Abstract

Two-photon interference with independent classical sources, in which superposition of two indistinguishable two-photon paths plays a key role, is of limited visibility with a maximum value of 50%. By using a random-phase grating to modulate the wavefront of a coherent light, we introduce superposition of multiple indistinguishable two-photon paths, which enhances the two-photon interference effect with a signature of visibility exceeding 50%. The result shows the importance of phase control in the control of high-order coherence of classical light.

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  1. P. Dirac, The Principles of Quantum Mechanics, 2nd edition (Oxford University, 1935).
  2. R. Brown and R. Twiss, “Correlation between photons in two coherent beams of light,” Nature177(4497), 27–29 (1956).
    [CrossRef]
  3. R. Brown and R. Twiss, “A test of new type of stellar interferometer on sirius,” Nature178(4541), 1046–1048 (1956).
    [CrossRef]
  4. U. Fano, “Quantum theory of interference effects in the mixing of light from phase-independent sources,” Am. J. Phys.29(8), 539–545 (1961).
    [CrossRef]
  5. J. Liu and G. Zhang, “Unified interpretation for second-order subwavelength interference based on Feynmans path-integral theory,” Phys. Rev. A82(1), 013822 (2010).
    [CrossRef]
  6. L. Mandel, “Photon interference and correlation effects produced by independent quantum sources,” Phys. Rev. A28(2), 929–943 (1983).
    [CrossRef]
  7. H. Paul, “Interference between independent photons,” Rev. Mod. Phys.58(1), 209–231 (1986).
    [CrossRef]
  8. Z. Ou, “Quantum theory of fourth-order interference,” Phys. Rev. A37(5), 1607–1619 (1988).
    [CrossRef] [PubMed]
  9. D. Klyshko, “Quantum optics: quantum, classical, and metaphysical aspects,” Phys. Usp.37(11), 1097–1123 (1994).
    [CrossRef]
  10. D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ‘ghost’ interference and diffraction,” Phys. Rev. Lett.74(18), 3600–3603 (1995).
    [CrossRef] [PubMed]
  11. E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett.82(14), 2868–2871 (1999).
    [CrossRef]
  12. K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett.89(21), 213601 (2002).
    [CrossRef] [PubMed]
  13. G. Scarcelli, A. Valencia, and Y. Shih, “Two-photon interference with thermal light,” Europhys. Lett.68(5), 618–624 (2004).
    [CrossRef]
  14. J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett.94(17), 173601 (2005).
    [CrossRef] [PubMed]
  15. Yan-Hua Zhai, Xi-Hao Chen, Da Zhang, and Ling-An Wu, “Two-photon interference with true thermal light,” Phys. Rev. A72(4),043805 (2005).
    [CrossRef]
  16. I. Agafonov, M. Chekhova, T. Iskhakov, and A. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A77(5), 053801 (2008).
    [CrossRef]
  17. D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett.92(20), 201102 (2008).
    [CrossRef]
  18. X. Chen, I. Agafonov, K. Luo, Q. Liu, R. Xian, M. Chekhova, and L. Wu, “High-visibility, high-order lensless ghost imaging with thermal light,” Opt. Lett.35(8), 1166–1168 (2010).
    [CrossRef] [PubMed]
  19. Y. Zhou, J. Simon, J. Liu, and Y. Shih, “Third-order correlation function and ghost imaging of chaotic thermal light in the photon counting regime,” Phys. Rev. A81(4), 043831 (2010).
    [CrossRef]
  20. R. Glauber, “The quantum theory of optical coherence,” Phys. Rev.130(6), 2529–2539 (1963).
    [CrossRef]
  21. R. Glauber, “Coherent and incoherent state of radiation field,” Phys. Rev.131(6), 2766–2788 (1963).
    [CrossRef]
  22. G. Brooker, Modern Classical Optics (Oxford University, 2003).
  23. Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nature Photonics4, 721–726 (2010).
    [CrossRef]

2010 (4)

J. Liu and G. Zhang, “Unified interpretation for second-order subwavelength interference based on Feynmans path-integral theory,” Phys. Rev. A82(1), 013822 (2010).
[CrossRef]

