Abstract

We report two-photon interference with continuous-wave multi-mode coherent light. We show that the two-photon interference, in terms of the detection time difference, reveals two-photon beating fringes with the visibility V = 0.5. While scanning the optical delay of the interferometer, Hong-Ou-Mandel dips or peaks are measured depending on the chosen detection time difference. The HOM dips/peaks are repeated when the optical delay and the first-order coherence revival period of the multi-mode coherent light are the same. These results help to understand the nature of two-photon interference and also can be useful for quantum information science.

© 2014 Optical Society of America

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  1. T. Young, Lectures on Natural Philosophy, Vol. I, p. 464 (Johnson, London, 1807).
  2. E. Hecht, Optics (Addision-Wesely, San Francisco, 2002).
  3. L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).
    [CrossRef]
  4. C.K. Hong, Z.Y. Ou, L. Mandel, “Measurement of sub picosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
    [CrossRef] [PubMed]
  5. J.G. Rarity, P.R. Tapster, R. Loudon, “Non-classical interference between independent sources,” J. Opt. B: Quantum Semiclass. Opt. 7, S171–S175 (2005).
    [CrossRef]
  6. A.K. Jha, Coherence property of the entangled two-photon field produced by parametric down-conversion, Ph.D. thesis, University of Rochester, NY, 2009.
  7. Z.Y. Ou, L. Mandel, “Observation of spatial quantum beating with separated photodetectors,” Phys. Rev. Lett. 61, 54–57 (1988).
    [CrossRef] [PubMed]
  8. T. Legero, T. Wilk, A. Kuhn, G. Rempe, “Time-resolved two-photon quantum interference,” Appl. Phys. B 77, 797–802 (2003).
    [CrossRef]
  9. T. Legero, T. Wilk, M. Hennrich, G. Rempe, A. Kuhn, “Quantum beat of two single photons,” Phys. Rev. Lett. 93, 070503 (2004).
    [CrossRef] [PubMed]
  10. T. Legero, T. Wilk, A. Kuhn, G. Rempe, “Characterization of single photons using two-photon interference,” Adv. Atom. Atom. Mol. Opt. Phys. 53, 253–289 (2006).
    [CrossRef]
  11. X.Y. Zou, L.J. Wang, L. Mandel, “Induced coherence and indistinguishability in optical interference,” Phys. Rev. Lett. 67, 318–321 (1991).
    [CrossRef] [PubMed]
  12. O. Kwon, Y.-S. Ra, Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0〉+ |0, N〉 state,” Phys. Rev. A 81, 063801 (2010).
    [CrossRef]
  13. H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett. 107, 160401 (2011).
    [CrossRef] [PubMed]
  14. Y.-S. Kim, J.-C. Lee, O. Kwon, Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys. 8, 117–120 (2012).
    [CrossRef]
  15. E. Knill, R. Laflamme, G.J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
    [CrossRef] [PubMed]
  16. P. Kok, W.J. Munro, K. Nemoto, T.C. Ralph, J.P. Dowiling, G.J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
    [CrossRef]
  17. K. Wang, D.-Z. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70, 041801 (2004).
    [CrossRef]
  18. J. Cheng, S.-S. Han, “Incoherent coincidence imaging and its applicability in X-ray diffraction,” Phys. Rev. Lett. 92, 093903 (2004).
    [CrossRef] [PubMed]
  19. J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, K. Wang, “Experimental observation of classical sub wavelength interference with a pseudo thermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
    [CrossRef]
  20. Y.H. Zhai, X.-H. Chen, D. Zhang, L.-A. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (2005).
    [CrossRef]
  21. Y.-S. Kim, O. Slattery, P.S. Kuo, X. Tang, “Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
    [CrossRef]
  22. L. de Broglie, J.A.E. Silva, “Interpretation of a Recent Experiment on Interference of Photon Beams,” Phys. Rev. 172, 1284–1285 (1968).
    [CrossRef]
  23. S.-Y. Baek, O. Kwon, Y.-H. Kim, “High-resolution mode-spacing measurement of the blue-violet diode laser using interference of fields created with time delays greater than the coherence time,” Jpn. J. Appl. Phys. 46, 7720–7723 (2007).
    [CrossRef]
  24. O. Kwon, Y.-S. Ra, Y.-H. Kim, “Coherence properties of spontaneous parametric down-conversion pumped by a multi-mode cw diode laser,” Opt. Express 17, 13059 (2009).
    [CrossRef] [PubMed]
  25. O. Kwon, K.-K. Park, Y.-S. Ra, Y.-S. Kim, Y.-H. Kim, “Time-bin entangled photon pairs from spontaneous parametric down-conversion pumped by a cw multi-mode diode laser,” Opt. Express 21, 25492 (2013).
    [CrossRef] [PubMed]

