Abstract

The first- and second-order temporal interference between two independent thermal and laser light beams is discussed by employing the superposition principle in Feynman’s path integral theory. It is concluded that the first-order temporal interference pattern can not be observed by superposing two independent thermal and laser light beams, while the second-order temporal interference pattern can be observed in the same condition. These predictions are experimentally verified by employing pseudothermal light to simulate thermal light. The relationship between the indistinguishability of alternatives and photons is analyzed. The conclusions are helpful to understand the interference of different kinds of light and the difference between the coherence properties of thermal and laser light.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  36. L. Mandel, “Photon interference and correlation effects produced by independent quantum sources,” Phys. Rev. A 28, 929–943 (1983).
    [Crossref]
  37. E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963).
    [Crossref]
  38. R. H. Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations in light. I. basic theory: the correlation between photons in coherent beams of radiation,” Proc. R. Soc. (London) A242, 300–324 (1957).
    [Crossref]
  39. R. H. Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations in light II. an experimental test of the theory for partially coherent light,” Proc. R. Soc. (London) A243, 291–319 (1958).
    [Crossref]
  40. Z. Y. Ou and L. Mandel, “Observation of spatial quantum beating with seperated photodetectors,” Phys. Rev. Lett. 61, 54–57 (1988).
    [Crossref] [PubMed]
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    [Crossref]

2014 (2)

J. B. Liu, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference between laser and thermal light,” Europhys. Lett. 105, 64007 (2014).
[Crossref]

Y. S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Two-photon interference with continuous-wave multi-mode coherent light,” Opt. Express 22, 3611–3620 (2014).
[Crossref] [PubMed]

2013 (2)

J. B. Liu, Y. Zhou, W. T. Wang, R. F. Liu, K. He, F. L. Li, and Z. Xu, “Spatial second-order interference of pseudothermal light in a Hong-Ou-Mandel interferometer,” Opt. Express 16, 19209–19218 (2013).
[Crossref]

Y. S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “‘Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
[Crossref]

2012 (1)

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod, Phys. 84, 777–838 (2012).
[Crossref]

2011 (3)

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

H. Chen, T. Peng, S. Karmakar, Z. D. Xie, and Y. H. Shih, “Observation of anticorrelation in incoherent thermal light fields,” Phys. Rev. A 84, 033835 (2011).
[Crossref]

J. B. Liu and G. Q. Zhang, “Observation on the incompatibility between the first-order and second-order interferences with laser beams,” Opt. Commun. 284, 2658–2661 (2011).
[Crossref]

2010 (3)

L. Q. Chen, C. L. Bian, G. W. Zhang, Z. Y. Ou, and W. P. Zhang, “Observation of temporal beating in first- and second-order intensity measurement between independent Raman Stokes fields in atomic vapor,” Phys. Rev. A 82, 033832 (2010).
[Crossref]

I. Afek, O. Ambar, and Y. Silberberg, “High-N00N states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[Crossref] [PubMed]

J. B. Liu and G. Q. Zhang, “Unified interpretation for second-order subwavelength interference based on Feyn-man’s path-integral theory,” Phys. Rev. A 83, 013822 (2010).
[Crossref]

2009 (1)

A. J. Bennett, R. B. Patel, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Interference of dissimilar photon sources,” Nature Phys. 5, 715–717 (2009).
[Crossref]

2008 (1)

R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometery with chirped laser pulses,” Nature Phys. 8, 864–868 (2008).
[Crossref]

2006 (1)

Y. H. Zhai, X. H. Chen, and L. A. Wu, “Two-photon interference with two independent pseudothermal sources,” Phys. Rev. A 74, 053807 (2006).
[Crossref]

1999 (2)

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S287 (1999).
[Crossref]

A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288–S297 (1999).
[Crossref]

1989 (1)

1988 (2)

Z. Y. Ou and L. Mandel, “Observation of spatial quantum beating with seperated photodetectors,” Phys. Rev. Lett. 61, 54–57 (1988).
[Crossref] [PubMed]