Y. Zhou, J. Simon, J. Liu, and Y. Shih, “Third-order correlation function and ghost imaging of chaotic thermal light in the photon counting regime,” Phys. Rev. A81(4), 043831 (2010).
[CrossRef]

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nature Photonics4, 721–726 (2010).
[CrossRef]

X. Chen, I. Agafonov, K. Luo, Q. Liu, R. Xian, M. Chekhova, and L. Wu, “High-visibility, high-order lensless ghost imaging with thermal light,” Opt. Lett.35(8), 1166–1168 (2010).
[CrossRef] [PubMed]

2008 (2)

I. Agafonov, M. Chekhova, T. Iskhakov, and A. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A77(5), 053801 (2008).
[CrossRef]

D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett.92(20), 201102 (2008).
[CrossRef]

2005 (2)

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett.94(17), 173601 (2005).
[CrossRef] [PubMed]

Yan-Hua Zhai, Xi-Hao Chen, Da Zhang, and Ling-An Wu, “Two-photon interference with true thermal light,” Phys. Rev. A72(4),043805 (2005).
[CrossRef]

2004 (1)

G. Scarcelli, A. Valencia, and Y. Shih, “Two-photon interference with thermal light,” Europhys. Lett.68(5), 618–624 (2004).
[CrossRef]

2002 (1)

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett.89(21), 213601 (2002).
[CrossRef] [PubMed]

1999 (1)

E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett.82(14), 2868–2871 (1999).
[CrossRef]

1995 (1)

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ‘ghost’ interference and diffraction,” Phys. Rev. Lett.74(18), 3600–3603 (1995).
[CrossRef] [PubMed]

1994 (1)

D. Klyshko, “Quantum optics: quantum, classical, and metaphysical aspects,” Phys. Usp.37(11), 1097–1123 (1994).
[CrossRef]

1988 (1)

Z. Ou, “Quantum theory of fourth-order interference,” Phys. Rev. A37(5), 1607–1619 (1988).
[CrossRef] [PubMed]

1986 (1)

H. Paul, “Interference between independent photons,” Rev. Mod. Phys.58(1), 209–231 (1986).
[CrossRef]

1983 (1)

L. Mandel, “Photon interference and correlation effects produced by independent quantum sources,” Phys. Rev. A28(2), 929–943 (1983).
[CrossRef]

1963 (2)

R. Glauber, “The quantum theory of optical coherence,” Phys. Rev.130(6), 2529–2539 (1963).
[CrossRef]

R. Glauber, “Coherent and incoherent state of radiation field,” Phys. Rev.131(6), 2766–2788 (1963).
[CrossRef]

1961 (1)

U. Fano, “Quantum theory of interference effects in the mixing of light from phase-independent sources,” Am. J. Phys.29(8), 539–545 (1961).
[CrossRef]

1956 (2)

R. Brown and R. Twiss, “Correlation between photons in two coherent beams of light,” Nature177(4497), 27–29 (1956).
[CrossRef]

R. Brown and R. Twiss, “A test of new type of stellar interferometer on sirius,” Nature178(4541), 1046–1048 (1956).
[CrossRef]

Agafonov, I.

X. Chen, I. Agafonov, K. Luo, Q. Liu, R. Xian, M. Chekhova, and L. Wu, “High-visibility, high-order lensless ghost imaging with thermal light,” Opt. Lett.35(8), 1166–1168 (2010).
[CrossRef] [PubMed]

I. Agafonov, M. Chekhova, T. Iskhakov, and A. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A77(5), 053801 (2008).
[CrossRef]

Bromberg, Y.

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nature Photonics4, 721–726 (2010).
[CrossRef]

Brooker, G.

G. Brooker, Modern Classical Optics (Oxford University, 2003).

Brown, R.

R. Brown and R. Twiss, “A test of new type of stellar interferometer on sirius,” Nature178(4541), 1046–1048 (1956).
[CrossRef]

R. Brown and R. Twiss, “Correlation between photons in two coherent beams of light,” Nature177(4497), 27–29 (1956).
[CrossRef]

Cao, D.

D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett.92(20), 201102 (2008).
[CrossRef]

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett.94(17), 173601 (2005).
[CrossRef] [PubMed]

Chekhova, M.

