Abstract

The spatial second-order interference of two independent pseudothermal light beams in a Hong-Ou-Mandel interferometer is studied experimentally and theoretically. The similar cosine modulation in the second-order coherence function as the one with entangled-photon pairs in a Hong-Ou-Mandel interferometer is observed. Two-photon interference based on Feynman’s path integral theory is employed to interpret the results. The experimental results and theoretical simulations agree with each other very well.

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  1. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurent of subpicosecond time intervals betweens two photons by interference,” Phys. Rev. Lett.59, 2044–2046 (1987).
    [CrossRef] [PubMed]
  2. Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett.61, 2921–2914 (1988).
    [CrossRef] [PubMed]
  3. L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys.71, S274–282 (1999).
    [CrossRef]
  4. P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a ’quantum eraser’: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A45, 7729–7739 (1992).
    [CrossRef] [PubMed]
  5. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett.68, 2421–2414 (1992).
    [CrossRef] [PubMed]
  6. M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett.91, 083601 (2003).
    [CrossRef] [PubMed]
  7. S. P. Walborn, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interference,” Phys. Rev. Lett.90, 143601 (2003).
    [CrossRef] [PubMed]
  8. O. Cosme, S. Pádua, F. A. Bovino, A. Mazzei, F. Sciarrino, and F. De Martini, “Hong-Ou-Mandel interferometer with one and two photon pairs,” Phys. Rev. A77, 053822 (2008).
    [CrossRef]
  9. Z. Y. Jeff Ou, Multi-Photon Quantum Interference (Springer Science+Business Media, LLC, 2007).
  10. Z. Y. Ou, E. C. G. Gage, B. E. Magill, and L. Mandel, “Fourth-order interference technique for determining the coherence time of a light beam,” J. Opt. Soc. Am. B6, 100–103 (1989).
    [CrossRef]
  11. R. Kaltenbaek, B. Blauensteiner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental Interference of Independent Photons,” Phys. Rev. Lett.96, 240502 (2006).
    [CrossRef] [PubMed]
  12. R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometry with chirped laser pulses,” Nat. Phys.4, 864–868 (2008).
    [CrossRef]
  13. H. Chen, T. Peng, S. Karmakar, Z. D. Xie, and Y. H. Shih, “Observation of anticorrelation in incoherent thermal light fields,” Phys. Rev. A84, 033835 (2011).
    [CrossRef]
  14. H. Kim, O. Kwon, W. Kim, and T. Kim, “Spatial two-photon interference in a Hong-Ou-Mandel interferometer,” Phys. Rev. A73, 023820 (2006).
    [CrossRef]
  15. B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A62, 043816 (2000).
    [CrossRef]
  16. S. Olivares and M. G. A. Paris, “Fidelity matters: the birth of entanglement in the mixing of gaussian states,” Phys. Rev. Lett.107, 170505 (2011).
    [CrossRef] [PubMed]
  17. G. Brida, I. P. Degiovanni, M. Genovese, A. Meda, S. Olivares, and M Paris, “The illusionist game and hidden correlations,” Phys. Scr.T153, 014006 (2013).
    [CrossRef]
  18. W. Martienssen and E. Spiller, “Coherence and fluctuation in light beams,” Am. J. Phys.32, 919–926 (1964).
    [CrossRef]
  19. R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature(London)177, 27–29 (1956); “A test of a new type of stellar interferometer on sirius,” Nature(London)178, 1046–1048 (1956).
    [CrossRef]
  20. R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev.131, 2766–2788 (1963).
    [CrossRef]
  21. E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett.10, 277–279 (1963).
    [CrossRef]
  22. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, Inc., 1965).
  23. Y. H. Shih, An Introduction to Quantum Optics (CRC Press, 2011).
  24. R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford Univ. Press, 2001).
  25. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Westview Press, Colorado, 1995).
  26. J. B. Liu and G. Q. Zhang, “Unified interpretation for second-order subwavelength interference based on Feyn-mans path-integral theory,” Phys. Rev. A82, 013822 (2010).
    [CrossRef]
  27. F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconuctors,” Nat. Phys.5, 267–270 (2009).
    [CrossRef]
  28. A. Nevet, A. Hayat, P. Ginzburg, and M. Orenstein, “Indistinguishable photon pairs from independent true chaotic sources,” Phys. Rev. Lett.107, 253601 (2011).
    [CrossRef]
  29. We thank the anonymous reviewer for bringing this method into our attention.

