Abstract

We discuss the possibility of quantum interferences and entanglement of photons that exist at different intervals of time, i.e., one photon being recorded before the other has been created. The corresponding two-photon correlation function is shown to violate Bell’s inequalities.

© 2011 Optical Society of America

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  1. C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
    [CrossRef]
  2. Y. H. Shih and C. O. Alley, Phys. Rev. Lett. 61, 2921 (1988).
    [CrossRef]
  3. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
    [CrossRef]
  4. M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, Phys. Rev. Lett. 71, 4287 (1993).
    [CrossRef]
  5. R. Kaltenbaek, B. Blauensteiner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, Phys. Rev. Lett. 96, 240502(2006).
    [CrossRef]
  6. J. Beugnon, M. Jones, J. Dingjan, B. Darquie, G. Messin, A. Browaeys, and P. Grangier, Nature 440, 779 (2006).
    [CrossRef]
  7. P. Maunz, D. Moehring, S. Olmschenk, K. Younge, D. Matsukevich, and C. Monroe, Nature Phys. 3, 538 (2007).
    [CrossRef]
  8. E. B. Flagg, A. Muller, S. V. Polyakov, A. Ling, A. Migdall, and G. S. Solomon, Phys. Rev. Lett. 104, 137401 (2010).
    [CrossRef]
  9. T. B. Pittman and J. D. Franson, Phys. Rev. Lett. 90, 240401 (2003).
    [CrossRef]
  10. A. J. Bennett, R. B. Patel, C. A. Nicoll, D. Ritchie, and A. J. Shields, Nature Phys. 5, 715 (2009).
    [CrossRef]
  11. P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 45, 7729 (1992).
    [CrossRef]
  12. T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 77, 1917 (1996).
    [CrossRef]
  13. J. D. Franson, Phys. Rev. Lett. 62, 2205 (1989).
    [CrossRef]
  14. A. Cabello, A. Rossi, G. Vallone, F. De Martini, and P. Mataloni, Phys. Rev. Lett. 102, 040401 (2009).
    [CrossRef]
  15. L. Mandel, Phys. Rev. A 28, 929 (1983).
    [CrossRef]
  16. C. Thiel, T. Bastin, J. Martin, E. Solano, J. von Zanthier, and G. S. Agarwal, Phys. Rev. Lett. 99, 133603 (2007).
    [CrossRef]
  17. J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974).
    [CrossRef]
  18. R. Wiegner, C. Thiel, J. von Zanthier, and G. S. Agarwal, Phys. Lett. A 374, 3405 (2010).
    [CrossRef]
  19. Note that to exclude communication between the two detectors during the measurement of the two photons the condition 2tR>t2−t1>tR must be satisfied. This could be fulfilled by placing the two detectors opposite to each other with respect to the two-photon sources. For example, for trapped Ca+ ions the natural linewidth of the D1 transition is γ=20 MHz and the lifetime (2πγ)−1=8 ns. If the distance between the ions and the detectors is r=1 m, then t2−t1>tR=r/c=3 ns can be easily fulfilled.

2010 (2)

E. B. Flagg, A. Muller, S. V. Polyakov, A. Ling, A. Migdall, and G. S. Solomon, Phys. Rev. Lett. 104, 137401 (2010).
[CrossRef]

R. Wiegner, C. Thiel, J. von Zanthier, and G. S. Agarwal, Phys. Lett. A 374, 3405 (2010).
[CrossRef]

2009 (2)

A. J. Bennett, R. B. Patel, C. A. Nicoll, D. Ritchie, and A. J. Shields, Nature Phys. 5, 715 (2009).
[CrossRef]

A. Cabello, A. Rossi, G. Vallone, F. De Martini, and P. Mataloni, Phys. Rev. Lett. 102, 040401 (2009).
[CrossRef]

2007 (2)

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

P. Maunz, D. Moehring, S. Olmschenk, K. Younge, D. Matsukevich, and C. Monroe, Nature Phys. 3, 538 (2007).
[CrossRef]

2006 (2)