X. Chen, I. Agafonov, K. Luo, Q. Liu, R. Xian, M. Chekhova, and L. Wu, “High-visibility, high-order lensless ghost imaging with thermal light,” Opt. Lett.35(8), 1166–1168 (2010).
[CrossRef] [PubMed]

I. Agafonov, M. Chekhova, T. Iskhakov, and A. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A77(5), 053801 (2008).
[CrossRef]

Chen, X.

Chen, Xi-Hao

Yan-Hua Zhai, Xi-Hao Chen, Da Zhang, and Ling-An Wu, “Two-photon interference with true thermal light,” Phys. Rev. A72(4),043805 (2005).
[CrossRef]

Dirac, P.

P. Dirac, The Principles of Quantum Mechanics, 2nd edition (Oxford University, 1935).

Edamatsu, K.

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett.89(21), 213601 (2002).
[CrossRef] [PubMed]

Fano, U.

U. Fano, “Quantum theory of interference effects in the mixing of light from phase-independent sources,” Am. J. Phys.29(8), 539–545 (1961).
[CrossRef]

Fonseca, E. J. S.

E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett.82(14), 2868–2871 (1999).
[CrossRef]

Gao, L.

D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett.92(20), 201102 (2008).
[CrossRef]

Glauber, R.

R. Glauber, “Coherent and incoherent state of radiation field,” Phys. Rev.131(6), 2766–2788 (1963).
[CrossRef]

R. Glauber, “The quantum theory of optical coherence,” Phys. Rev.130(6), 2529–2539 (1963).
[CrossRef]

Huang, F.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett.94(17), 173601 (2005).
[CrossRef] [PubMed]

Iskhakov, T.

I. Agafonov, M. Chekhova, T. Iskhakov, and A. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A77(5), 053801 (2008).
[CrossRef]

Itoh, T.

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett.89(21), 213601 (2002).
[CrossRef] [PubMed]

Klyshko, D.

D. Klyshko, “Quantum optics: quantum, classical, and metaphysical aspects,” Phys. Usp.37(11), 1097–1123 (1994).
[CrossRef]

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ‘ghost’ interference and diffraction,” Phys. Rev. Lett.74(18), 3600–3603 (1995).
[CrossRef] [PubMed]

Lahini, Y.

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nature Photonics4, 721–726 (2010).
[CrossRef]

Li, H.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett.94(17), 173601 (2005).
[CrossRef] [PubMed]

Lin, L.

D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett.92(20), 201102 (2008).
[CrossRef]

Liu, J.

Y. Zhou, J. Simon, J. Liu, and Y. Shih, “Third-order correlation function and ghost imaging of chaotic thermal light in the photon counting regime,” Phys. Rev. A81(4), 043831 (2010).
[CrossRef]

J. Liu and G. Zhang, “Unified interpretation for second-order subwavelength interference based on Feynmans path-integral theory,” Phys. Rev. A82(1), 013822 (2010).
[CrossRef]

Liu, Q.

Luo, K.

Mandel, L.

L. Mandel, “Photon interference and correlation effects produced by independent quantum sources,” Phys. Rev. A28(2), 929–943 (1983).
[CrossRef]

Monken, C. H.

E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett.82(14), 2868–2871 (1999).
[CrossRef]

Ou, Z.

Z. Ou, “Quantum theory of fourth-order interference,” Phys. Rev. A37(5), 1607–1619 (1988).
[CrossRef] [PubMed]

Pádua, S.

E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett.82(14), 2868–2871 (1999).
[CrossRef]

Paul, H.

H. Paul, “Interference between independent photons,” Rev. Mod. Phys.58(1), 209–231 (1986).
[CrossRef]

Penin, A.

I. Agafonov, M. Chekhova, T. Iskhakov, and A. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A77(5), 053801 (2008).
[CrossRef]

Scarcelli, G.

G. Scarcelli, A. Valencia, and Y. Shih, “Two-photon interference with thermal light,” Europhys. Lett.68(5), 618–624 (2004).
[CrossRef]

Sergienko, A. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ‘ghost’ interference and diffraction,” Phys. Rev. Lett.74(18), 3600–3603 (1995).
[CrossRef] [PubMed]

Shih, Y.