2013

G. Brida, I. P. Degiovanni, M. Genovese, A. Meda, S. Olivares, and M Paris, “The illusionist game and hidden correlations,” Phys. Scr.T153, 014006 (2013).
[CrossRef]

2011

H. Chen, T. Peng, S. Karmakar, Z. D. Xie, and Y. H. Shih, “Observation of anticorrelation in incoherent thermal light fields,” Phys. Rev. A84, 033835 (2011).
[CrossRef]

S. Olivares and M. G. A. Paris, “Fidelity matters: the birth of entanglement in the mixing of gaussian states,” Phys. Rev. Lett.107, 170505 (2011).
[CrossRef] [PubMed]

A. Nevet, A. Hayat, P. Ginzburg, and M. Orenstein, “Indistinguishable photon pairs from independent true chaotic sources,” Phys. Rev. Lett.107, 253601 (2011).
[CrossRef]

2010

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

2009

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconuctors,” Nat. Phys.5, 267–270 (2009).
[CrossRef]

2008

R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometry with chirped laser pulses,” Nat. Phys.4, 864–868 (2008).
[CrossRef]

O. Cosme, S. Pádua, F. A. Bovino, A. Mazzei, F. Sciarrino, and F. De Martini, “Hong-Ou-Mandel interferometer with one and two photon pairs,” Phys. Rev. A77, 053822 (2008).
[CrossRef]

2006

R. Kaltenbaek, B. Blauensteiner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental Interference of Independent Photons,” Phys. Rev. Lett.96, 240502 (2006).
[CrossRef] [PubMed]

H. Kim, O. Kwon, W. Kim, and T. Kim, “Spatial two-photon interference in a Hong-Ou-Mandel interferometer,” Phys. Rev. A73, 023820 (2006).
[CrossRef]

2003

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett.91, 083601 (2003).
[CrossRef] [PubMed]

S. P. Walborn, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interference,” Phys. Rev. Lett.90, 143601 (2003).
[CrossRef] [PubMed]

2000

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A62, 043816 (2000).
[CrossRef]

1999

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys.71, S274–282 (1999).
[CrossRef]

1992

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a ’quantum eraser’: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A45, 7729–7739 (1992).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett.68, 2421–2414 (1992).
[CrossRef] [PubMed]

1989

1988

Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett.61, 2921–2914 (1988).
[CrossRef] [PubMed]

1987

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurent of subpicosecond time intervals betweens two photons by interference,” Phys. Rev. Lett.59, 2044–2046 (1987).
[CrossRef] [PubMed]

1964

W. Martienssen and E. Spiller, “Coherence and fluctuation in light beams,” Am. J. Phys.32, 919–926 (1964).
[CrossRef]

1963

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

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett.10, 277–279 (1963).
[CrossRef]

1956

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature(London)177, 27–29 (1956); “A test of a new type of stellar interferometer on sirius,” Nature(London)178, 1046–1048 (1956).
[CrossRef]

Abouraddy, A. F.

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A62, 043816 (2000).
[CrossRef]

Alley, C. O.

Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett.61, 2921–2914 (1988).
[CrossRef] [PubMed]

Aspelmeyer, M.

R. Kaltenbaek, B. Blauensteiner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental Interference of Independent Photons,” Phys. Rev. Lett.96, 240502 (2006).
[CrossRef] [PubMed]

Biggerstaff, D. N.

