Abstract

We consider the inverse scattering problem that arises in two-photon quantum imaging with interferometric measurements. We show that the two-point correlation function of the field contains information about the scattering medium at a spatial frequency of twice the Rayleigh bandwidth. The linearized inverse problem, however, yields reconstructions with a resolution of λ/2, where λ is the wavelength of light.

© 2010 Optical Society of America

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  1. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733(2000).
    [CrossRef] [PubMed]
  2. M. D’Angelo, M. V. Chekhova, and Y. Shih, Phys. Rev. Lett. 87, 013602 (2001).
    [CrossRef] [PubMed]
  3. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, Phys. Rev. A 54, R4649 (1996).
    [CrossRef] [PubMed]
  4. E. J. S. Fonseca, C. H. Monken, and S. Padua, Phys. Rev. Lett. 82, 2868 (1999).
    [CrossRef]
  5. A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, J. Opt. B 6, S575 (2004).
    [CrossRef]
  6. J. Beugnon, M. P. A. Jones, J. Dingjan, B. Darquie, G. Messin, A. Browaeys, and P. Grangier, Nature 440, 779 (2006).
    [CrossRef] [PubMed]
  7. R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
    [CrossRef] [PubMed]
  8. C. W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble, Nature 438, 828 (2005).
    [CrossRef] [PubMed]
  9. M. O. Scully and K. Druhl, Phys. Rev. A 25, 2208(1982).
    [CrossRef]
  10. S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, Phys. Rev. Lett. 83, 5158 (1999).
    [CrossRef]
  11. C. Cabrillo, J. I. Cirac, P. Garcia-Fernandez, and P. Zoller, Phys. Rev. A 59, 1025 (1999).
    [CrossRef]
  12. F. Dubin, D. Rotter, M. Mukherjee, C. Russo, J. Eschner, and R. Blatt, Phys. Rev. Lett. 98, 183003 (2007).
    [CrossRef] [PubMed]
  13. K. Edamatsu, R. Shimizu, and T. Itoh, Phys. Rev. Lett. 89, 213601 (2002).
    [CrossRef] [PubMed]
  14. A. V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, Phys. Rev. A 79, 013827 (2009).
    [CrossRef]
  15. M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
    [CrossRef] [PubMed]
  16. T. Thiel, J. Bastin, E. Martin, J. Solano, J. von Zanthier, and G. S. Agarwal, Phys. Rev. Lett. 99, 133603 (2007).
    [CrossRef] [PubMed]
  17. P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, Nature 429, 158 (2004).
    [CrossRef] [PubMed]
  18. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  19. P. de Vries, D. V. van Coevorden, and A. Lagendijk, Rev. Mod. Phys. 70, 447 (1998).
    [CrossRef]
  20. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  21. A. J. Devaney, Phys. Rev. Lett. 62, 2385 (1989).
    [CrossRef] [PubMed]
  22. G. Gbur and E. Wolf, Opt. Lett. 27, 1890 (2002).
    [CrossRef]

2009 (1)

A. V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, Phys. Rev. A 79, 013827 (2009).
[CrossRef]

2007 (2)

T. Thiel, J. Bastin, E. Martin, J. Solano, J. von Zanthier, and G. S. Agarwal, Phys. Rev. Lett. 99, 133603 (2007).
[CrossRef] [PubMed]

F. Dubin, D. Rotter, M. Mukherjee, C. Russo, J. Eschner, and R. Blatt, Phys. Rev. Lett. 98, 183003 (2007).
[CrossRef] [PubMed]

2006 (1)

J. Beugnon, M. P. A. Jones, J. Dingjan, B. Darquie, G. Messin, A. Browaeys, and P. Grangier, Nature 440, 779 (2006).
[CrossRef] [PubMed]

2005 (1)

C. W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble, Nature 438, 828 (2005).
[CrossRef] [PubMed]

2004 (4)

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef] [PubMed]

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, Nature 429, 158 (2004).
[CrossRef] [PubMed]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
[CrossRef] [PubMed]

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, J. Opt. B 6, S575 (2004).
[CrossRef]

2002 (2)

G. Gbur and E. Wolf, Opt. Lett. 27, 1890 (2002).
[CrossRef]

K. Edamatsu, R. Shimizu, and T. Itoh, Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

2001 (1)

M. D’Angelo, M. V. Chekhova, and Y. Shih, Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

2000 (1)

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733(2000).
[CrossRef] [PubMed]