Y. Zhou, J. Simon, J. Liu, and Y. Shih, “Third-order correlation function and ghost imaging of chaotic thermal light in the photon counting regime,” Phys. Rev. A81(4), 043831 (2010).
[CrossRef]

G. Scarcelli, A. Valencia, and Y. Shih, “Two-photon interference with thermal light,” Europhys. Lett.68(5), 618–624 (2004).
[CrossRef]

Shih, Y. H.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ‘ghost’ interference and diffraction,” Phys. Rev. Lett.74(18), 3600–3603 (1995).
[CrossRef] [PubMed]

Shimizu, R.

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett.89(21), 213601 (2002).
[CrossRef] [PubMed]

Silberberg, Y.

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nature Photonics4, 721–726 (2010).
[CrossRef]

Simon, J.

Y. Zhou, J. Simon, J. Liu, and Y. Shih, “Third-order correlation function and ghost imaging of chaotic thermal light in the photon counting regime,” Phys. Rev. A81(4), 043831 (2010).
[CrossRef]

Small, E.

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nature Photonics4, 721–726 (2010).
[CrossRef]

Strekalov, D. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ‘ghost’ interference and diffraction,” Phys. Rev. Lett.74(18), 3600–3603 (1995).
[CrossRef] [PubMed]

Sun, X.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett.94(17), 173601 (2005).
[CrossRef] [PubMed]

Twiss, R.

R. Brown and R. Twiss, “A test of new type of stellar interferometer on sirius,” Nature178(4541), 1046–1048 (1956).
[CrossRef]

R. Brown and R. Twiss, “Correlation between photons in two coherent beams of light,” Nature177(4497), 27–29 (1956).
[CrossRef]

Valencia, A.

G. Scarcelli, A. Valencia, and Y. Shih, “Two-photon interference with thermal light,” Europhys. Lett.68(5), 618–624 (2004).
[CrossRef]

Wang, K.

D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett.92(20), 201102 (2008).
[CrossRef]

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett.94(17), 173601 (2005).
[CrossRef] [PubMed]

Wu, L.

Wu, Ling-An

Yan-Hua Zhai, Xi-Hao Chen, Da Zhang, and Ling-An Wu, “Two-photon interference with true thermal light,” Phys. Rev. A72(4),043805 (2005).
[CrossRef]

Xian, R.

Xiong, J.

D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett.92(20), 201102 (2008).
[CrossRef]

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett.94(17), 173601 (2005).
[CrossRef] [PubMed]

Zhai, Yan-Hua

Yan-Hua Zhai, Xi-Hao Chen, Da Zhang, and Ling-An Wu, “Two-photon interference with true thermal light,” Phys. Rev. A72(4),043805 (2005).
[CrossRef]

Zhang, Da

Yan-Hua Zhai, Xi-Hao Chen, Da Zhang, and Ling-An Wu, “Two-photon interference with true thermal light,” Phys. Rev. A72(4),043805 (2005).
[CrossRef]

Zhang, G.

J. Liu and G. Zhang, “Unified interpretation for second-order subwavelength interference based on Feynmans path-integral theory,” Phys. Rev. A82(1), 013822 (2010).
[CrossRef]

Zhang, S.

D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett.92(20), 201102 (2008).
[CrossRef]

Zhou, Y.

Y. Zhou, J. Simon, J. Liu, and Y. Shih, “Third-order correlation function and ghost imaging of chaotic thermal light in the photon counting regime,” Phys. Rev. A81(4), 043831 (2010).
[CrossRef]

Am. J. Phys. (1)

U. Fano, “Quantum theory of interference effects in the mixing of light from phase-independent sources,” Am. J. Phys.29(8), 539–545 (1961).
[CrossRef]

Appl. Phys. Lett. (1)

D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett.92(20), 201102 (2008).
[CrossRef]

Europhys. Lett. (1)

G. Scarcelli, A. Valencia, and Y. Shih, “Two-photon interference with thermal light,” Europhys. Lett.68(5), 618–624 (2004).
[CrossRef]

Nature (2)

R. Brown and R. Twiss, “Correlation between photons in two coherent beams of light,” Nature177(4497), 27–29 (1956).
[CrossRef]

R. Brown and R. Twiss, “A test of new type of stellar interferometer on sirius,” Nature178(4541), 1046–1048 (1956).
[CrossRef]