Z. Y. Ou, E. C. Gage, B. E. Magill, and L. Mandel, “Observation of beating between blue and green light,” Opt. Commun. 69, 1–5 (1988).
[Crossref]

1986 (1)

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

1983 (1)

L. Mandel, “Photon interference and correlation effects produced by independent quantum sources,” Phys. Rev. A 28, 929–943 (1983).
[Crossref]

1967 (1)

R. L. Pfleegor and L. Mandel, “Interference of independent photon beams,” Phys. Rev. 159, 1084–1088 (1967).
[Crossref]

1965 (1)

L. Mandel and E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[Crossref]

1964 (1)

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

1963 (5)

M. S. Lipsett and L. Mandel, “Coherence time measurement of light from a ruby optical maser,” Nature (Loudon) 199, 553–555 (1963).
[Crossref]

G. Magyar and L. Mandel, “Interference fringes produced by superposition of two independent maser light beams,” Nature (Loudon) 198, 255–256 (1963).
[Crossref]

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

R. J. Glauber, “Coherent and incoherent states of 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]

1962 (1)

1958 (1)

R. H. Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations in light II. an experimental test of the theory for partially coherent light,” Proc. R. Soc. (London) A243, 291–319 (1958).
[Crossref]

1957 (1)

R. H. Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations in light. I. basic theory: the correlation between photons in coherent beams of radiation,” Proc. R. Soc. (London) A242, 300–324 (1957).
[Crossref]

1956 (1)

R. H. Brown and R. Q. Twiss, “Corrrelation between photons in two coherent beams of light,” Nature (Loudon) 177, 27–29 (1956);
[Crossref]

1917 (1)

A. Einstein, “On the quantum theory of radiation,” Phys. Zs. 18, 121–135 (1917).

Afek, I.

I. Afek, O. Ambar, and Y. Silberberg, “High-N00N states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[Crossref] [PubMed]

Ambar, O.

I. Afek, O. Ambar, and Y. Silberberg, “High-N00N states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[Crossref] [PubMed]

Ballik, E. A.

Bennett, A. J.

A. J. Bennett, R. B. Patel, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Interference of dissimilar photon sources,” Nature Phys. 5, 715–717 (2009).
[Crossref]

Bian, C. L.

L. Q. Chen, C. L. Bian, G. W. Zhang, Z. Y. Ou, and W. P. Zhang, “Observation of temporal beating in first- and second-order intensity measurement between independent Raman Stokes fields in atomic vapor,” Phys. Rev. A 82, 033832 (2010).
[Crossref]

Biggerstaff, D. N.

R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometery with chirped laser pulses,” Nature Phys. 8, 864–868 (2008).
[Crossref]

Bond, W. L.

Born, M.

M. Born and E. Wolf, Principle of Optics, 7. (Cambridge University Press, Cambridge, 1999).
[Crossref]

Brown, R. H.

R. H. Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations in light II. an experimental test of the theory for partially coherent light,” Proc. R. Soc. (London) A243, 291–319 (1958).
[Crossref]

R. H. Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations in light. I. basic theory: the correlation between photons in coherent beams of radiation,” Proc. R. Soc. (London) A242, 300–324 (1957).
[Crossref]

R. H. Brown and R. Q. Twiss, “Corrrelation between photons in two coherent beams of light,” Nature (Loudon) 177, 27–29 (1956);
[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. A 84, 033835 (2011).
[Crossref]

J. B. Liu, Y. Zhou, H. B. Zheng, H. Chen, F. L. Li, and Z. Xu, “Two-photon interference with non-identical photons,” arXiv: physics.optics, 1412.2308 (2014).

Chen, L. Q.

L. Q. Chen, C. L. Bian, G. W. Zhang, Z. Y. Ou, and W. P. Zhang, “Observation of temporal beating in first- and second-order intensity measurement between independent Raman Stokes fields in atomic vapor,” Phys. Rev. A 82, 033832 (2010).
[Crossref]

Chen, X. H.