R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometry with chirped laser pulses,” Nat. Phys.4, 864–868 (2008).
[CrossRef]

Blauensteiner, B.

R. Kaltenbaek, B. Blauensteiner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental Interference of Independent Photons,” Phys. Rev. Lett.96, 240502 (2006).
[CrossRef] [PubMed]

Boitier, F.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconuctors,” Nat. Phys.5, 267–270 (2009).
[CrossRef]

Bovino, F. A.

O. Cosme, S. Pádua, F. A. Bovino, A. Mazzei, F. Sciarrino, and F. De Martini, “Hong-Ou-Mandel interferometer with one and two photon pairs,” Phys. Rev. A77, 053822 (2008).
[CrossRef]

Brida, G.

G. Brida, I. P. Degiovanni, M. Genovese, A. Meda, S. Olivares, and M Paris, “The illusionist game and hidden correlations,” Phys. Scr.T153, 014006 (2013).
[CrossRef]

Chen, H.

H. Chen, T. Peng, S. Karmakar, Z. D. Xie, and Y. H. Shih, “Observation of anticorrelation in incoherent thermal light fields,” Phys. Rev. A84, 033835 (2011).
[CrossRef]

Chiao, R. Y.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett.68, 2421–2414 (1992).
[CrossRef] [PubMed]

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a ’quantum eraser’: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A45, 7729–7739 (1992).
[CrossRef] [PubMed]

Cosme, O.

O. Cosme, S. Pádua, F. A. Bovino, A. Mazzei, F. Sciarrino, and F. De Martini, “Hong-Ou-Mandel interferometer with one and two photon pairs,” Phys. Rev. A77, 053822 (2008).
[CrossRef]

De Martini, F.

O. Cosme, S. Pádua, F. A. Bovino, A. Mazzei, F. Sciarrino, and F. De Martini, “Hong-Ou-Mandel interferometer with one and two photon pairs,” Phys. Rev. A77, 053822 (2008).
[CrossRef]

de Oliveira, A. N.

S. P. Walborn, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interference,” Phys. Rev. Lett.90, 143601 (2003).
[CrossRef] [PubMed]

Degiovanni, I. P.

G. Brida, I. P. Degiovanni, M. Genovese, A. Meda, S. Olivares, and M Paris, “The illusionist game and hidden correlations,” Phys. Scr.T153, 014006 (2013).
[CrossRef]

Fabre, C.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconuctors,” Nat. Phys.5, 267–270 (2009).
[CrossRef]

Feynman, R. P.

R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, Inc., 1965).

Gage, E. C. G.

Genovese, M.

G. Brida, I. P. Degiovanni, M. Genovese, A. Meda, S. Olivares, and M Paris, “The illusionist game and hidden correlations,” Phys. Scr.T153, 014006 (2013).
[CrossRef]

Ginzburg, P.

A. Nevet, A. Hayat, P. Ginzburg, and M. Orenstein, “Indistinguishable photon pairs from independent true chaotic sources,” Phys. Rev. Lett.107, 253601 (2011).
[CrossRef]

Glauber, R. J.

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

Godard, A.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconuctors,” Nat. Phys.5, 267–270 (2009).
[CrossRef]

Hanbury Brown, R.

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature(London)177, 27–29 (1956); “A test of a new type of stellar interferometer on sirius,” Nature(London)178, 1046–1048 (1956).
[CrossRef]

Hayat, A.

A. Nevet, A. Hayat, P. Ginzburg, and M. Orenstein, “Indistinguishable photon pairs from independent true chaotic sources,” Phys. Rev. Lett.107, 253601 (2011).
[CrossRef]

Hibbs, A. R.

R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, Inc., 1965).

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurent of subpicosecond time intervals betweens two photons by interference,” Phys. Rev. Lett.59, 2044–2046 (1987).
[CrossRef] [PubMed]

Jeff Ou, Z. Y.

