Abstract

Two experiments of four-photon interference are performed with two pairs of photons from parametric downconversion with the help of asymmetric beam splitters. The first experiment is a generalization of the Hong–Ou–Mandel interference effect to two pairs of photons while the second one utilizes this effect to demonstrate a four-photon de Broglie wavelength of λ4 by projection measurement.

© 2007 Optical Society of America

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References

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  1. L. Mandel, Rev. Mod. Phys. 71, S274 (1999).
    [CrossRef]
  2. A. Zeilinger, Rev. Mod. Phys. 71, S288 (1999).
    [CrossRef]
  3. D. M. Greenberger, M. A. Home, and A. Zeilinger, in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, M.Katafos, ed. (Kluwer Academic, 1989).
  4. D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345 (1999).
    [CrossRef]
  5. J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, Phys. Rev. A 54, R4649 (1996).
    [CrossRef] [PubMed]
  6. Z. Y. Ou, Phys. Rev. A 55, 2598 (1997).
    [CrossRef]
  7. 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]
  8. P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, Nature 429, 158 (2004).
    [CrossRef] [PubMed]
  9. M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
    [CrossRef] [PubMed]
  10. C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
    [CrossRef] [PubMed]
  11. Z. Y. Ou, J.-K. Rhee, and L. J. Wang, Phys. Rev. Lett. 83, 959 (1999).
    [CrossRef]
  12. H. Wang and T. Kobayashi, Phys. Rev. A 71, 021802(R) (2005).
    [CrossRef]
  13. K. Sanaka, K. J. Resch, and A. Zeilinger, Phys. Rev. Lett. 96, 083601 (2006).
    [CrossRef] [PubMed]
  14. J. Jacobson, G. Björk, I. Chuang and Y. Yamamoto, Phys. Rev. Lett. 74, 4835 (1995).
    [CrossRef] [PubMed]
  15. B. H. Liu, F. W. Sun, Y. X. Gong, Y. F. Huang, Z. Y. Ou, and G. C. Guo, arxix.org e-print archives quant-ph/06/0266, October 31, 2006, http://arxiv.org/abs/quant-ph/0610266.
  16. R. A. Campos, B., E. A. Saleh, and M. C. Teich, Phys. Rev. A 40, 1371 (1989).
    [CrossRef] [PubMed]
  17. S. Takeuchi, Opt. Lett. 26, 843 (2001).
    [CrossRef]
  18. Z. Y. Ou, J.-K. Rhee, and L. J. Wang, Phys. Rev. A 60, 593 (1999).
    [CrossRef]
  19. K. Tsujino, H. F. Hofmann, S. Takeuchi, and K. Sasaki, Phys. Rev. Lett. 92, 153602 (2004).
    [CrossRef] [PubMed]
  20. Z. Y. Ou, Phys. Rev. A 72, 053814 (2005).
    [CrossRef]
  21. A more detailed multimode theory similar to Refs. will take into account the temporal mismatch between the two pairs of downconverted photons. This theory will be presented elsewhere.

2006 (1)

K. Sanaka, K. J. Resch, and A. Zeilinger, Phys. Rev. Lett. 96, 083601 (2006).
[CrossRef] [PubMed]

2005 (2)

H. Wang and T. Kobayashi, Phys. Rev. A 71, 021802(R) (2005).
[CrossRef]

Z. Y. Ou, Phys. Rev. A 72, 053814 (2005).
[CrossRef]

2004 (3)

K. Tsujino, H. F. Hofmann, S. Takeuchi, and K. Sasaki, Phys. Rev. Lett. 92, 153602 (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]

2001 (1)

2000 (1)

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 (5)

L. Mandel, Rev. Mod. Phys. 71, S274 (1999).
[CrossRef]

A. Zeilinger, Rev. Mod. Phys. 71, S288 (1999).
[CrossRef]

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345 (1999).
[CrossRef]