2013 (2)

2012 (1)

Y.-S. Kim, J.-C. Lee, O. Kwon, Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys. 8, 117–120 (2012).
[CrossRef]

2011 (1)

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett. 107, 160401 (2011).
[CrossRef] [PubMed]

2010 (1)

O. Kwon, Y.-S. Ra, Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0〉+ |0, N〉 state,” Phys. Rev. A 81, 063801 (2010).
[CrossRef]

2009 (1)

2007 (2)

S.-Y. Baek, O. Kwon, Y.-H. Kim, “High-resolution mode-spacing measurement of the blue-violet diode laser using interference of fields created with time delays greater than the coherence time,” Jpn. J. Appl. Phys. 46, 7720–7723 (2007).
[CrossRef]

P. Kok, W.J. Munro, K. Nemoto, T.C. Ralph, J.P. Dowiling, G.J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

2006 (1)

T. Legero, T. Wilk, A. Kuhn, G. Rempe, “Characterization of single photons using two-photon interference,” Adv. Atom. Atom. Mol. Opt. Phys. 53, 253–289 (2006).
[CrossRef]

2005 (3)

J.G. Rarity, P.R. Tapster, R. Loudon, “Non-classical interference between independent sources,” J. Opt. B: Quantum Semiclass. Opt. 7, S171–S175 (2005).
[CrossRef]

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, K. Wang, “Experimental observation of classical sub wavelength interference with a pseudo thermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef]

Y.H. Zhai, X.-H. Chen, D. Zhang, L.-A. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (2005).
[CrossRef]

2004 (3)

K. Wang, D.-Z. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70, 041801 (2004).
[CrossRef]

J. Cheng, S.-S. Han, “Incoherent coincidence imaging and its applicability in X-ray diffraction,” Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef] [PubMed]

T. Legero, T. Wilk, M. Hennrich, G. Rempe, A. Kuhn, “Quantum beat of two single photons,” Phys. Rev. Lett. 93, 070503 (2004).
[CrossRef] [PubMed]

2003 (1)

T. Legero, T. Wilk, A. Kuhn, G. Rempe, “Time-resolved two-photon quantum interference,” Appl. Phys. B 77, 797–802 (2003).
[CrossRef]

2001 (1)

E. Knill, R. Laflamme, G.J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

1999 (1)

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).
[CrossRef]

1991 (1)

X.Y. Zou, L.J. Wang, L. Mandel, “Induced coherence and indistinguishability in optical interference,” Phys. Rev. Lett. 67, 318–321 (1991).
[CrossRef] [PubMed]

1988 (1)

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

1987 (1)

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

1968 (1)

L. de Broglie, J.A.E. Silva, “Interpretation of a Recent Experiment on Interference of Photon Beams,” Phys. Rev. 172, 1284–1285 (1968).
[CrossRef]

Bae, J.

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett. 107, 160401 (2011).
[CrossRef] [PubMed]

Baek, S.-Y.

S.-Y. Baek, O. Kwon, Y.-H. Kim, “High-resolution mode-spacing measurement of the blue-violet diode laser using interference of fields created with time delays greater than the coherence time,” Jpn. J. Appl. Phys. 46, 7720–7723 (2007).
[CrossRef]

Cao, D.-Z.

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, K. Wang, “Experimental observation of classical sub wavelength interference with a pseudo thermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef]

K. Wang, D.-Z. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70, 041801 (2004).
[CrossRef]

Chen, X.-H.

Y.H. Zhai, X.-H. Chen, D. Zhang, L.-A. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (2005).
[CrossRef]

Cheng, J.

J. Cheng, S.-S. Han, “Incoherent coincidence imaging and its applicability in X-ray diffraction,” Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef] [PubMed]

de Broglie, L.

L. de Broglie, J.A.E. Silva, “Interpretation of a Recent Experiment on Interference of Photon Beams,” Phys. Rev. 172, 1284–1285 (1968).
[CrossRef]

Dowiling, J.P.

P. Kok, W.J. Munro, K. Nemoto, T.C. Ralph, J.P. Dowiling, G.J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

Han, S.-S.