Y. H. Zhai, X. H. Chen, and L. A. Wu, “Two-photon interference with two independent pseudothermal sources,” Phys. Rev. A 74, 053807 (2006).
[Crossref]

Chen, Z. B.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod, Phys. 84, 777–838 (2012).
[Crossref]

Dirac, P. A. M.

P. A. M. Dirac, The Principles of Quantum Mechanics4. (Science Press, Beijing, 2008).

Einstein, A.

A. Einstein, “On the quantum theory of radiation,” Phys. Zs. 18, 121–135 (1917).

Feynman, R. P.

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

Gage, E. C.

Z. Y. Ou, E. C. Gage, B. E. Magill, and L. Mandel, “Fourth-order interference technique for determining the coherence time of a light beam,” J. Opt. Soc. Am. B 6, 100–103 (1989).
[Crossref]

Z. Y. Ou, E. C. Gage, B. E. Magill, and L. Mandel, “Observation of beating between blue and green light,” Opt. Commun. 69, 1–5 (1988).
[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, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[Crossref]

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

He, K.

J. B. Liu, Y. Zhou, W. T. Wang, R. F. Liu, K. He, F. L. Li, and Z. Xu, “Spatial second-order interference of pseudothermal light in a Hong-Ou-Mandel interferometer,” Opt. Express 16, 19209–19218 (2013).
[Crossref]

Hibbs, A. R.

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

Javan, A.

Kaltenbaek, R.

R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometery with chirped laser pulses,” Nature Phys. 8, 864–868 (2008).
[Crossref]

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. A 84, 033835 (2011).
[Crossref]

Kim, Y. S.

Y. S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Two-photon interference with continuous-wave multi-mode coherent light,” Opt. Express 22, 3611–3620 (2014).
[Crossref] [PubMed]

Y. S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “‘Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
[Crossref]

Kuo, P. S.

Y. S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Two-photon interference with continuous-wave multi-mode coherent light,” Opt. Express 22, 3611–3620 (2014).
[Crossref] [PubMed]

Y. S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “‘Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
[Crossref]

Lavoie, J.

R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometery with chirped laser pulses,” Nature Phys. 8, 864–868 (2008).
[Crossref]

Li, F. L.

J. B. Liu, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference between laser and thermal light,” Europhys. Lett. 105, 64007 (2014).
[Crossref]

J. B. Liu, Y. Zhou, W. T. Wang, R. F. Liu, K. He, F. L. Li, and Z. Xu, “Spatial second-order interference of pseudothermal light in a Hong-Ou-Mandel interferometer,” Opt. Express 16, 19209–19218 (2013).
[Crossref]

J. B. Liu, Y. Zhou, H. B. Zheng, H. Chen, F. L. Li, and Z. Xu, “Two-photon interference with non-identical photons,” arXiv: physics.optics, 1412.2308 (2014).

Lipsett, M. S.

M. S. Lipsett and L. Mandel, “Coherence time measurement of light from a ruby optical maser,” Nature (Loudon) 199, 553–555 (1963).
[Crossref]

Liu, J. B.

J. B. Liu, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference between laser and thermal light,” Europhys. Lett. 105, 64007 (2014).
[Crossref]

J. B. Liu, Y. Zhou, W. T. Wang, R. F. Liu, K. He, F. L. Li, and Z. Xu, “Spatial second-order interference of pseudothermal light in a Hong-Ou-Mandel interferometer,” Opt. Express 16, 19209–19218 (2013).
[Crossref]

J. B. Liu and G. Q. Zhang, “Observation on the incompatibility between the first-order and second-order interferences with laser beams,” Opt. Commun. 284, 2658–2661 (2011).
[Crossref]

J. B. Liu and G. Q. Zhang, “Unified interpretation for second-order subwavelength interference based on Feyn-man’s path-integral theory,” Phys. Rev. A 83, 013822 (2010).
[Crossref]

J. B. Liu, Y. Zhou, H. B. Zheng, H. Chen, F. L. Li, and Z. Xu, “Two-photon interference with non-identical photons,” arXiv: physics.optics, 1412.2308 (2014).

Liu, R. F.