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, Phys. Rev. A 60, 593 (1999).
[CrossRef]

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, Phys. Rev. Lett. 83, 959 (1999).
[CrossRef]

1997 (1)

Z. Y. Ou, Phys. Rev. A 55, 2598 (1997).
[CrossRef]

1996 (1)

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

1995 (1)

J. Jacobson, G. Björk, I. Chuang and Y. Yamamoto, Phys. Rev. Lett. 74, 4835 (1995).
[CrossRef] [PubMed]

1989 (1)

R. A. Campos, B., E. A. Saleh, and M. C. Teich, Phys. Rev. A 40, 1371 (1989).
[CrossRef] [PubMed]

1987 (1)

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

Abrams, D. S.

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]

Aspelmeyer, M.

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

Björk, G.

J. Jacobson, G. Björk, I. Chuang and Y. Yamamoto, Phys. Rev. Lett. 74, 4835 (1995).
[CrossRef] [PubMed]

Bollinger, J. J.

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

Boto, N.

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]

Bouwmeester, D.

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345 (1999).
[CrossRef]

Braunstein, S. L.

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]

Campos, R. A.

R. A. Campos, B., E. A. Saleh, and M. C. Teich, Phys. Rev. A 40, 1371 (1989).
[CrossRef] [PubMed]

Chuang, I.

J. Jacobson, G. Björk, I. Chuang and Y. Yamamoto, Phys. Rev. Lett. 74, 4835 (1995).
[CrossRef] [PubMed]

Daniell, M.

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345 (1999).
[CrossRef]

Dowling, J. P.

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]

Gasparoni, S.

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

Gong, Y. X.

B. H. Liu, F. W. Sun, Y. X. Gong, Y. F. Huang, Z. Y. Ou, and G. C. Guo, arxix.org e-print archives quant-ph/06/0266, October 31, 2006, http://arxiv.org/abs/quant-ph/0610266.

Greenberger, D. M.

D. M. Greenberger, M. A. Home, and A. Zeilinger, in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, M.Katafos, ed. (Kluwer Academic, 1989).

Guo, G. C.

B. H. Liu, F. W. Sun, Y. X. Gong, Y. F. Huang, Z. Y. Ou, and G. C. Guo, arxix.org e-print archives quant-ph/06/0266, October 31, 2006, http://arxiv.org/abs/quant-ph/0610266.

Heinzen, D. J.

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

Hofmann, H. F.

K. Tsujino, H. F. Hofmann, S. Takeuchi, and K. Sasaki, Phys. Rev. Lett. 92, 153602 (2004).
[CrossRef] [PubMed]

Home, M. A.

D. M. Greenberger, M. A. Home, and A. Zeilinger, in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, M.Katafos, ed. (Kluwer Academic, 1989).

Hong, C. K.

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

Huang, Y. F.

B. H. Liu, F. W. Sun, Y. X. Gong, Y. F. Huang, Z. Y. Ou, and G. C. Guo, arxix.org e-print archives quant-ph/06/0266, October 31, 2006, http://arxiv.org/abs/quant-ph/0610266.

Itano, W. M.

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

Jacobson, J.

J. Jacobson, G. Björk, I. Chuang and Y. Yamamoto, Phys. Rev. Lett. 74, 4835 (1995).
[CrossRef] [PubMed]

Kobayashi, T.

H. Wang and T. Kobayashi, Phys. Rev. A 71, 021802(R) (2005).
[CrossRef]

Kok, P.

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]

Liu, B. H.

B. H. Liu, F. W. Sun, Y. X. Gong, Y. F. Huang, Z. Y. Ou, and G. C. Guo, arxix.org e-print archives quant-ph/06/0266, October 31, 2006, http://arxiv.org/abs/quant-ph/0610266.

Lundeen, J. S.

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

Mandel, L.

L. Mandel, Rev. Mod. Phys. 71, S274 (1999).
[CrossRef]

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

Mitchell, M. W.

