Abstract

The Lau effect is an interference phenomenon in which two transmission gratings are located in tandem and illuminated incoherently. Here we report the experimental observation of the quantum Lau effect using a two-photon entangled source. Two experimental schemes are proposed and performed. In one scheme, two gratings are nonlocally set in two different paths of two field modes. However, in the other scheme, only one grating is employed to receive the two-mode photons. In both schemes, the Lau interference patterns can be reproduced in a two-photon coincidence measurement where one photon is collected by a bucket detector.

© 2013 Optical Society of America

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References

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  1. E. Lau, Ann. Phys. 437, 417 (1948).
    [CrossRef]
  2. J. Jahns and A.W. Lohmann, Opt. Commun. 28, 263 (1979).
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2011 (1)

X. -B. Song, H. -B. Wang, J. Xiong, K. Wang, X. Zhang, K. -H. Luo, and L.-A. Wu, Phys. Rev. Lett. 107, 033902 (2011).
[CrossRef]

2010 (1)

2007 (1)

M. Thakur, C. Quan, and C. J. Tay, Opt. Laser Technol. 39, 453 (2007).
[CrossRef]

2001 (1)

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

1999 (1)

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

1995 (2)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef]

1988 (1)

1984 (1)

J. Jahns, A. W. Lohmann, and J. Ojeda-Castaneda, Opt. Acta 31, 313 (1984).
[CrossRef]

1983 (1)

K. H. Brenner, A.W. Lohmann, and J. Ojeda-Castaneda, Opt. Commun. 46, 14 (1983).
[CrossRef]

1982 (1)

1979 (3)

J. Jahns and A.W. Lohmann, Opt. Commun. 28, 263 (1979).
[CrossRef]

F. Gori, Opt. Commun. 31, 4 (1979).
[CrossRef]

R. Sudol and B. J. Thompson, Opt. Commun. 31, 105 (1979).
[CrossRef]

1948 (1)

E. Lau, Ann. Phys. 437, 417 (1948).
[CrossRef]

Bevins, N.

Brenner, K. H.

K. H. Brenner, A.W. Lohmann, and J. Ojeda-Castaneda, Opt. Commun. 46, 14 (1983).
[CrossRef]

Cartwright, S.

Chekhova, M. V.

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

Chen, G. H.

D’Angelo, M.

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

Fonseca, E. J. S.

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

Gori, F.

F. Gori, Opt. Commun. 31, 4 (1979).
[CrossRef]

Jahns, J.

J. Jahns, A. W. Lohmann, and J. Ojeda-Castaneda, Opt. Acta 31, 313 (1984).
[CrossRef]

J. Jahns and A.W. Lohmann, Opt. Commun. 28, 263 (1979).
[CrossRef]

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef]

Lau, E.

E. Lau, Ann. Phys. 437, 417 (1948).
[CrossRef]

Leith, E.N.

Lohmann, A. W.

J. Jahns, A. W. Lohmann, and J. Ojeda-Castaneda, Opt. Acta 31, 313 (1984).
[CrossRef]

Lohmann, A.W.

K. H. Brenner, A.W. Lohmann, and J. Ojeda-Castaneda, Opt. Commun. 46, 14 (1983).
[CrossRef]

J. Jahns and A.W. Lohmann, Opt. Commun. 28, 263 (1979).
[CrossRef]

Luo, K. -H.

X. -B. Song, H. -B. Wang, J. Xiong, K. Wang, X. Zhang, K. -H. Luo, and L.-A. Wu, Phys. Rev. Lett. 107, 033902 (2011).
[CrossRef]

Monken, C. H.

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

Ojeda-Castaneda, J.

J. Jahns, A. W. Lohmann, and J. Ojeda-Castaneda, Opt. Acta 31, 313 (1984).
[CrossRef]

K. H. Brenner, A.W. Lohmann, and J. Ojeda-Castaneda, Opt. Commun. 46, 14 (1983).
[CrossRef]

Pádua, S.

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

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

Qi, Z.

Quan, C.

M. Thakur, C. Quan, and C. J. Tay, Opt. Laser Technol. 39, 453 (2007).
[CrossRef]

Sergienko, A. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef]

Shih, Y. H.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

Shih, Y.-H.

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

Song, X. -B.

X. -B. Song, H. -B. Wang, J. Xiong, K. Wang, X. Zhang, K. -H. Luo, and L.-A. Wu, Phys. Rev. Lett. 107, 033902 (2011).
[CrossRef]

Strekalov, D. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

Sudol, R.

R. Sudol and B. J. Thompson, Opt. Commun. 31, 105 (1979).
[CrossRef]

Swanson, G. J.

Tay, C. J.

M. Thakur, C. Quan, and C. J. Tay, Opt. Laser Technol. 39, 453 (2007).
[CrossRef]

Thakur, M.

M. Thakur, C. Quan, and C. J. Tay, Opt. Laser Technol. 39, 453 (2007).
[CrossRef]

Thompson, B. J.