J. B. Liu, Y. Zhou, W. T. Wang, R. F. Liu, K. He, F. L. Li, and Z. Xu, “Spatial second-order interference of pseudothermal light in a Hong-Ou-Mandel interferometer,” Opt. Express 16, 19209–19218 (2013).
[Crossref]

Loudon, R.

R. Loudon, The Quantum Theory of Light, 3. (Oxford University Press, New York, 2000).

Lu, C. Y.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod, Phys. 84, 777–838 (2012).
[Crossref]

Magill, B. E.

Z. Y. Ou, E. C. Gage, B. E. Magill, and L. Mandel, “Fourth-order interference technique for determining the coherence time of a light beam,” J. Opt. Soc. Am. B 6, 100–103 (1989).
[Crossref]

Z. Y. Ou, E. C. Gage, B. E. Magill, and L. Mandel, “Observation of beating between blue and green light,” Opt. Commun. 69, 1–5 (1988).
[Crossref]

Magyar, G.

G. Magyar and L. Mandel, “Interference fringes produced by superposition of two independent maser light beams,” Nature (Loudon) 198, 255–256 (1963).
[Crossref]

Mandel, L.

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S287 (1999).
[Crossref]

Z. Y. Ou, E. C. Gage, B. E. Magill, and L. Mandel, “Fourth-order interference technique for determining the coherence time of a light beam,” J. Opt. Soc. Am. B 6, 100–103 (1989).
[Crossref]

Z. Y. Ou, E. C. Gage, B. E. Magill, and L. Mandel, “Observation of beating between blue and green light,” Opt. Commun. 69, 1–5 (1988).
[Crossref]

Z. Y. Ou and L. Mandel, “Observation of spatial quantum beating with seperated photodetectors,” Phys. Rev. Lett. 61, 54–57 (1988).
[Crossref] [PubMed]

L. Mandel, “Photon interference and correlation effects produced by independent quantum sources,” Phys. Rev. A 28, 929–943 (1983).
[Crossref]

R. L. Pfleegor and L. Mandel, “Interference of independent photon beams,” Phys. Rev. 159, 1084–1088 (1967).
[Crossref]

L. Mandel and E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[Crossref]

G. Magyar and L. Mandel, “Interference fringes produced by superposition of two independent maser light beams,” Nature (Loudon) 198, 255–256 (1963).
[Crossref]

M. S. Lipsett and L. Mandel, “Coherence time measurement of light from a ruby optical maser,” Nature (Loudon) 199, 553–555 (1963).
[Crossref]

Martienssen, W.

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

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]

Nicoll, C. A.

A. J. Bennett, R. B. Patel, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Interference of dissimilar photon sources,” Nature Phys. 5, 715–717 (2009).
[Crossref]

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.

L. Q. Chen, C. L. Bian, G. W. Zhang, Z. Y. Ou, and W. P. Zhang, “Observation of temporal beating in first- and second-order intensity measurement between independent Raman Stokes fields in atomic vapor,” Phys. Rev. A 82, 033832 (2010).
[Crossref]

Z. Y. Ou, E. C. Gage, B. E. Magill, and L. Mandel, “Fourth-order interference technique for determining the coherence time of a light beam,” J. Opt. Soc. Am. B 6, 100–103 (1989).
[Crossref]

Z. Y. Ou, E. C. Gage, B. E. Magill, and L. Mandel, “Observation of beating between blue and green light,” Opt. Commun. 69, 1–5 (1988).
[Crossref]

Z. Y. Ou and L. Mandel, “Observation of spatial quantum beating with seperated photodetectors,” Phys. Rev. Lett. 61, 54–57 (1988).
[Crossref] [PubMed]

Pan, J. W.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod, Phys. 84, 777–838 (2012).
[Crossref]

Patel, R. B.

A. J. Bennett, R. B. Patel, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Interference of dissimilar photon sources,” Nature Phys. 5, 715–717 (2009).
[Crossref]

Paul, H.

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

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. A 84, 033835 (2011).
[Crossref]

Peskin, M. E.

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

Pfleegor, R. L.