J. Cheng, S.-S. Han, “Incoherent coincidence imaging and its applicability in X-ray diffraction,” Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef] [PubMed]

Hecht, E.

E. Hecht, Optics (Addision-Wesely, San Francisco, 2002).

Hennrich, M.

T. Legero, T. Wilk, M. Hennrich, G. Rempe, A. Kuhn, “Quantum beat of two single photons,” Phys. Rev. Lett. 93, 070503 (2004).
[CrossRef] [PubMed]

Hong, C.K.

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

Huang, F.

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, K. Wang, “Experimental observation of classical sub wavelength interference with a pseudo thermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef]

Jha, A.K.

A.K. Jha, Coherence property of the entangled two-photon field produced by parametric down-conversion, Ph.D. thesis, University of Rochester, NY, 2009.

Kim, Y.-H.

O. Kwon, K.-K. Park, Y.-S. Ra, Y.-S. Kim, Y.-H. Kim, “Time-bin entangled photon pairs from spontaneous parametric down-conversion pumped by a cw multi-mode diode laser,” Opt. Express 21, 25492 (2013).
[CrossRef] [PubMed]

Y.-S. Kim, J.-C. Lee, O. Kwon, Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys. 8, 117–120 (2012).
[CrossRef]

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett. 107, 160401 (2011).
[CrossRef] [PubMed]

O. Kwon, Y.-S. Ra, Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0〉+ |0, N〉 state,” Phys. Rev. A 81, 063801 (2010).
[CrossRef]

O. Kwon, Y.-S. Ra, Y.-H. Kim, “Coherence properties of spontaneous parametric down-conversion pumped by a multi-mode cw diode laser,” Opt. Express 17, 13059 (2009).
[CrossRef] [PubMed]

S.-Y. Baek, O. Kwon, Y.-H. Kim, “High-resolution mode-spacing measurement of the blue-violet diode laser using interference of fields created with time delays greater than the coherence time,” Jpn. J. Appl. Phys. 46, 7720–7723 (2007).
[CrossRef]

Kim, Y.-S.

O. Kwon, K.-K. Park, Y.-S. Ra, Y.-S. Kim, Y.-H. Kim, “Time-bin entangled photon pairs from spontaneous parametric down-conversion pumped by a cw multi-mode diode laser,” Opt. Express 21, 25492 (2013).
[CrossRef] [PubMed]

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

Y.-S. Kim, J.-C. Lee, O. Kwon, Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys. 8, 117–120 (2012).
[CrossRef]

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett. 107, 160401 (2011).
[CrossRef] [PubMed]

Knill, E.

E. Knill, R. Laflamme, G.J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

Kok, P.

P. Kok, W.J. Munro, K. Nemoto, T.C. Ralph, J.P. Dowiling, G.J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

Kuhn, A.

T. Legero, T. Wilk, A. Kuhn, G. Rempe, “Characterization of single photons using two-photon interference,” Adv. Atom. Atom. Mol. Opt. Phys. 53, 253–289 (2006).
[CrossRef]

T. Legero, T. Wilk, M. Hennrich, G. Rempe, A. Kuhn, “Quantum beat of two single photons,” Phys. Rev. Lett. 93, 070503 (2004).
[CrossRef] [PubMed]

T. Legero, T. Wilk, A. Kuhn, G. Rempe, “Time-resolved two-photon quantum interference,” Appl. Phys. B 77, 797–802 (2003).
[CrossRef]

Kuo, P.S.

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

Kwon, O.

O. Kwon, K.-K. Park, Y.-S. Ra, Y.-S. Kim, Y.-H. Kim, “Time-bin entangled photon pairs from spontaneous parametric down-conversion pumped by a cw multi-mode diode laser,” Opt. Express 21, 25492 (2013).
[CrossRef] [PubMed]

Y.-S. Kim, J.-C. Lee, O. Kwon, Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys. 8, 117–120 (2012).
[CrossRef]

O. Kwon, Y.-S. Ra, Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0〉+ |0, N〉 state,” Phys. Rev. A 81, 063801 (2010).
[CrossRef]

O. Kwon, Y.-S. Ra, Y.-H. Kim, “Coherence properties of spontaneous parametric down-conversion pumped by a multi-mode cw diode laser,” Opt. Express 17, 13059 (2009).
[CrossRef] [PubMed]

S.-Y. Baek, O. Kwon, Y.-H. Kim, “High-resolution mode-spacing measurement of the blue-violet diode laser using interference of fields created with time delays greater than the coherence time,” Jpn. J. Appl. Phys. 46, 7720–7723 (2007).
[CrossRef]

Laflamme, R.