1999 (4)

E. J. S. Fonseca, C. H. Monken, and S. Padua, Phys. Rev. Lett. 82, 2868 (1999).
[CrossRef]

S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, Phys. Rev. Lett. 83, 5158 (1999).
[CrossRef]

C. Cabrillo, J. I. Cirac, P. Garcia-Fernandez, and P. Zoller, Phys. Rev. A 59, 1025 (1999).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

1998 (1)

P. de Vries, D. V. van Coevorden, and A. Lagendijk, Rev. Mod. Phys. 70, 447 (1998).
[CrossRef]

1996 (1)

J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, Phys. Rev. A 54, R4649 (1996).
[CrossRef] [PubMed]

1995 (1)

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

1989 (1)

A. J. Devaney, Phys. Rev. Lett. 62, 2385 (1989).
[CrossRef] [PubMed]

1982 (1)

M. O. Scully and K. Druhl, Phys. Rev. A 25, 2208(1982).
[CrossRef]

Abrams, D. S.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733(2000).
[CrossRef] [PubMed]

Agarwal, G. S.

T. Thiel, J. Bastin, E. Martin, J. Solano, J. von Zanthier, and G. S. Agarwal, Phys. Rev. Lett. 99, 133603 (2007).
[CrossRef] [PubMed]

Aspelmeyer, M.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, Nature 429, 158 (2004).
[CrossRef] [PubMed]

Bastin, J.

T. Thiel, J. Bastin, E. Martin, J. Solano, J. von Zanthier, and G. S. Agarwal, Phys. Rev. Lett. 99, 133603 (2007).
[CrossRef] [PubMed]

Bennink, R. S.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef] [PubMed]

Bentley, S. J.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef] [PubMed]

Beugnon, J.

J. Beugnon, M. P. A. Jones, J. Dingjan, B. Darquie, G. Messin, A. Browaeys, and P. Grangier, Nature 440, 779 (2006).
[CrossRef] [PubMed]

Blatt, R.

F. Dubin, D. Rotter, M. Mukherjee, C. Russo, J. Eschner, and R. Blatt, Phys. Rev. Lett. 98, 183003 (2007).
[CrossRef] [PubMed]

Bollinger, J.

J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, Phys. Rev. A 54, R4649 (1996).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Bose, S.

S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, Phys. Rev. Lett. 83, 5158 (1999).
[CrossRef]

Boto, A. N.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733(2000).
[CrossRef] [PubMed]

Boyd, R. W.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef] [PubMed]

Braunstein, S. L.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733(2000).
[CrossRef] [PubMed]

Browaeys, A.

J. Beugnon, M. P. A. Jones, J. Dingjan, B. Darquie, G. Messin, A. Browaeys, and P. Grangier, Nature 440, 779 (2006).
[CrossRef] [PubMed]

Cabrillo, C.

C. Cabrillo, J. I. Cirac, P. Garcia-Fernandez, and P. Zoller, Phys. Rev. A 59, 1025 (1999).
[CrossRef]

Chekhova, M. V.

M. D’Angelo, M. V. Chekhova, and Y. Shih, Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

Chou, C. W.

C. W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble, Nature 438, 828 (2005).
[CrossRef] [PubMed]

Cirac, J. I.

C. Cabrillo, J. I. Cirac, P. Garcia-Fernandez, and P. Zoller, Phys. Rev. A 59, 1025 (1999).
[CrossRef]

D’Angelo, M.

M. D’Angelo, M. V. Chekhova, and Y. Shih, Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

Darquie, B.

J. Beugnon, M. P. A. Jones, J. Dingjan, B. Darquie, G. Messin, A. Browaeys, and P. Grangier, Nature 440, 779 (2006).
[CrossRef] [PubMed]

de Riedmatten, H.

C. W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble, Nature 438, 828 (2005).
[CrossRef] [PubMed]

de Vries, P.

P. de Vries, D. V. van Coevorden, and A. Lagendijk, Rev. Mod. Phys. 70, 447 (1998).
[CrossRef]

Devaney, A. J.

A. J. Devaney, Phys. Rev. Lett. 62, 2385 (1989).
[CrossRef] [PubMed]

Dingjan, J.

J. Beugnon, M. P. A. Jones, J. Dingjan, B. Darquie, G. Messin, A. Browaeys, and P. Grangier, Nature 440, 779 (2006).
[CrossRef] [PubMed]

Dowling, J. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733(2000).
[CrossRef] [PubMed]

Druhl, K.