R. L. Pfleegor and L. Mandel, “Interference of independent photon beams,” Phys. Rev. 159, 1084–1088 (1967).
[Crossref]

Resch, K. J.

R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometery with chirped laser pulses,” Nature Phys. 8, 864–868 (2008).
[Crossref]

Ritchie, D. A.

A. J. Bennett, R. B. Patel, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Interference of dissimilar photon sources,” Nature Phys. 5, 715–717 (2009).
[Crossref]

Schroeder, D. V.

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

Shields, A. J.

A. J. Bennett, R. B. Patel, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Interference of dissimilar photon sources,” Nature Phys. 5, 715–717 (2009).
[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. A 84, 033835 (2011).
[Crossref]

Y. H. Shih, An Introduction to Quantum Optics: Photons and Biphoton Physics (CRC Press, Taylor & Francis, London, 2011).

Silberberg, Y.

I. Afek, O. Ambar, and Y. Silberberg, “High-N00N states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[Crossref] [PubMed]

Slattery, O.

Y. S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Two-photon interference with continuous-wave multi-mode coherent light,” Opt. Express 22, 3611–3620 (2014).
[Crossref] [PubMed]

Y. S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “‘Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
[Crossref]

Spiller, E.

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

Sudarshan, E. C. G.

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

Tang, X.

Y. S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Two-photon interference with continuous-wave multi-mode coherent light,” Opt. Express 22, 3611–3620 (2014).
[Crossref] [PubMed]

Y. S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “‘Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
[Crossref]

Twiss, R. Q.

R. H. Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations in light II. an experimental test of the theory for partially coherent light,” Proc. R. Soc. (London) A243, 291–319 (1958).
[Crossref]

R. H. Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations in light. I. basic theory: the correlation between photons in coherent beams of radiation,” Proc. R. Soc. (London) A242, 300–324 (1957).
[Crossref]

R. H. Brown and R. Q. Twiss, “Corrrelation between photons in two coherent beams of light,” Nature (Loudon) 177, 27–29 (1956);
[Crossref]

Wang, W. T.

J. B. Liu, Y. Zhou, W. T. Wang, R. F. Liu, K. He, F. L. Li, and Z. Xu, “Spatial second-order interference of pseudothermal light in a Hong-Ou-Mandel interferometer,” Opt. Express 16, 19209–19218 (2013).
[Crossref]

Weinfurter, H.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod, Phys. 84, 777–838 (2012).
[Crossref]

Wolf, E.

L. Mandel and E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[Crossref]

M. Born and E. Wolf, Principle of Optics, 7. (Cambridge University Press, Cambridge, 1999).
[Crossref]

Wu, L. A.

Y. H. Zhai, X. H. Chen, and L. A. Wu, “Two-photon interference with two independent pseudothermal sources,” Phys. Rev. A 74, 053807 (2006).
[Crossref]

Xie, Z. D.

H. Chen, T. Peng, S. Karmakar, Z. D. Xie, and Y. H. Shih, “Observation of anticorrelation in incoherent thermal light fields,” Phys. Rev. A 84, 033835 (2011).
[Crossref]

Xu, Z.

J. B. Liu, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference between laser and thermal light,” Europhys. Lett. 105, 64007 (2014).
[Crossref]

J. B. Liu, Y. Zhou, W. T. Wang, R. F. Liu, K. He, F. L. Li, and Z. Xu, “Spatial second-order interference of pseudothermal light in a Hong-Ou-Mandel interferometer,” Opt. Express 16, 19209–19218 (2013).
[Crossref]

J. B. Liu, Y. Zhou, H. B. Zheng, H. Chen, F. L. Li, and Z. Xu, “Two-photon interference with non-identical photons,” arXiv: physics.optics, 1412.2308 (2014).

Zeilinger, A.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod, Phys. 84, 777–838 (2012).
[Crossref]

A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288–S297 (1999).
[Crossref]

Zhai, Y. H.

Y. H. Zhai, X. H. Chen, and L. A. Wu, “Two-photon interference with two independent pseudothermal sources,” Phys. Rev. A 74, 053807 (2006).
[Crossref]

Zhang, G. Q.

