantum Electron. 6, 68-80 (1970).
[CrossRef]

Y. Fainman, E. Klancnik, S. H. Lee, "Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3," Opt. Eng. 25, 228-234 (1986).

P. A. Laferriere, C. J. Wetterer, L. P. Schelonka, M. A. Kramer, "Spatial-frequency selection using downconversion optical parametric amplification," J. Appl. Phys. 65, 3347-3350 (1989).
[CrossRef]

F. Devaux, E. Lantz, A. Lacourt, D. Gindre, H. Maillotte, P. A. Doreau, T. Laurent, "Picosecond parametric amplification of a monochromatic image," Nonlinear Opt. 11, 25-37 (1995).

F. Devaux and E. Lantz, "Parametric amplification of a polychromatic image," J. Opt. Soc. Am. B 12, 2245-2252 (1995).
[CrossRef]

F. Devaux and E. Lantz, "Ultrahigh-speed imaging by parametric image amplification," Opt. Commun. 118, 25-27 (1995).
[CrossRef]

J. Watson, P. Georges, T. Lepine, B. Alonzi, A. Brun, "Imaging in diffuse media with ultrafast degenerate optical parametric amplification," Opt. Lett. 20, 231-233 (1995).
[CrossRef] [PubMed]

S. M. Cameron, D. E. Bliss, M. W. Kimmel, "Gated frequency-resolved optical imaging with an optical parametric amplifier for medical applications," Proc. SPIE 2679, 195-203 (1996).
[CrossRef]

E. Lantz and F. Devaux, "Parametric amplification of images," Quantum Semiclassic. Opt. 9, 279-286 (1997).
[CrossRef]

S.-K. Choi, M. L. Marable, and P. Kumar, "Observation of quantum noise correlations in parametric image amplification," in Quantum Electronics and Laser Science, Vol. 12 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C. 1997), pp. 94-95.

O. Aytuer and P. Kumar, "Pulsed twin beams of light," Phys. Rev. Lett. 65, 1551-1554 (1990).
[CrossRef] [PubMed]

A. Gavrielides, P. Peterson, D. Cardimona, "Diffractive imaging in three-wave interactions," J. Appl. Phys. 62, 2640-2645 (1987).
[CrossRef]

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Figures (4)

Figure 1.
Figure 1.

Theoretical plots of the quantum-noise reduction as a function of spatial frequency for the case of a low-pass amplifier with Δk = 0(a), band-pass amplifier with Δk = -0.95rad/mm (b). Also shown are the amplified signal and generated idler for a spatially narrowband bare (input) signal centered at ξ = 0 in (a), and ξ = 16 mm-1 in (b).

Figure 2.
Figure 2.

Experimental layout for parametric image amplification (top) and measurement of quantum-noise correlations (bottom).

Figure 3.
Figure 3.

(a) Bare signal, amplified signal, and idler patterns in the output image plane. (b) Bare signal pattern in the output Fourier plane. (c) Amplified signal pattern in the output Fourier plane with the OPA aligned for low-pass amplification. (d) Same as in (c) but with the OPA aligned for band-pass amplification.

Figure 4.
Figure 4.

Noise reduction as a function of (a) OPA gain and (b) phase mismatch Δk.

Equations (7)

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b ̂ s = μ a ̂ s + ν a ̂ i ,
b ̂ i = μ a ̂ i + ν a ̂ s ,
g = μ 2 ,
R = 1 η + η μ 2 + ν 2 .
μ ( q ) = { cosh ( h ) + i Δ k eff 2 [ sinh ( h ) ( h ) ] } exp ( i Δ k eff 2 ) ,
ν ( q ) = { iκℓ 2 [ sinh ( h ) ( h ) ] } exp ( i Δ k eff 2 ) ,
Δ k eff ( q ) = Δ k + q 2 2 ( 1 k s + 1 k i ) .

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