R. Kaltenbaek, B. Blauensteiner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, Phys. Rev. Lett. 96, 240502(2006).
[CrossRef]

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

2003 (1)

T. B. Pittman and J. D. Franson, Phys. Rev. Lett. 90, 240401 (2003).
[CrossRef]

1996 (1)

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 77, 1917 (1996).
[CrossRef]

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef]

1993 (1)

M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, Phys. Rev. Lett. 71, 4287 (1993).
[CrossRef]

1992 (1)

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 45, 7729 (1992).
[CrossRef]

1989 (1)

J. D. Franson, Phys. Rev. Lett. 62, 2205 (1989).
[CrossRef]

1988 (1)

Y. H. Shih and C. O. Alley, Phys. Rev. Lett. 61, 2921 (1988).
[CrossRef]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[CrossRef]

1983 (1)

L. Mandel, Phys. Rev. A 28, 929 (1983).
[CrossRef]

1974 (1)

J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974).
[CrossRef]

Agarwal, G. S.

R. Wiegner, C. Thiel, J. von Zanthier, and G. S. Agarwal, Phys. Lett. A 374, 3405 (2010).
[CrossRef]

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

Alley, C. O.

Y. H. Shih and C. O. Alley, Phys. Rev. Lett. 61, 2921 (1988).
[CrossRef]

Aspelmeyer, M.

R. Kaltenbaek, B. Blauensteiner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, Phys. Rev. Lett. 96, 240502(2006).
[CrossRef]

Bastin, T.

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

Bennett, A. J.

A. J. Bennett, R. B. Patel, C. A. Nicoll, D. Ritchie, and A. J. Shields, Nature Phys. 5, 715 (2009).
[CrossRef]

Beugnon, J.

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

Blauensteiner, B.

R. Kaltenbaek, B. Blauensteiner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, Phys. Rev. Lett. 96, 240502(2006).
[CrossRef]

Browaeys, A.

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

Cabello, A.

A. Cabello, A. Rossi, G. Vallone, F. De Martini, and P. Mataloni, Phys. Rev. Lett. 102, 040401 (2009).
[CrossRef]

Chiao, R. Y.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 45, 7729 (1992).
[CrossRef]

Clauser, J. F.

J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974).
[CrossRef]

Darquie, B.

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

De Martini, F.

A. Cabello, A. Rossi, G. Vallone, F. De Martini, and P. Mataloni, Phys. Rev. Lett. 102, 040401 (2009).
[CrossRef]

Dingjan, J.

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

Ekert, A. K.

M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, Phys. Rev. Lett. 71, 4287 (1993).
[CrossRef]

Flagg, E. B.

E. B. Flagg, A. Muller, S. V. Polyakov, A. Ling, A. Migdall, and G. S. Solomon, Phys. Rev. Lett. 104, 137401 (2010).
[CrossRef]

Franson, J. D.

T. B. Pittman and J. D. Franson, Phys. Rev. Lett. 90, 240401 (2003).
[CrossRef]

J. D. Franson, Phys. Rev. Lett. 62, 2205 (1989).
[CrossRef]

Grangier, P.

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

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[CrossRef]

Horne, M. A.

M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, Phys. Rev. Lett. 71, 4287 (1993).
[CrossRef]

J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974).
[CrossRef]

Jones, M.

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

Kaltenbaek, R.

R. Kaltenbaek, B. Blauensteiner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, Phys. Rev. Lett. 96, 240502(2006).
[CrossRef]

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef]

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 45, 7729 (1992).
[CrossRef]

Ling, A.

E. B. Flagg, A. Muller, S. V. Polyakov, A. Ling, A. Migdall, and G. S. Solomon, Phys. Rev. Lett. 104, 137401 (2010).
[CrossRef]

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[CrossRef]

L. Mandel, Phys. Rev. A 28, 929 (1983).
[CrossRef]

Martin, J.