J. B. Liu and G. Q. Zhang, “Observation on the incompatibility between the first-order and second-order interferences with laser beams,” Opt. Commun. 284, 2658–2661 (2011).
[Crossref]

J. B. Liu and G. Q. Zhang, “Unified interpretation for second-order subwavelength interference based on Feyn-man’s path-integral theory,” Phys. Rev. A 83, 013822 (2010).
[Crossref]

Zhang, G. W.

L. Q. Chen, C. L. Bian, G. W. Zhang, Z. Y. Ou, and W. P. Zhang, “Observation of temporal beating in first- and second-order intensity measurement between independent Raman Stokes fields in atomic vapor,” Phys. Rev. A 82, 033832 (2010).
[Crossref]

Zhang, W. P.

L. Q. Chen, C. L. Bian, G. W. Zhang, Z. Y. Ou, and W. P. Zhang, “Observation of temporal beating in first- and second-order intensity measurement between independent Raman Stokes fields in atomic vapor,” Phys. Rev. A 82, 033832 (2010).
[Crossref]

Zheng, H. B.

J. B. Liu, Y. Zhou, H. B. Zheng, H. Chen, F. L. Li, and Z. Xu, “Two-photon interference with non-identical photons,” arXiv: physics.optics, 1412.2308 (2014).

Zhou, Y.

J. B. Liu, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference between laser and thermal light,” Europhys. Lett. 105, 64007 (2014).
[Crossref]

J. B. Liu, Y. Zhou, W. T. Wang, R. F. Liu, K. He, F. L. Li, and Z. Xu, “Spatial second-order interference of pseudothermal light in a Hong-Ou-Mandel interferometer,” Opt. Express 16, 19209–19218 (2013).
[Crossref]

J. B. Liu, Y. Zhou, H. B. Zheng, H. Chen, F. L. Li, and Z. Xu, “Two-photon interference with non-identical photons,” arXiv: physics.optics, 1412.2308 (2014).

Zukowski, M.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod, Phys. 84, 777–838 (2012).
[Crossref]

Am. J. Phys. (1)

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

Europhys. Lett. (1)

J. B. Liu, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference between laser and thermal light,” Europhys. Lett. 105, 64007 (2014).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

Nature (Loudon) (3)

G. Magyar and L. Mandel, “Interference fringes produced by superposition of two independent maser light beams,” Nature (Loudon) 198, 255–256 (1963).
[Crossref]

M. S. Lipsett and L. Mandel, “Coherence time measurement of light from a ruby optical maser,” Nature (Loudon) 199, 553–555 (1963).
[Crossref]

R. H. Brown and R. Q. Twiss, “Corrrelation between photons in two coherent beams of light,” Nature (Loudon) 177, 27–29 (1956);
[Crossref]

Nature Phys. (2)

A. J. Bennett, R. B. Patel, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Interference of dissimilar photon sources,” Nature Phys. 5, 715–717 (2009).
[Crossref]

R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometery with chirped laser pulses,” Nature Phys. 8, 864–868 (2008).
[Crossref]

Opt. Commun. (2)

J. B. Liu and G. Q. Zhang, “Observation on the incompatibility between the first-order and second-order interferences with laser beams,” Opt. Commun. 284, 2658–2661 (2011).
[Crossref]

Z. Y. Ou, E. C. Gage, B. E. Magill, and L. Mandel, “Observation of beating between blue and green light,” Opt. Commun. 69, 1–5 (1988).
[Crossref]

Opt. Express (2)

Y. S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Two-photon interference with continuous-wave multi-mode coherent light,” Opt. Express 22, 3611–3620 (2014).
[Crossref] [PubMed]

J. B. Liu, Y. Zhou, W. T. Wang, R. F. Liu, K. He, F. L. Li, and Z. Xu, “Spatial second-order interference of pseudothermal light in a Hong-Ou-Mandel interferometer,” Opt. Express 16, 19209–19218 (2013).
[Crossref]

Phys. Rev. (3)