M. O. Scully and K. Druhl, Phys. Rev. A 25, 2208(1982).
[CrossRef]

Dubin, F.

F. Dubin, D. Rotter, M. Mukherjee, C. Russo, J. Eschner, and R. Blatt, Phys. Rev. Lett. 98, 183003 (2007).
[CrossRef] [PubMed]

Edamatsu, K.

K. Edamatsu, R. Shimizu, and T. Itoh, Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

Eschner, J.

F. Dubin, D. Rotter, M. Mukherjee, C. Russo, J. Eschner, and R. Blatt, Phys. Rev. Lett. 98, 183003 (2007).
[CrossRef] [PubMed]

Felinto, D.

C. W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble, Nature 438, 828 (2005).
[CrossRef] [PubMed]

Fonseca, E. J. S.

E. J. S. Fonseca, C. H. Monken, and S. Padua, Phys. Rev. Lett. 82, 2868 (1999).
[CrossRef]

Garcia-Fernandez, P.

C. Cabrillo, J. I. Cirac, P. Garcia-Fernandez, and P. Zoller, Phys. Rev. A 59, 1025 (1999).
[CrossRef]

Gasparoni, S.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, Nature 429, 158 (2004).
[CrossRef] [PubMed]

Gbur, G.

Giovannetti, A. V.

A. V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, Phys. Rev. A 79, 013827 (2009).
[CrossRef]

Grangier, P.

J. Beugnon, M. P. A. Jones, J. Dingjan, B. Darquie, G. Messin, A. Browaeys, and P. Grangier, Nature 440, 779 (2006).
[CrossRef] [PubMed]

Heinzen, D. J.

J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, Phys. Rev. A 54, R4649 (1996).
[CrossRef] [PubMed]

Howell, J. C.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef] [PubMed]

Itano, W. M.

J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, Phys. Rev. A 54, R4649 (1996).
[CrossRef] [PubMed]

Itoh, T.

K. Edamatsu, R. Shimizu, and T. Itoh, Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

Jones, M. P. A.

J. Beugnon, M. P. A. Jones, J. Dingjan, B. Darquie, G. Messin, A. Browaeys, and P. Grangier, Nature 440, 779 (2006).
[CrossRef] [PubMed]

Kimble, H. J.

C. W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble, Nature 438, 828 (2005).
[CrossRef] [PubMed]

Knight, P. L.

S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, Phys. Rev. Lett. 83, 5158 (1999).
[CrossRef]

Kok, P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733(2000).
[CrossRef] [PubMed]

Lagendijk, A.

P. de Vries, D. V. van Coevorden, and A. Lagendijk, Rev. Mod. Phys. 70, 447 (1998).
[CrossRef]

Lloyd, S.

A. V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, Phys. Rev. A 79, 013827 (2009).
[CrossRef]

Lundeen, J. S.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
[CrossRef] [PubMed]

Maccone, L.

A. V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, Phys. Rev. A 79, 013827 (2009).
[CrossRef]

Mandel, L.

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

Martin, E.

T. Thiel, J. Bastin, E. Martin, J. Solano, J. von Zanthier, and G. S. Agarwal, Phys. Rev. Lett. 99, 133603 (2007).
[CrossRef] [PubMed]

Messin, G.

J. Beugnon, M. P. A. Jones, J. Dingjan, B. Darquie, G. Messin, A. Browaeys, and P. Grangier, Nature 440, 779 (2006).
[CrossRef] [PubMed]

Mitchell, M. W.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
[CrossRef] [PubMed]

Monken, C. H.

E. J. S. Fonseca, C. H. Monken, and S. Padua, Phys. Rev. Lett. 82, 2868 (1999).
[CrossRef]

Mukherjee, M.

F. Dubin, D. Rotter, M. Mukherjee, C. Russo, J. Eschner, and R. Blatt, Phys. Rev. Lett. 98, 183003 (2007).
[CrossRef] [PubMed]

Muthukrishnan, A.

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, J. Opt. B 6, S575 (2004).
[CrossRef]

Padua, S.

E. J. S. Fonseca, C. H. Monken, and S. Padua, Phys. Rev. Lett. 82, 2868 (1999).
[CrossRef]

Pan, J. W.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, Nature 429, 158 (2004).
[CrossRef] [PubMed]

Plenio, M. B.

S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, Phys. Rev. Lett. 83, 5158 (1999).
[CrossRef]

Polyakov, S. V.