Nature Photonics (1)

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nature Photonics4, 721–726 (2010).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (2)

R. Glauber, “The quantum theory of optical coherence,” Phys. Rev.130(6), 2529–2539 (1963).
[CrossRef]

R. Glauber, “Coherent and incoherent state of radiation field,” Phys. Rev.131(6), 2766–2788 (1963).
[CrossRef]

Phys. Rev. A (6)

Z. Ou, “Quantum theory of fourth-order interference,” Phys. Rev. A37(5), 1607–1619 (1988).
[CrossRef] [PubMed]

J. Liu and G. Zhang, “Unified interpretation for second-order subwavelength interference based on Feynmans path-integral theory,” Phys. Rev. A82(1), 013822 (2010).
[CrossRef]

L. Mandel, “Photon interference and correlation effects produced by independent quantum sources,” Phys. Rev. A28(2), 929–943 (1983).
[CrossRef]

Y. Zhou, J. Simon, J. Liu, and Y. Shih, “Third-order correlation function and ghost imaging of chaotic thermal light in the photon counting regime,” Phys. Rev. A81(4), 043831 (2010).
[CrossRef]

Yan-Hua Zhai, Xi-Hao Chen, Da Zhang, and Ling-An Wu, “Two-photon interference with true thermal light,” Phys. Rev. A72(4),043805 (2005).
[CrossRef]

I. Agafonov, M. Chekhova, T. Iskhakov, and A. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A77(5), 053801 (2008).
[CrossRef]

Phys. Rev. Lett. (4)

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett.94(17), 173601 (2005).
[CrossRef] [PubMed]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ‘ghost’ interference and diffraction,” Phys. Rev. Lett.74(18), 3600–3603 (1995).
[CrossRef] [PubMed]

E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett.82(14), 2868–2871 (1999).
[CrossRef]

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett.89(21), 213601 (2002).
[CrossRef] [PubMed]

Phys. Usp. (1)

D. Klyshko, “Quantum optics: quantum, classical, and metaphysical aspects,” Phys. Usp.37(11), 1097–1123 (1994).
[CrossRef]

Rev. Mod. Phys. (1)

H. Paul, “Interference between independent photons,” Rev. Mod. Phys.58(1), 209–231 (1986).
[CrossRef]

Other (2)

G. Brooker, Modern Classical Optics (Oxford University, 2003).

P. Dirac, The Principles of Quantum Mechanics, 2nd edition (Oxford University, 1935).

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Figures (5)

Fig. 1
Fig. 1

Two indistinguishable two-photon paths for a pair of independent photons S1 and S2 to trigger a coincidence count. D1 and D2 are two single-photon detectors.

Fig. 2
Fig. 2

(a) Schematic diagram for the designed random-phase grating with N slits. The inset shows the random phases encoded on the light waves transmitting through the respective slits of the grating, in which the elementary phase ϕ changes with time randomly. (b) Schematic diagram for detecting the two-photon interference of the light wave transmitting through the N-slit random-phase grating in the Fraunhofer zone, where f is the focal length of the lens.

Fig. 3
Fig. 3

The dependence of the two-photon interference visibility V on the slit number N of the random-phase grating.

Fig. 4
Fig. 4

Schematic diagram of the experimental setup. A single mode 780-nm laser was introduced as the light source. A N-slit amplitude mask (N = 2, 3, 4 and 5, b = 72 μm and d = 400 μm) and a SLM were used to construct the random-phase grating shown in Fig. 2. A CCD camera was located at the focal plane of the lens L to measure the intensity distribution and the second-order spatial correlation function.

Fig. 5
Fig. 5

The single-photon interference and the two-photon interference of light on the detection plane at different conditions. The empty circles are the experimental data, while the red curves are the theoretical fits. The first column shows the stationary single-photon interference fringes with the normal N-slit gratings, where the red curves are the theoretical fits using the multiple-slit single-photon interference function sin2(Nβd/2)/sin2(βd/2). The second column shows the averaged intensity distributions with the N-slit random-phase gratings, in which each is a result over 10000 realizations of the random elementary phase ϕ, and the red curves are the theoretical fits using Eq. (3). And the third column represents the two-photon interference fringes with the N-slit random-phase gratings, in which the red curves are the theoretical fits with Eq. (6). Note that the vertical scale range increases from top to bottom in the third column, indicating an increase of the fringe visibility with increasing slit number N. Here we used a CCD camera to measure the intensity distributions on the detection plane, as shown in Fig. 4. In all cases, the slit number N of the grating was set to be 2, 3, 4 and 5, respectively.