R. L. Pfleegor and L. Mandel, “Interference of independent photon beams,” Phys. Rev. 159, 1084–1088 (1967).
[Crossref]

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

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

Phys. Rev. A (6)

Y. S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “‘Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
[Crossref]

Y. H. Zhai, X. H. Chen, and L. A. Wu, “Two-photon interference with two independent pseudothermal sources,” Phys. Rev. A 74, 053807 (2006).
[Crossref]

L. Q. Chen, C. L. Bian, G. W. Zhang, Z. Y. Ou, and W. P. Zhang, “Observation of temporal beating in first- and second-order intensity measurement between independent Raman Stokes fields in atomic vapor,” Phys. Rev. A 82, 033832 (2010).
[Crossref]

H. Chen, T. Peng, S. Karmakar, Z. D. Xie, and Y. H. Shih, “Observation of anticorrelation in incoherent thermal light fields,” Phys. Rev. A 84, 033835 (2011).
[Crossref]

J. B. Liu and G. Q. Zhang, “Unified interpretation for second-order subwavelength interference based on Feyn-man’s path-integral theory,” Phys. Rev. A 83, 013822 (2010).
[Crossref]

L. Mandel, “Photon interference and correlation effects produced by independent quantum sources,” Phys. Rev. A 28, 929–943 (1983).
[Crossref]

Phys. Rev. Lett. (3)

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

Z. Y. Ou and L. Mandel, “Observation of spatial quantum beating with seperated photodetectors,” Phys. Rev. Lett. 61, 54–57 (1988).
[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]

Phys. Zs. (1)

A. Einstein, “On the quantum theory of radiation,” Phys. Zs. 18, 121–135 (1917).

Proc. R. Soc. (London) (2)

R. H. Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations in light. I. basic theory: the correlation between photons in coherent beams of radiation,” Proc. R. Soc. (London) A242, 300–324 (1957).
[Crossref]

R. H. Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations in light II. an experimental test of the theory for partially coherent light,” Proc. R. Soc. (London) A243, 291–319 (1958).
[Crossref]

Rev. Mod, Phys. (1)

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod, Phys. 84, 777–838 (2012).
[Crossref]

Rev. Mod. Phys. (4)

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S287 (1999).
[Crossref]

A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288–S297 (1999).
[Crossref]

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

L. Mandel and E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[Crossref]

Science (1)

I. Afek, O. Ambar, and Y. Silberberg, “High-N00N states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[Crossref] [PubMed]

Other (7)

J. B. Liu, Y. Zhou, H. B. Zheng, H. Chen, F. L. Li, and Z. Xu, “Two-photon interference with non-identical photons,” arXiv: physics.optics, 1412.2308 (2014).

R. Loudon, The Quantum Theory of Light, 3. (Oxford University Press, New York, 2000).

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

M. Born and E. Wolf, Principle of Optics, 7. (Cambridge University Press, Cambridge, 1999).
[Crossref]

P. A. M. Dirac, The Principles of Quantum Mechanics4. (Science Press, Beijing, 2008).

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

Y. H. Shih, An Introduction to Quantum Optics: Photons and Biphoton Physics (CRC Press, Taylor & Francis, London, 2011).

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Figures (6)