R. Sudol and B. J. Thompson, Opt. Commun. 31, 105 (1979).
[CrossRef]

Wang, H. -B.

X. -B. Song, H. -B. Wang, J. Xiong, K. Wang, X. Zhang, K. -H. Luo, and L.-A. Wu, Phys. Rev. Lett. 107, 033902 (2011).
[CrossRef]

Wang, K.

X. -B. Song, H. -B. Wang, J. Xiong, K. Wang, X. Zhang, K. -H. Luo, and L.-A. Wu, Phys. Rev. Lett. 107, 033902 (2011).
[CrossRef]

Wu, L.-A.

X. -B. Song, H. -B. Wang, J. Xiong, K. Wang, X. Zhang, K. -H. Luo, and L.-A. Wu, Phys. Rev. Lett. 107, 033902 (2011).
[CrossRef]

Xiong, J.

X. -B. Song, H. -B. Wang, J. Xiong, K. Wang, X. Zhang, K. -H. Luo, and L.-A. Wu, Phys. Rev. Lett. 107, 033902 (2011).
[CrossRef]

Zambelli, J.

Zhang, X.

X. -B. Song, H. -B. Wang, J. Xiong, K. Wang, X. Zhang, K. -H. Luo, and L.-A. Wu, Phys. Rev. Lett. 107, 033902 (2011).
[CrossRef]

Ann. Phys. (1)

E. Lau, Ann. Phys. 437, 417 (1948).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Opt. Acta (1)

J. Jahns, A. W. Lohmann, and J. Ojeda-Castaneda, Opt. Acta 31, 313 (1984).
[CrossRef]

Opt. Commun. (4)

K. H. Brenner, A.W. Lohmann, and J. Ojeda-Castaneda, Opt. Commun. 46, 14 (1983).
[CrossRef]

J. Jahns and A.W. Lohmann, Opt. Commun. 28, 263 (1979).
[CrossRef]

F. Gori, Opt. Commun. 31, 4 (1979).
[CrossRef]

R. Sudol and B. J. Thompson, Opt. Commun. 31, 105 (1979).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (1)

M. Thakur, C. Quan, and C. J. Tay, Opt. Laser Technol. 39, 453 (2007).
[CrossRef]

Phys. Rev. A (1)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

Phys. Rev. Lett. (4)

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef]

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

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

X. -B. Song, H. -B. Wang, J. Xiong, K. Wang, X. Zhang, K. -H. Luo, and L.-A. Wu, Phys. Rev. Lett. 107, 033902 (2011).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Experimental setups of two-photon Lau effect: (a) two-gratings scheme and (b) one-grating scheme. PBS, polarizing beamsplitter; CF, cutoff filter; IF, interference filter; CC, coincidence counting by a point detector D1 and a bucket detector D2.

Fig. 2.
Fig. 2.

Experimental results of the two-photon Lau interference patterns for the two-gratings scheme: (a) L=zs1+zi1=zT and (b) L=zs1+zi1=(3/2)zT. In Figs. 2 and 3, the blue circles and red stars represent the coincidence counts and single counts at D1, respectively. The solid lines indicate the theoretical curves.

Fig. 3.
Fig. 3.

Experimental results of the two-photon Lau interference patterns for the one-grating scheme: (a) L=2zs1=zT and (b) L=2zs1=(3/2)zT.

Equations (11)

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

hs(x1,x0)=ki2πfzs1exp[ik(zs1+zs2+f)]exp[ik(fzs2)2f2x12]T1(x)exp[ik2zs1(xx0)2ikx1xf]dx,
hi(x2,x0)=ki2πzi1zi2exp[ik(zi1+zi2)]T2(x)exp[ik2zi1(xx0)2+ik2zi2(x2x)2]dx,
|ψ=dx1dx2C(x1,x2)as(x1)ai(x2)|0,
0|Es(+)(x1)Ei(+)(x2)|ψhs(x1,x0)hi(x2,x0)dx0.
R(x1,x2)|0|Es(+)(x1)Ei(+)(x2)|ψ|2.
R(x1)=R(x1,x2)dx2dx2|T2(x2)|2|dx1T1(x1)exp{ik2L[x122x1(x2+Lx1f)]}|2,
dx1T1(x1)exp{ik2L[x122x1(x2+Lx1f)]}=exp{ik2L(x2+Lx1f)2}×dx1T1(x1)exp{ik2L[x1(x2+Lx1f)]2}=exp{ik2L(x2+Lx1f)2}T1(x2+Lx1f),
R(x1)dx2|T2(x2)T1(x2+Lx1/f)|2.
R(x1)dx2T2(x2)T1(x2+Lx1/f).
T(x)=n=bdsinc(nbd)exp(i2nπxd).
R(x1)nb1b2dsinc(nb1d)sinc(nb2d)exp(i2nπLx1fd).

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