C. W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble, Nature 438, 828 (2005).
[CrossRef] [PubMed]

Rotter, D.

F. Dubin, D. Rotter, M. Mukherjee, C. Russo, J. Eschner, and R. Blatt, Phys. Rev. Lett. 98, 183003 (2007).
[CrossRef] [PubMed]

Russo, C.

F. Dubin, D. Rotter, M. Mukherjee, C. Russo, J. Eschner, and R. Blatt, Phys. Rev. Lett. 98, 183003 (2007).
[CrossRef] [PubMed]

Scully, M. O.

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, J. Opt. B 6, S575 (2004).
[CrossRef]

M. O. Scully and K. Druhl, Phys. Rev. A 25, 2208(1982).
[CrossRef]

Shapiro, J. H.

A. V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, Phys. Rev. A 79, 013827 (2009).
[CrossRef]

Shih, Y.

M. D’Angelo, M. V. Chekhova, and Y. Shih, Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

Shimizu, R.

K. Edamatsu, R. Shimizu, and T. Itoh, Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

Solano, J.

T. Thiel, J. Bastin, E. Martin, J. Solano, J. von Zanthier, and G. S. Agarwal, Phys. Rev. Lett. 99, 133603 (2007).
[CrossRef] [PubMed]

Steinberg, A. M.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
[CrossRef] [PubMed]

Thiel, T.

T. Thiel, J. Bastin, E. Martin, J. Solano, J. von Zanthier, and G. S. Agarwal, Phys. Rev. Lett. 99, 133603 (2007).
[CrossRef] [PubMed]

Ursin, R.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, Nature 429, 158 (2004).
[CrossRef] [PubMed]

van Coevorden, D. V.

P. de Vries, D. V. van Coevorden, and A. Lagendijk, Rev. Mod. Phys. 70, 447 (1998).
[CrossRef]

van Enk, S. J.

C. W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble, Nature 438, 828 (2005).
[CrossRef] [PubMed]

Vedral, V.

S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, Phys. Rev. Lett. 83, 5158 (1999).
[CrossRef]

von Zanthier, J.

T. Thiel, J. Bastin, E. Martin, J. Solano, J. von Zanthier, and G. S. Agarwal, Phys. Rev. Lett. 99, 133603 (2007).
[CrossRef] [PubMed]

Walther, P.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, Nature 429, 158 (2004).
[CrossRef] [PubMed]

Williams, C. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733(2000).
[CrossRef] [PubMed]

Wineland, D. J.

J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, Phys. Rev. A 54, R4649 (1996).
[CrossRef] [PubMed]

Wolf, E.

G. Gbur and E. Wolf, Opt. Lett. 27, 1890 (2002).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

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

Zeilinger, A.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, Nature 429, 158 (2004).
[CrossRef] [PubMed]

Zoller, P.

C. Cabrillo, J. I. Cirac, P. Garcia-Fernandez, and P. Zoller, Phys. Rev. A 59, 1025 (1999).
[CrossRef]

Zubairy, M. S.

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, J. Opt. B 6, S575 (2004).
[CrossRef]

J. Opt. B (1)

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, J. Opt. B 6, S575 (2004).
[CrossRef]

Nature (4)

J. Beugnon, M. P. A. Jones, J. Dingjan, B. Darquie, G. Messin, A. Browaeys, and P. Grangier, Nature 440, 779 (2006).
[CrossRef] [PubMed]

C. W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble, Nature 438, 828 (2005).
[CrossRef] [PubMed]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
[CrossRef] [PubMed]

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, Nature 429, 158 (2004).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. A (4)

A. V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, Phys. Rev. A 79, 013827 (2009).
[CrossRef]

C. Cabrillo, J. I. Cirac, P. Garcia-Fernandez, and P. Zoller, Phys. Rev. A 59, 1025 (1999).
[CrossRef]

M. O. Scully and K. Druhl, Phys. Rev. A 25, 2208(1982).
[CrossRef]

J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, Phys. Rev. A 54, R4649 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (9)

E. J. S. Fonseca, C. H. Monken, and S. Padua, Phys. Rev. Lett. 82, 2868 (1999).
[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733(2000).
[CrossRef] [PubMed]

M. D’Angelo, M. V. Chekhova, and Y. Shih, Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, Phys. Rev. Lett. 83, 5158 (1999).
[CrossRef]

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef] [PubMed]

F. Dubin, D. Rotter, M. Mukherjee, C. Russo, J. Eschner, and R. Blatt, Phys. Rev. Lett. 98, 183003 (2007).
[CrossRef] [PubMed]

K. Edamatsu, R. Shimizu, and T. Itoh, Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

T. Thiel, J. Bastin, E. Martin, J. Solano, J. von Zanthier, and G. S. Agarwal, Phys. Rev. Lett. 99, 133603 (2007).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

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[CrossRef]

Other (2)

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Figures (1)

Fig. 1
Fig. 1

Illustrating the experiment.