Fig. 1
Fig. 1 The first- and second-order interference of thermal and laser light beams. ST and SL are point thermal and laser light sources, respectively. D1 and D2 are two single-photon detectors. BS: 1:1 non-polarizing beam splitter. C: single-photon count detection system. CC: two-photon coincidence count detection system.
Fig. 2
Fig. 2 The experimental setup for the first- and second-order interference of pseudothermal and laser light. Laser: 780 nm single-mode laser with bandwidth of 200 kHz. P: Polarizer. BS: 1:1 non-polarizing beam splitter. W: half-wave plate. RG: Rotating ground glass. S: Light source. L: Lens. M: Mirror. AOM: Acoustooptic modulator. H: Pinhole. FBS: Fiber beam splitter. D: Single-photon detector. CC: two-photon coincidence count detection system. See text for details.
Fig. 3
Fig. 3 The measured single-photon counting rates and two-photon coincidence counts. In (a), R1 and R2 are single-photon counting rates of D1 and D2, respectively. t is the collection time. In (b), CC is two-photon coincidence counts. t1 −t2 is the time difference between the two single-photon detection events within a two-photon coincidence count. The red line in (b) is sine function fitting with minimum sum of squares of error. The data in (a) and (b) is recorded simultaneously in a single experimental run.
Fig. 4
Fig. 4 The second-order temporal beatings when the frequency shifts of AOM are 212.51 MHz, 200.66 MHz, and 195.28 MHz for (a), (b) and (c), respectively. The red lines are sine function fitting with minimum sum of squares of error.
Fig. 5
Fig. 5 Visibility of the second-order temporal beating versus the angle of the half-wave plate. The red line is sine function fitting with minimum sum of squares of error.
Fig. 6
Fig. 6 Two different situations for two photons in a HOM interferometer.I: input port. F: Filter. Other symbols are the same as the ones in Figs. 1 and 2.

Equations (10)

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

P j ( r , t ) = | A j 1 ( r , t ) + A j 2 ( r , t ) | 2 ,
P j ( 1 ) ( r , t ) = | e i ( φ L j + π / 2 ) K L 1 ( r , t ) + e i φ T j K T 1 ( r , t ) | 2 ,
P ( 1 ) ( r , t ) = j P j ( 1 ) ( r , t ) | e i ( φ L j + π / 2 ) K L 1 ( r , t ) + e i φ T j K T 1 ( r , t ) | 2 ,
P ( 1 ) ( r , t ) = | K L 1 ( r , t ) | 2 + | K T 1 ( r , t ) | 2 ,
P j ( 2 ) ( r 1 , t 1 ; r 2 , t 2 ) = | e i φ T j A K T 1 e i ( φ T j B + π 2 ) K T 2 + e i ( φ T j A + π 2 ) K T 2 e i φ T j B K T 1 + e i ( φ L j + π 2 ) K L 1 e i φ L j K L 2 + e i φ T j A K T 1 e i φ L j K L 2 + e i ( φ T j A + π 2 ) K T 2 e i ( φ L j + π 2 ) K L 1 + e i φ T j B K T 1 e i φ L j K L 2 + e i ( φ T j B + π 2 ) K T 2 e i ( φ L j + π 2 ) K L 1 | 2 .
P ( 2 ) ( r 1 , t 1 ; r 2 , t 2 ) = j P j ( 2 ) ( r 1 , t 1 ; r 2 , t 2 ) | e i φ T j A K T 1 e i ( φ T j B + π 2 ) K T 2 + e i ( φ T j A + π 2 ) K T 2 e i φ T j B K T 1 + e i ( φ L j + π 2 ) K L 1 e i φ L j K L 2 + e i φ T j A K T 1 e i φ L j K L 2 + e i ( φ T j A + π 2 ) K T 2 e i ( φ L j + π 2 ) K L 1 + e i φ T j B K T 1 e i φ L j K L 2 + e i ( φ T j A + π 2 ) K T 2 e i ( φ L j + π 2 ) K L 1 | 2 ,
P ( 2 ) ( r 1 , t 1 ; r 2 , t 2 ) = | K T 1 K T 2 + K T 2 K T 1 | 2 + | K L 1 K L 2 | 2 + | K T 1 K L 2 K T 2 K L 1 | 2 + | K T 1 K L 2 K T 2 K L 1 | 2 .
K α , β = exp [ i ( k α β r α β ω α t β ) ] r α β ,
P ( 2 ) ( t 1 t 2 ) 7 + 2 s i n c 2 Δ ω T ( t 1 t 2 ) 2 4 cos [ Δ ω T L ( t 1 t 2 ) ] s i n c Δ ω T ( t 1 t 2 ) 2 .
P ( 2 ) ( t 1 t 2 ) 7 + 2 s i n c 2 Δ ω T ( t 1 t 2 ) 2 + 4 cos [ Δ ω T L ( t 1 t 2 ) ] s i n c Δ ω T ( t 1 t 2 ) 2 .

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