Abstract

We propose to make use of quantum entanglement for extracting holographic information about a remote 3-D object in a confined space which light enters, but from which it cannot escape. Light scattered from the object is detected in this confined space entirely without the benefit of spatial resolution. Quantum holography offers this possibility by virtue of the fourth-order quantum coherence inherent in entangled beams.

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References

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  1. E. Schr�dinger, "Die gegenwartige Situation in der Quantenmechanik," Naturwissenchaften 23, 807-812, 823-828, 844-849 (1935).
    [CrossRef]
  2. A. Einstein, in The Born-Einstein Letters (Walker, New York, 1971), p. 158, translated by I. Born.
  3. D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
    [CrossRef] [PubMed]
  4. D. Gabor, "Microscopy by reconstructed wavefronts, I," Proc. Roy. Soc. (London) A197, 454 (1949).
  5. J. F. Clauser, A. Shimony, "Bell's Theorem. Experimental tests and implications," Rep. Prog. Phys. 41, 1881-1927 (1978).
    [CrossRef]
  6. D. N. Klyshko, Photons and Nonlinear Optics (Nauka, Moscow, 1980) [translation: Gordon and Breach, New York, 1988].
  7. B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, "Duality between partial coherence and partial entanglement," Phys. Rev. A 62, 043816 (2000).
    [CrossRef]
  8. A. V. Belinskii and D. N. Klyshko, "Two-photon optics: diffraction, holography, and transformation of two-dimensional signals," Zh. Eksp. Teor. Fiz. 105, 487-493 (1994) [Sov. Phys. JETP 78, 259-262 (1994)].
  9. A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Role of entanglement in two-photon imaging," Phys. Rev. Lett. 87, 123602 (2001).
    [CrossRef] [PubMed]
  10. W. H. Louisell, A. Yariv, and A. E. Siegman, "Quantum fluctuations and noise in parametric processes. I," Phys. Rev. 124, 1646-1654 (1961).
    [CrossRef]
  11. D. N. Klyshko, "Coherent decay of photons in a nonlinear medium," Pis'ma Zh. Eksp. Teor. Fiz. 6, 490-492 (1967) [Sov. Phys. JETP Lett. 6, 23-25 (1967)].
  12. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, New York, 1995).
  13. T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, "Two-photon geometric optics," Phys. Rev. A 53, 2804-2815 (1996).
    [CrossRef] [PubMed]
  14. T. Kreis, P. Aswendt, and R. H�fling, "Hologram reconstruction using a digital micromirror device," Opt. Eng. 40, 926-933 (2001).
    [CrossRef]
  15. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Ch. 4.
    [CrossRef]

Other (15)

E. Schr�dinger, "Die gegenwartige Situation in der Quantenmechanik," Naturwissenchaften 23, 807-812, 823-828, 844-849 (1935).
[CrossRef]

A. Einstein, in The Born-Einstein Letters (Walker, New York, 1971), p. 158, translated by I. Born.

D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

D. Gabor, "Microscopy by reconstructed wavefronts, I," Proc. Roy. Soc. (London) A197, 454 (1949).

J. F. Clauser, A. Shimony, "Bell's Theorem. Experimental tests and implications," Rep. Prog. Phys. 41, 1881-1927 (1978).
[CrossRef]

D. N. Klyshko, Photons and Nonlinear Optics (Nauka, Moscow, 1980) [translation: Gordon and Breach, New York, 1988].

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, "Duality between partial coherence and partial entanglement," Phys. Rev. A 62, 043816 (2000).
[CrossRef]

A. V. Belinskii and D. N. Klyshko, "Two-photon optics: diffraction, holography, and transformation of two-dimensional signals," Zh. Eksp. Teor. Fiz. 105, 487-493 (1994) [Sov. Phys. JETP 78, 259-262 (1994)].

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Role of entanglement in two-photon imaging," Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef] [PubMed]

W. H. Louisell, A. Yariv, and A. E. Siegman, "Quantum fluctuations and noise in parametric processes. I," Phys. Rev. 124, 1646-1654 (1961).
[CrossRef]

D. N. Klyshko, "Coherent decay of photons in a nonlinear medium," Pis'ma Zh. Eksp. Teor. Fiz. 6, 490-492 (1967) [Sov. Phys. JETP Lett. 6, 23-25 (1967)].

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, New York, 1995).