Z. Y. Jeff Ou, Multi-Photon Quantum Interference (Springer Science+Business Media, LLC, 2007).

Kaltenbaek, R.

R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometry with chirped laser pulses,” Nat. Phys.4, 864–868 (2008).
[CrossRef]

R. Kaltenbaek, B. Blauensteiner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental Interference of Independent Photons,” Phys. Rev. Lett.96, 240502 (2006).
[CrossRef] [PubMed]

Karmakar, S.

H. Chen, T. Peng, S. Karmakar, Z. D. Xie, and Y. H. Shih, “Observation of anticorrelation in incoherent thermal light fields,” Phys. Rev. A84, 033835 (2011).
[CrossRef]

Kim, H.

H. Kim, O. Kwon, W. Kim, and T. Kim, “Spatial two-photon interference in a Hong-Ou-Mandel interferometer,” Phys. Rev. A73, 023820 (2006).
[CrossRef]

Kim, T.

H. Kim, O. Kwon, W. Kim, and T. Kim, “Spatial two-photon interference in a Hong-Ou-Mandel interferometer,” Phys. Rev. A73, 023820 (2006).
[CrossRef]

Kim, W.

H. Kim, O. Kwon, W. Kim, and T. Kim, “Spatial two-photon interference in a Hong-Ou-Mandel interferometer,” Phys. Rev. A73, 023820 (2006).
[CrossRef]

Kwiat, P. G.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett.68, 2421–2414 (1992).
[CrossRef] [PubMed]

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a ’quantum eraser’: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A45, 7729–7739 (1992).
[CrossRef] [PubMed]

Kwon, O.

H. Kim, O. Kwon, W. Kim, and T. Kim, “Spatial two-photon interference in a Hong-Ou-Mandel interferometer,” Phys. Rev. A73, 023820 (2006).
[CrossRef]

Lavoie, J.

R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometry with chirped laser pulses,” Nat. Phys.4, 864–868 (2008).
[CrossRef]

Liu, J. B.

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

Loudon, R.

R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford Univ. Press, 2001).

Magill, B. E.

Mandel, L.

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys.71, S274–282 (1999).
[CrossRef]

Z. Y. Ou, E. C. G. Gage, B. E. Magill, and L. Mandel, “Fourth-order interference technique for determining the coherence time of a light beam,” J. Opt. Soc. Am. B6, 100–103 (1989).
[CrossRef]

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurent of subpicosecond time intervals betweens two photons by interference,” Phys. Rev. Lett.59, 2044–2046 (1987).
[CrossRef] [PubMed]

Martienssen, W.

W. Martienssen and E. Spiller, “Coherence and fluctuation in light beams,” Am. J. Phys.32, 919–926 (1964).
[CrossRef]

Mazzei, A.

O. Cosme, S. Pádua, F. A. Bovino, A. Mazzei, F. Sciarrino, and F. De Martini, “Hong-Ou-Mandel interferometer with one and two photon pairs,” Phys. Rev. A77, 053822 (2008).
[CrossRef]

Meda, A.

G. Brida, I. P. Degiovanni, M. Genovese, A. Meda, S. Olivares, and M Paris, “The illusionist game and hidden correlations,” Phys. Scr.T153, 014006 (2013).
[CrossRef]

Monken, C. H.

S. P. Walborn, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interference,” Phys. Rev. Lett.90, 143601 (2003).
[CrossRef] [PubMed]

Nasr, M. B.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett.91, 083601 (2003).
[CrossRef] [PubMed]

Nevet, A.

A. Nevet, A. Hayat, P. Ginzburg, and M. Orenstein, “Indistinguishable photon pairs from independent true chaotic sources,” Phys. Rev. Lett.107, 253601 (2011).
[CrossRef]

Olivares, S.

G. Brida, I. P. Degiovanni, M. Genovese, A. Meda, S. Olivares, and M Paris, “The illusionist game and hidden correlations,” Phys. Scr.T153, 014006 (2013).
[CrossRef]

S. Olivares and M. G. A. Paris, “Fidelity matters: the birth of entanglement in the mixing of gaussian states,” Phys. Rev. Lett.107, 170505 (2011).
[CrossRef] [PubMed]

Orenstein, M.