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

Ou, Z. Y.

Z. Y. Ou, Phys. Rev. A 72, 053814 (2005).
[CrossRef]

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, Phys. Rev. A 60, 593 (1999).
[CrossRef]

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, Phys. Rev. Lett. 83, 959 (1999).
[CrossRef]

Z. Y. Ou, Phys. Rev. A 55, 2598 (1997).
[CrossRef]

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

B. H. Liu, F. W. Sun, Y. X. Gong, Y. F. Huang, Z. Y. Ou, and G. C. Guo, arxix.org e-print archives quant-ph/06/0266, October 31, 2006, http://arxiv.org/abs/quant-ph/0610266.

Pan, J.-W.

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

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345 (1999).
[CrossRef]

Resch, K. J.

K. Sanaka, K. J. Resch, and A. Zeilinger, Phys. Rev. Lett. 96, 083601 (2006).
[CrossRef] [PubMed]

Rhee, J.-K.

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, Phys. Rev. A 60, 593 (1999).
[CrossRef]

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, Phys. Rev. Lett. 83, 959 (1999).
[CrossRef]

Saleh, B. E. A.

R. A. Campos, B., E. A. Saleh, and M. C. Teich, Phys. Rev. A 40, 1371 (1989).
[CrossRef] [PubMed]

Sanaka, K.

K. Sanaka, K. J. Resch, and A. Zeilinger, Phys. Rev. Lett. 96, 083601 (2006).
[CrossRef] [PubMed]

Sasaki, K.

K. Tsujino, H. F. Hofmann, S. Takeuchi, and K. Sasaki, Phys. Rev. Lett. 92, 153602 (2004).
[CrossRef] [PubMed]

Steinberg, A. M.

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

Sun, F. W.

B. H. Liu, F. W. Sun, Y. X. Gong, Y. F. Huang, Z. Y. Ou, and G. C. Guo, arxix.org e-print archives quant-ph/06/0266, October 31, 2006, http://arxiv.org/abs/quant-ph/0610266.

Takeuchi, S.

K. Tsujino, H. F. Hofmann, S. Takeuchi, and K. Sasaki, Phys. Rev. Lett. 92, 153602 (2004).
[CrossRef] [PubMed]

S. Takeuchi, Opt. Lett. 26, 843 (2001).
[CrossRef]

Teich, M. C.

R. A. Campos, B., E. A. Saleh, and M. C. Teich, Phys. Rev. A 40, 1371 (1989).
[CrossRef] [PubMed]

Tsujino, K.

K. Tsujino, H. F. Hofmann, S. Takeuchi, and K. Sasaki, Phys. Rev. Lett. 92, 153602 (2004).
[CrossRef] [PubMed]

Ursin, R.

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

Walther, P.

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

Wang, H.

H. Wang and T. Kobayashi, Phys. Rev. A 71, 021802(R) (2005).
[CrossRef]

Wang, L. J.

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, Phys. Rev. A 60, 593 (1999).
[CrossRef]

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, Phys. Rev. Lett. 83, 959 (1999).
[CrossRef]

Weinfurter, H.

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345 (1999).
[CrossRef]

Williams, C. P.

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

Yamamoto, Y.

J. Jacobson, G. Björk, I. Chuang and Y. Yamamoto, Phys. Rev. Lett. 74, 4835 (1995).
[CrossRef] [PubMed]

Zeilinger, A.

K. Sanaka, K. J. Resch, and A. Zeilinger, Phys. Rev. Lett. 96, 083601 (2006).
[CrossRef] [PubMed]

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

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345 (1999).
[CrossRef]

A. Zeilinger, Rev. Mod. Phys. 71, S288 (1999).
[CrossRef]

D. M. Greenberger, M. A. Home, and A. Zeilinger, in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, M.Katafos, ed. (Kluwer Academic, 1989).