Equations (9)

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E ^ ( + ) ( x j ) b 2 b 2 e i β j x s d x s n = 1 N e i ( n 1 ) β j d e i ( n 1 ) ϕ a ^ .
G ( 1 ) ( x j , x j ) = E * ( x j ) E ( x j ) ,
G ( 1 ) ( x j , x j ) N [ sin ( β j b / 2 ) β j b / 2 ] 2 .
G ( 2 ) ( x 1 , x 2 ) = E * ( x 1 ) E * ( x 2 ) E ( x 1 ) E ( x 2 ) .
G ( 2 ) ( x 1 , x 2 ) l = 0 2 N 2 | j = 1 2 b 2 b 2 e i β j x s d x s × ( m , n ) ; m + n 2 = l [ e i ( n 1 ) ( β 1 d ϕ ) e i ( m 1 ) ( β 2 d ϕ ) + ( 1 δ ( m n ) ) e i ( n 1 ) ( β 2 d ϕ ) e i ( m 1 ) ( β 1 d ϕ ) ] | 2 j = 1 2 [ sin ( β j b / 2 ) β j b / 2 ] 2 × l = 0 2 N 2 | ( m , n ) ; m + n 2 = l [ e i n β 1 d e i m β 2 d + ( 1 δ ( m n ) ) e i n β 2 d e i m β 1 d ] | 2 ,
g ( 2 ) ( x 1 , x 2 ) = G ( 2 ) ( x 1 , x 2 ) G ( 1 ) ( x 1 , x 1 ) G ( 1 ) ( x 2 , x 2 ) = 1 N 2 l = N N 1 sin 2 ( ( l + 1 ) ( β 1 β 2 ) d / 2 ) sin 2 ( ( β 1 β 2 ) d / 2 ) .
G ( 2 ) ( x 1 , x 2 ) = | E ( x 1 ) E ( x 2 ) | 2 | j = 1 2 b 2 b 2 e i β j x s d x s × n = 1 N m = 1 N e i ( n 1 ) ( β 1 d ϕ ) e i ( m 1 ) ( β 2 d ϕ ) | 2
e i ( n 1 ) ( β 1 d ϕ ) e i ( m 1 ) ( β 2 d ϕ ) e i ( n 1 ) ( β 1 d ϕ ) e i ( m 1 ) ( β 2 d ϕ )
g ( 2 ) ( x 1 , x 2 ) = G ( 2 ) ( x 1 , x 2 ) G ( 1 ) ( x 1 , x 1 ) G ( 1 ) ( x 2 , x 2 ) = 1 N 2 l = 0 2 N 2 | ( m , n ) ; m + n 2 = l [ e i n β 1 d e i m β 2 d + ( 1 δ ( m n ) ) e i n β 2 d e i m β 1 d ] | 2 = 1 N 2 l = 0 N 1 | m = 1 l + 1 e i m β 1 d e i ( l + 2 m ) β 2 d | 2 + l = N 2 N 2 | m = l + 2 N N e i m β 1 d e i ( l + 2 m ) β 2 d | 2 = 1 N 2 l = 0 N 1 | m = 1 l + 1 e i m ( β 1 β 2 d ) | 2 + l = N 2 N 2 | m = l + 2 N N e i m ( β 1 β 2 ) d | 2 = 1 N 2 l = 0 N 1 sin 2 ( ( l + 1 ) ( β 1 β 2 ) d / 2 ) sin 2 ( ( β 1 β 2 ) d / 2 ) + l = N 2 N 2 sin 2 ( ( l + 1 2 N ) ( β 1 β 2 ) d / 2 ) sin 2 ( ( β 1 β 2 ) d / 2 ) = 1 N 2 l = N N 1 sin 2 ( ( l + 1 ) ( β 1 β 2 ) d / 2 ) sin 2 ( ( β 1 β 2 ) d / 2 ) .

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