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

Mataloni, P.

A. Cabello, A. Rossi, G. Vallone, F. De Martini, and P. Mataloni, Phys. Rev. Lett. 102, 040401 (2009).
[CrossRef]

Matsukevich, D.

P. Maunz, D. Moehring, S. Olmschenk, K. Younge, D. Matsukevich, and C. Monroe, Nature Phys. 3, 538 (2007).
[CrossRef]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef]

Maunz, P.

P. Maunz, D. Moehring, S. Olmschenk, K. Younge, D. Matsukevich, and C. Monroe, Nature Phys. 3, 538 (2007).
[CrossRef]

Messin, G.

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

Migdall, A.

E. B. Flagg, A. Muller, S. V. Polyakov, A. Ling, A. Migdall, and G. S. Solomon, Phys. Rev. Lett. 104, 137401 (2010).
[CrossRef]

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 77, 1917 (1996).
[CrossRef]

Moehring, D.

P. Maunz, D. Moehring, S. Olmschenk, K. Younge, D. Matsukevich, and C. Monroe, Nature Phys. 3, 538 (2007).
[CrossRef]

Monroe, C.

P. Maunz, D. Moehring, S. Olmschenk, K. Younge, D. Matsukevich, and C. Monroe, Nature Phys. 3, 538 (2007).
[CrossRef]

Muller, A.

E. B. Flagg, A. Muller, S. V. Polyakov, A. Ling, A. Migdall, and G. S. Solomon, Phys. Rev. Lett. 104, 137401 (2010).
[CrossRef]

Nicoll, C. A.

A. J. Bennett, R. B. Patel, C. A. Nicoll, D. Ritchie, and A. J. Shields, Nature Phys. 5, 715 (2009).
[CrossRef]

Olmschenk, S.

P. Maunz, D. Moehring, S. Olmschenk, K. Younge, D. Matsukevich, and C. Monroe, Nature Phys. 3, 538 (2007).
[CrossRef]

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[CrossRef]

Patel, R. B.

A. J. Bennett, R. B. Patel, C. A. Nicoll, D. Ritchie, and A. J. Shields, Nature Phys. 5, 715 (2009).
[CrossRef]

Pittman, T. B.

T. B. Pittman and J. D. Franson, Phys. Rev. Lett. 90, 240401 (2003).
[CrossRef]

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 77, 1917 (1996).
[CrossRef]

Polyakov, S. V.

E. B. Flagg, A. Muller, S. V. Polyakov, A. Ling, A. Migdall, and G. S. Solomon, Phys. Rev. Lett. 104, 137401 (2010).
[CrossRef]

Ritchie, D.

A. J. Bennett, R. B. Patel, C. A. Nicoll, D. Ritchie, and A. J. Shields, Nature Phys. 5, 715 (2009).
[CrossRef]

Rossi, A.

A. Cabello, A. Rossi, G. Vallone, F. De Martini, and P. Mataloni, Phys. Rev. Lett. 102, 040401 (2009).
[CrossRef]

Rubin, M. H.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 77, 1917 (1996).
[CrossRef]

Sergienko, A. V.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 77, 1917 (1996).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef]

Shields, A. J.

A. J. Bennett, R. B. Patel, C. A. Nicoll, D. Ritchie, and A. J. Shields, Nature Phys. 5, 715 (2009).
[CrossRef]

Shih, Y.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef]

Shih, Y. H.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 77, 1917 (1996).
[CrossRef]

Y. H. Shih and C. O. Alley, Phys. Rev. Lett. 61, 2921 (1988).
[CrossRef]

Solano, E.

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

Solomon, G. S.

E. B. Flagg, A. Muller, S. V. Polyakov, A. Ling, A. Migdall, and G. S. Solomon, Phys. Rev. Lett. 104, 137401 (2010).
[CrossRef]

Steinberg, A. M.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 45, 7729 (1992).
[CrossRef]

Strekalov, D. V.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 77, 1917 (1996).
[CrossRef]

Thiel, C.