Nature (2)

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]

Opt. Lett. (1)

Phys. Rev. A (6)

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, Phys. Rev. A 60, 593 (1999).
[CrossRef]

R. A. Campos, B., E. A. Saleh, and M. C. Teich, Phys. Rev. A 40, 1371 (1989).
[CrossRef] [PubMed]

H. Wang and T. Kobayashi, Phys. Rev. A 71, 021802(R) (2005).
[CrossRef]

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

Z. Y. Ou, Phys. Rev. A 55, 2598 (1997).
[CrossRef]

Z. Y. Ou, Phys. Rev. A 72, 053814 (2005).
[CrossRef]

Phys. Rev. Lett. (7)

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]

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

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, Phys. Rev. Lett. 83, 959 (1999).
[CrossRef]

K. Sanaka, K. J. Resch, and A. Zeilinger, Phys. Rev. Lett. 96, 083601 (2006).
[CrossRef] [PubMed]

J. Jacobson, G. Björk, I. Chuang and Y. Yamamoto, Phys. Rev. Lett. 74, 4835 (1995).
[CrossRef] [PubMed]

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345 (1999).
[CrossRef]

K. Tsujino, H. F. Hofmann, S. Takeuchi, and K. Sasaki, Phys. Rev. Lett. 92, 153602 (2004).
[CrossRef] [PubMed]

Rev. Mod. Phys. (2)

L. Mandel, Rev. Mod. Phys. 71, S274 (1999).
[CrossRef]

A. Zeilinger, Rev. Mod. Phys. 71, S288 (1999).
[CrossRef]

Other (3)

D. M. Greenberger, M. A. Home, and A. Zeilinger, in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, M.Katafos, ed. (Kluwer Academic, 1989).

B. H. Liu, F. W. Sun, Y. X. Gong, Y. F. Huang, Z. Y. Ou, and G. C. Guo, arxix.org e-print archives quant-ph/06/0266, October 31, 2006, http://arxiv.org/abs/quant-ph/0610266.

A more detailed multimode theory similar to Refs. will take into account the temporal mismatch between the two pairs of downconverted photons. This theory will be presented elsewhere.

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Figures (5)

Fig. 1
Fig. 1

(a) Hong–Ou–Mandel interferometer with asymmetric beam splitter and (b) formation of an interferometer for the de Broglie wavelength of four photons.

Fig. 2
Fig. 2

Layout of the experiment. PBS, polarization beam splitter; HWP, half-wave plate; PS, phase shifter; IF, interference filter; D1–D4, photodetectors.

Fig. 3
Fig. 3

Four-photon coincidence as a function of the relative, delay Δ between the H and V polarizations.

Fig. 4
Fig. 4

Four-photon coincidence as a function of the rotation angle of HWP2.

Fig. 5
Fig. 5

Four-photon coincidence as a function of the phase difference φ between H and V polarizations. HWP1 is set at (a) θ = 13.7 ° and (b) θ = 13.1 ° .

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Ψ 4 out = 6 T R ( 4 A , 0 B + 0 A , 4 B ) + 6 T R ( T R ) ( 3 A , 1 B 1 A , 3 B ) + [ ( T R ) 2 2 T R ] 2 A , 2 B .
P 4 ( 2 C , 2 D ) 1 + cos 4 φ ,
C ̂ = ( A ̂ + e j φ B ̂ ) 2 , A ̂ = T a ̂ + R b ̂ ,
D ̂ = ( e j φ B ̂ A ̂ ) 2 , B ̂ = T b ̂ R a ̂ ,
P 4 ( θ ) = C [ ( 1 1.5 sin 2 4 θ ) 2 + ( 3 sin 2 4 θ 1 ) × ( 1 sin 2 4 θ ) ( 1 E A ) 2 ] ,
P 4 ( 2 C , 2 D ) = C ( 1 + V 4 cos 4 φ + V 2 cos 2 φ ) ,

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