A. Nevet, A. Hayat, P. Ginzburg, and M. Orenstein, “Indistinguishable photon pairs from independent true chaotic sources,” Phys. Rev. Lett.107, 253601 (2011).
[CrossRef]

Ou, Z. Y.

Z. Y. Ou, E. C. G. Gage, B. E. Magill, and L. Mandel, “Fourth-order interference technique for determining the coherence time of a light beam,” J. Opt. Soc. Am. B6, 100–103 (1989).
[CrossRef]

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurent of subpicosecond time intervals betweens two photons by interference,” Phys. Rev. Lett.59, 2044–2046 (1987).
[CrossRef] [PubMed]

Pádua, S.

O. Cosme, S. Pádua, F. A. Bovino, A. Mazzei, F. Sciarrino, and F. De Martini, “Hong-Ou-Mandel interferometer with one and two photon pairs,” Phys. Rev. A77, 053822 (2008).
[CrossRef]

S. P. Walborn, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interference,” Phys. Rev. Lett.90, 143601 (2003).
[CrossRef] [PubMed]

Paris, M

G. Brida, I. P. Degiovanni, M. Genovese, A. Meda, S. Olivares, and M Paris, “The illusionist game and hidden correlations,” Phys. Scr.T153, 014006 (2013).
[CrossRef]

Paris, M. G. A.

S. Olivares and M. G. A. Paris, “Fidelity matters: the birth of entanglement in the mixing of gaussian states,” Phys. Rev. Lett.107, 170505 (2011).
[CrossRef] [PubMed]

Peng, T.

H. Chen, T. Peng, S. Karmakar, Z. D. Xie, and Y. H. Shih, “Observation of anticorrelation in incoherent thermal light fields,” Phys. Rev. A84, 033835 (2011).
[CrossRef]

Peskin, M. E.

M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Westview Press, Colorado, 1995).

Resch, K. J.

R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometry with chirped laser pulses,” Nat. Phys.4, 864–868 (2008).
[CrossRef]

Rosencher, E.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconuctors,” Nat. Phys.5, 267–270 (2009).
[CrossRef]

Saleh, B. E. A.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett.91, 083601 (2003).
[CrossRef] [PubMed]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A62, 043816 (2000).
[CrossRef]

Schroeder, D. V.

M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Westview Press, Colorado, 1995).

Sciarrino, F.

O. Cosme, S. Pádua, F. A. Bovino, A. Mazzei, F. Sciarrino, and F. De Martini, “Hong-Ou-Mandel interferometer with one and two photon pairs,” Phys. Rev. A77, 053822 (2008).
[CrossRef]

Sergienko, A. V.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett.91, 083601 (2003).
[CrossRef] [PubMed]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A62, 043816 (2000).
[CrossRef]

Shih, Y. H.

H. Chen, T. Peng, S. Karmakar, Z. D. Xie, and Y. H. Shih, “Observation of anticorrelation in incoherent thermal light fields,” Phys. Rev. A84, 033835 (2011).
[CrossRef]

Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett.61, 2921–2914 (1988).
[CrossRef] [PubMed]

Y. H. Shih, An Introduction to Quantum Optics (CRC Press, 2011).

Spiller, E.

W. Martienssen and E. Spiller, “Coherence and fluctuation in light beams,” Am. J. Phys.32, 919–926 (1964).
[CrossRef]

Steinberg, A. M.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a ’quantum eraser’: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A45, 7729–7739 (1992).
[CrossRef] [PubMed]

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We thank the anonymous reviewer for bringing this method into our attention.

