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.

© 2001 Optical Society of America

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References

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  1. E. Schrödinger, “Die gegenwartige Situation in der Quantenmechanik,” Naturwissenchaften23, 807–812, 823–828, 844–849 (1935).
    [Crossref]
  2. A. Einstein in The Born-Einstein Letters (Walker, New York, 1971), p. 158, translated byI. 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 and 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. JETP78, 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, “Twophoton geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
    [Crossref] [PubMed]
  14. T. Kreis, P. Aswendt, and R. Höfling, “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]

2001 (2)

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]

T. Kreis, P. Aswendt, and R. Höfling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40, 926–933 (2001).
[Crossref]

2000 (1)

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]

1996 (1)

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Twophoton geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

1978 (1)

J. F. Clauser and A. Shimony, “Bell’s Theorem. Experimental tests and implications,” Rep. Prog. Phys. 41, 1881–1927 (1978).
[Crossref]

1961 (1)

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes. I,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

1949 (1)

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

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[Crossref] [PubMed]

Abouraddy, A. F.

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]

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]

Aswendt, P.

T. Kreis, P. Aswendt, and R. Höfling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40, 926–933 (2001).
[Crossref]

Belinskii, A. V.

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. JETP78, 259–262 (1994)].

Born, I.

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

Clauser, J. F.

J. F. Clauser and A. Shimony, “Bell’s Theorem. Experimental tests and implications,” Rep. Prog. Phys. 41, 1881–1927 (1978).
[Crossref]

Einstein, A.

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

Gabor, D.

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

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[Crossref] [PubMed]

Höfling, R.

T. Kreis, P. Aswendt, and R. Höfling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40, 926–933 (2001).
[Crossref]

Klyshko, D. N.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Twophoton geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

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)].

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

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. JETP78, 259–262 (1994)].

Kreis, T.

T. Kreis, P. Aswendt, and R. Höfling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40, 926–933 (2001).
[Crossref]

Louisell, W. H.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes. I,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

Mandel, L.

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

Pittman, T. B.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Twophoton geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

Rubin, M. H.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Twophoton geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

Saleh, B. E. A.

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]

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]

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

Schrödinger, E.

E. Schrödinger, “Die gegenwartige Situation in der Quantenmechanik,” Naturwissenchaften23, 807–812, 823–828, 844–849 (1935).
[Crossref]

Sergienko, A. V.

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]

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]

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Twophoton geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

Shih, Y. H.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Twophoton geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

Shimony, A.

J. F. Clauser and A. Shimony, “Bell’s Theorem. Experimental tests and implications,” Rep. Prog. Phys. 41, 1881–1927 (1978).
[Crossref]

Siegman, A. E.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes. I,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

Strekalov, D. V.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Twophoton geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

Teich, M. C.

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]

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]

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

Wolf, E.

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

Yariv, A.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes. I,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[Crossref] [PubMed]

Opt. Eng. (1)

T. Kreis, P. Aswendt, and R. Höfling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40, 926–933 (2001).
[Crossref]

Phys. Rev. (1)

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes. I,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

Phys. Rev. A (2)

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Twophoton geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

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]

Phys. Rev. Lett. (1)

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]

Proc. Roy. Soc. (London) (1)

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

Rep. Prog. Phys. (1)

J. F. Clauser and A. Shimony, “Bell’s Theorem. Experimental tests and implications,” Rep. Prog. Phys. 41, 1881–1927 (1978).
[Crossref]

Other (7)

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

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. JETP78, 259–262 (1994)].

E. Schrödinger, “Die gegenwartige Situation in der Quantenmechanik,” Naturwissenchaften23, 807–812, 823–828, 844–849 (1935).
[Crossref]

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

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).

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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