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, "Two-photon geometric optics," Phys. Rev. A 53, 2804-2815 (1996).
[CrossRef] [PubMed]

T. Kreis, P. Aswendt, and R. H�fling, "Hologram reconstruction using a digital micromirror device," Opt. Eng. 40, 926-933 (2001).
[CrossRef]

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Ch. 4.
[CrossRef]

Supplementary Material (1)

» Media 1: GIF (37 KB)     

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Figures (2)

Figure 1.
Figure 1.

Quantum holography. S is a source of entangled-photon pairs. C is a (remote) single-photon- sensitive integrating sphere that comprises the wall of the chamber concealing the hidden object (bust of Plato). D is a (local) 2-D single-photon-sensitive scanning or array detector. h 1 and h 2 represent the optical systems that deliver the entangled photons from S to C and D, respectively. The quantity 2(x 2) is the marginal coincidence rate, which is the hologram of the concealed object. Thin and thick lines represent optical and electrical signals, respectively. [Media 1]

Figure 2.
Figure 2.

Quantum holography of a single point scatterer located at point x (1) inside C. All quantities are defined in the text.

Equations (15)

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Ψ = S d x d x φ ( x ) δ ( x x ) 1 x 1 x ,
p ( x 1 , x 2 ) S d x φ ( x ) h 1 ( x 1 , x ) h 2 ( x 2 , x ) 2 .
p ¯ 2 ( x 2 ) = C d x 1 p ( x 1 , x 2 ) S d x d x φ ( x ) φ * ( x ) h 2 ( x 2 , x ) h 2 * ( x 2 , x ) g 1 ( x , x ) ,
h 1 ( x 1 , x ) = h ( 0 ) ( x 1 , x ) + h ( 1 ) ( x 1 , x ( 1 ) ) ε ( x ( 1 ) ) h I ( 1 ) ( x ( 1 ) , x ) .
p ¯ 2 ( x 2 ) p ¯ 2 ( 0 ) ( x 2 ) + p ¯ 2 ( 1 ) ( x 2 ) + { ε ( x ( 1 ) ) r ( x 2 , x ( 1 ) ) q ( x 2 , x ( 1 ) ) + c . c . } ,
p ¯ 2 ( 1 ) ( x 2 ) = ε ( x ( 1 ) ) 2 β ( x ( 1 ) , x ( 1 ) ) q ( x 2 , x ( 1 ) ) 2 ,
β ( x ( 1 ) , x ( 1 ) ) = d x 1 h ( 1 ) ( x 1 , x ( 1 ) ) 2 ,
q ( x 2 , x ( 1 ) ) = d x φ ( x ) h 2 ( x 2 , x ) h 1 ( 1 ) ( x ( 1 ) , x ) ,
r ( x 2 , x ( 1 ) ) = d x φ * ( x ) f ( x ( 1 ) , x ) h 2 * ( x 2 , x ) ,
f ( x ( 1 ) , x ) = d x 1 h ( 0 ) * ( x 1 , x ) h ( 1 ) ( x 1 , x ( 1 ) ) ,
h 1 ( x 1 , x ) = h ( 0 ) ( x 1 , x ) + j = 1 N h ( j ) ( x 1 , x ( j ) ) ε ( x ( j ) ) h 1 ( j ) ( x ( j ) , x ) ,
p ¯ 2 ( x 2 ) p ¯ 2 ( 0 ) ( x 2 ) + p ¯ 2 ( Σ ) ( x 2 ) + { j = 1 N ε ( x ( j ) ) r ( x 2 , x ( j ) ) q ( x 2 , x ( j ) ) + c . c . } ,
p ¯ 2 ( Σ ) ( x 2 ) = j = 1 N p ¯ 2 ( j ) ( x 2 ) + 2 Re { j = 1 , i = j + 1 N ε ( x ( j ) ) ε * ( x ( i ) ) β ( x ( j ) , x ( i ) ) q ( x 2 , x ( j ) ) q * ( x 2 , x ( i ) ) } ,
p ¯ 2 ( j ) ( x 2 ) = ε ( x ( j ) ) 2 β ( x ( j ) , x ( j ) ) q ( x 2 , x ( j ) ) 2 ,
β ( x ( j ) , x ( i ) ) = d x 1 h ( j ) ( x 1 , x ( j ) ) h ( i ) * ( x 1 , x ( i ) ) ,

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