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Figures (3)

Fig. 1
Fig. 1

HOM interferometer with two independent pseudothermal light beams. Laser: Single-mode cw laser with central wavelength λ = 780 nm. BS: 50:50 non-polarized beam splitter. HP: Half wave plate. M: Mirror. L: Lens. RG: Rotating ground glass. D: Single-photon detector. In the inset, Sj: Source j (j = 1, and 2). S′2: Virtual source image of S2 respect to BS2. The lengthes of S1 and S2 are l1 and l2, respectively. The distance between the middle points of S1 and S′2 is d. The distances between the source planes and the detector planes all equal z.

Fig. 2
Fig. 2

The spatial second-order coherence functions of two independent pseudothermal light beams in a HOM interferometer. (a) and (b) are the second-order coherence functions of the fields emitted by S1 and S2 when the other source is blocked, respectively. (c) and (d) are second-order spatial coherence functions when the light beams emitted by S1 and S2 have orthogonal and parallel polarizations, respectively. The dots with error bars are experimental results and the red lines are theoretical simulations employed the following equations. The coordinates of all four experiments are the same. It is well-known that the two-photon spatial bunching peak of thermal light is observed when the two detectors are in the symmetric positions ((a) and (b)). Hence the second-order interference dip in (d) is also observed when the two detectors are in the symmetric positions. Please see text for detail.

Fig. 3
Fig. 3

Second-order coherence function vs. d when the photons emitted by S1 and S2 have parallel polarizations. Simulated parameters are the same as the ones in Fig. 2 except the visibility is ideal. Please refer to Fig. 1 for the meaning of d.

Tables (1)

Tables Icon

Table 1 Extra phases correspond to different pathes

Equations (9)

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G ( 2 ) ( r 1 , t 1 ; r 2 , t 2 ) = | i , j , m , n = 1 , 2 m n A aim , bjn | 2 ,
G ( 2 ) ( r 1 , t 1 ; r 2 , t 2 ) = | exp i ( φ a 2 + φ b 2 + π 2 ) ( A a 21 , b 22 + A a 22 , b 21 ) + exp i ( φ a 1 + φ b 1 + π 2 ) ( A a 11 , b 12 + A a 12 , b 11 ) + exp i ( φ a 2 + φ b 1 ) ( A a 22 , b 11 A a 21 , b 12 ) + exp i ( φ a 1 + φ b 2 ) ( A a 11 , b 22 A a 12 , b 21 ) | 2 ,
G ( 2 ) ( r 1 , t 1 ; r 2 , t 2 ) = | A a 21 , b 22 + A a 22 , b 21 | 2 + | A a 11 , b 12 + A a 12 , b 11 | 2 + | A a 22 , b 11 A a 21 , b 12 | 2 + | A a 11 , b 22 A a 12 , b 21 | 2 .
A aim , bjn = A aim A bjn ,
A bjn = exp i ( k jn r jn ω t n ) r j n .
± d 2 l 2 ± d 2 + l 2 exp [ i k ( x 1 x 2 ) x z ] d x = l exp [ i k ( x 1 x 2 ) ( ± d ) 2 z ] sinc [ k ( x 1 x 2 ) l 2 z ] ,
G ( 2 ) ( x 1 x 2 ) = l 1 2 [ 1 + sinc 2 π l 1 λ z ( x 1 x 2 ) ] + l 2 2 [ 1 + sinc 2 π l 2 λ z ( x 1 x 2 ) ] + 2 l 1 l 2 { 1 cos [ 2 π d λ z ( x 1 x 2 ) ] × sinc π l 1 λ z ( x 1 x 2 ) sinc π l 2 λ z ( x 1 x 2 ) } ,
g ( 2 ) ( x 1 x 2 ) = 1 + 1 2 sinc 2 [ π l λ z ( x 1 x 2 ) ] ,
g ( 2 ) ( x 1 x 2 ) = 1 + 1 2 sinc 2 π l λ z ( x 1 x 2 ) 1 2 cos [ 2 π d λ z ( x 1 x 2 ) ] sinc 2 π l λ z ( x 1 x 2 ) .

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