Equations (22)

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E ( + ) ( x ) = 1 2 [ G ( x , y 1 ) | 0 1 1 1 | + G ( x , y 2 ) | 0 2 1 2 | ] .
2 G ( x , y ) + k 0 2 ( 1 + 4 π η ( x ) ) G ( x , y ) = 4 π δ ( x y ) ,
Γ ( 1 ) ( x ) = ψ | E ( ) ( x ) E ( + ) ( x ) | ψ ,
Γ ( 2 ) ( x 1 , x 2 ) = ψ | E ( ) ( x 1 ) E ( ) ( x 2 ) E ( + ) ( x 2 ) E ( + ) ( x 1 ) | ψ ,
Γ ( 1 ) ( x ) = 1 2 [ | G ( x , y 1 ) | 2 + | G ( x , y 2 ) | 2 ] ,
Γ ( 2 ) ( x 1 , x 2 ) = 1 4 | G ( x 1 , y 1 ) G ( x 2 , y 2 ) + G ( x 1 , y 2 ) G ( x 2 , y 1 ) | 2 .
Γ c ( 2 ) ( x 1 , x 2 ) = Γ ( 2 ) ( x 1 , x 2 ) Γ ( 1 ) ( x 1 ) Γ ( 1 ) ( x 2 ) .
Γ c ( 2 ) ( x 1 , x 2 ) = 1 4 G ( x 1 , y 1 ) G * ( x 1 , y 2 ) G * ( x 2 , y 1 ) G ( x 2 , y 2 ) + c . c . .
G ( x , y ) = G 0 ( x , y ) + k 0 2 G 0 ( x , z ) η ( z ) G ( z , y ) d 3 z ,
G 0 ( x , y ) = e i k 0 | x y | | x y | .
G ( x , y ) = G 0 ( x , y ) + α k 0 2 G 0 ( x , x 0 ) G 0 ( x 0 , y ) ,
α = α 0 1 α 0 k 0 2 / ( π a ) + i α 0 k 0 3 ,
G 0 ( x , y ) e i k 0 r r e i k 0 x ^ · y , | x | | y | ,
Γ ( 1 ) ( x ) cos [ k 0 ( x ^ + y ^ ) · x 0 k 0 R ] + .
Γ c ( 2 ) ( x 1 , x 2 ) cos [ k 0 ( x ^ 1 + x ^ 2 + y ^ 1 + y ^ 2 ) · x 0 ] + .
G ( x , y ) = G 0 ( x , y ) e ϕ ( x , y ) .
ϕ ( x , y ) = k 0 2 G 0 ( x , y ) G 0 ( x , z ) η ( z ) G 0 ( z , y ) d 3 z .
ϕ ( x , y ) = A ( x , y ) η ˜ ( k 0 ( x ^ + y ^ ) ) ,
A ( x , y ) = k 0 2 G 0 ( x , y ) e i k 0 ( | x | + | y | ) | x | | y | .
Γ c ( 2 ) ( x 1 , x 2 ) = Γ 0 ( x 1 , x 2 ) e Φ ( x 1 , x 2 ) + c . c . ,
Γ 0 ( x 1 , x 2 ) = 1 4 G 0 ( x 1 , y 1 ) G 0 * ( x 1 , y 2 ) G 0 * ( x 2 , y 1 ) G 0 ( x 2 , y 2 ) ,
Φ ( x 1 , x 2 ) = A ( x 1 , y 1 ) η ˜ ( k 0 ( x ^ 1 + y ^ 1 ) ) + A * ( x 1 , y 2 ) η ˜ * ( k 0 ( x ^ 1 + y ^ 2 ) ) + A * ( x 2 , y 1 ) η ˜ * ( k 0 ( x ^ 2 + y ^ 1 ) ) + A ( x 2 , y 2 ) η ˜ ( k 0 ( x ^ 2 + y ^ 2 ) ) .

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