R. Wiegner, C. Thiel, J. von Zanthier, and G. S. Agarwal, Phys. Lett. A 374, 3405 (2010).
[CrossRef]

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

Vallone, G.

A. Cabello, A. Rossi, G. Vallone, F. De Martini, and P. Mataloni, Phys. Rev. Lett. 102, 040401 (2009).
[CrossRef]

von Zanthier, J.

R. Wiegner, C. Thiel, J. von Zanthier, and G. S. Agarwal, Phys. Lett. A 374, 3405 (2010).
[CrossRef]

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

Weinfurter, H.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef]

Wiegner, R.

R. Wiegner, C. Thiel, J. von Zanthier, and G. S. Agarwal, Phys. Lett. A 374, 3405 (2010).
[CrossRef]

Younge, K.

P. Maunz, D. Moehring, S. Olmschenk, K. Younge, D. Matsukevich, and C. Monroe, Nature Phys. 3, 538 (2007).
[CrossRef]

Zeilinger, A.

R. Kaltenbaek, B. Blauensteiner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, Phys. Rev. Lett. 96, 240502(2006).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef]

M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, Phys. Rev. Lett. 71, 4287 (1993).
[CrossRef]

Zukowski, M.

R. Kaltenbaek, B. Blauensteiner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, Phys. Rev. Lett. 96, 240502(2006).
[CrossRef]

M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, Phys. Rev. Lett. 71, 4287 (1993).
[CrossRef]

Nature (1)

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

Nature Phys. (2)

P. Maunz, D. Moehring, S. Olmschenk, K. Younge, D. Matsukevich, and C. Monroe, Nature Phys. 3, 538 (2007).
[CrossRef]

A. J. Bennett, R. B. Patel, C. A. Nicoll, D. Ritchie, and A. J. Shields, Nature Phys. 5, 715 (2009).
[CrossRef]

Phys. Lett. A (1)

R. Wiegner, C. Thiel, J. von Zanthier, and G. S. Agarwal, Phys. Lett. A 374, 3405 (2010).
[CrossRef]

Phys. Rev. A (2)

L. Mandel, Phys. Rev. A 28, 929 (1983).
[CrossRef]

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 45, 7729 (1992).
[CrossRef]

Phys. Rev. D (1)

J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974).
[CrossRef]

Phys. Rev. Lett. (11)

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 77, 1917 (1996).
[CrossRef]

J. D. Franson, Phys. Rev. Lett. 62, 2205 (1989).
[CrossRef]

A. Cabello, A. Rossi, G. Vallone, F. De Martini, and P. Mataloni, Phys. Rev. Lett. 102, 040401 (2009).
[CrossRef]

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

E. B. Flagg, A. Muller, S. V. Polyakov, A. Ling, A. Migdall, and G. S. Solomon, Phys. Rev. Lett. 104, 137401 (2010).
[CrossRef]

T. B. Pittman and J. D. Franson, Phys. Rev. Lett. 90, 240401 (2003).
[CrossRef]

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[CrossRef]

Y. H. Shih and C. O. Alley, Phys. Rev. Lett. 61, 2921 (1988).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef]

M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, Phys. Rev. Lett. 71, 4287 (1993).
[CrossRef]

R. Kaltenbaek, B. Blauensteiner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, Phys. Rev. Lett. 96, 240502(2006).
[CrossRef]

Other (1)

Note that to exclude communication between the two detectors during the measurement of the two photons the condition 2tR>t2−t1>tR must be satisfied. This could be fulfilled by placing the two detectors opposite to each other with respect to the two-photon sources. For example, for trapped Ca+ ions the natural linewidth of the D1 transition is γ=20 MHz and the lifetime (2πγ)−1=8 ns. If the distance between the ions and the detectors is r=1 m, then t2−t1>tR=r/c=3 ns can be easily fulfilled.

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