E. Knill, R. Laflamme, G.J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

Lee, J.-C.

Y.-S. Kim, J.-C. Lee, O. Kwon, Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys. 8, 117–120 (2012).
[CrossRef]

Legero, T.

T. Legero, T. Wilk, A. Kuhn, G. Rempe, “Characterization of single photons using two-photon interference,” Adv. Atom. Atom. Mol. Opt. Phys. 53, 253–289 (2006).
[CrossRef]

T. Legero, T. Wilk, M. Hennrich, G. Rempe, A. Kuhn, “Quantum beat of two single photons,” Phys. Rev. Lett. 93, 070503 (2004).
[CrossRef] [PubMed]

T. Legero, T. Wilk, A. Kuhn, G. Rempe, “Time-resolved two-photon quantum interference,” Appl. Phys. B 77, 797–802 (2003).
[CrossRef]

Li, H.-G.

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, K. Wang, “Experimental observation of classical sub wavelength interference with a pseudo thermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef]

Lim, H.-T.

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett. 107, 160401 (2011).
[CrossRef] [PubMed]

Loudon, R.

J.G. Rarity, P.R. Tapster, R. Loudon, “Non-classical interference between independent sources,” J. Opt. B: Quantum Semiclass. Opt. 7, S171–S175 (2005).
[CrossRef]

Mandel, L.

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).
[CrossRef]

X.Y. Zou, L.J. Wang, L. Mandel, “Induced coherence and indistinguishability in optical interference,” Phys. Rev. Lett. 67, 318–321 (1991).
[CrossRef] [PubMed]

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

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

Milburn, G.J.

P. Kok, W.J. Munro, K. Nemoto, T.C. Ralph, J.P. Dowiling, G.J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

E. Knill, R. Laflamme, G.J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

Munro, W.J.

P. Kok, W.J. Munro, K. Nemoto, T.C. Ralph, J.P. Dowiling, G.J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

Nemoto, K.

P. Kok, W.J. Munro, K. Nemoto, T.C. Ralph, J.P. Dowiling, G.J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

Ou, Z.Y.

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

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

Park, K.-K.

Ra, Y.-S.

O. Kwon, K.-K. Park, Y.-S. Ra, Y.-S. Kim, Y.-H. Kim, “Time-bin entangled photon pairs from spontaneous parametric down-conversion pumped by a cw multi-mode diode laser,” Opt. Express 21, 25492 (2013).
[CrossRef] [PubMed]

H.-T. Lim, Y.-S. Kim, Y.-S. Ra, J. Bae, Y.-H. Kim, “Experimental realization of an approximate partial transpose for photonic two-qubit systems,” Phys. Rev. Lett. 107, 160401 (2011).
[CrossRef] [PubMed]

O. Kwon, Y.-S. Ra, Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled |N, 0〉+ |0, N〉 state,” Phys. Rev. A 81, 063801 (2010).
[CrossRef]

O. Kwon, Y.-S. Ra, Y.-H. Kim, “Coherence properties of spontaneous parametric down-conversion pumped by a multi-mode cw diode laser,” Opt. Express 17, 13059 (2009).
[CrossRef] [PubMed]

Ralph, T.C.

P. Kok, W.J. Munro, K. Nemoto, T.C. Ralph, J.P. Dowiling, G.J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

Rarity, J.G.

J.G. Rarity, P.R. Tapster, R. Loudon, “Non-classical interference between independent sources,” J. Opt. B: Quantum Semiclass. Opt. 7, S171–S175 (2005).
[CrossRef]

Rempe, G.

T. Legero, T. Wilk, A. Kuhn, G. Rempe, “Characterization of single photons using two-photon interference,” Adv. Atom. Atom. Mol. Opt. Phys. 53, 253–289 (2006).
[CrossRef]

T. Legero, T. Wilk, M. Hennrich, G. Rempe, A. Kuhn, “Quantum beat of two single photons,” Phys. Rev. Lett. 93, 070503 (2004).
[CrossRef] [PubMed]

T. Legero, T. Wilk, A. Kuhn, G. Rempe, “Time-resolved two-photon quantum interference,” Appl. Phys. B 77, 797–802 (2003).
[CrossRef]

Silva, J.A.E.

L. de Broglie, J.A.E. Silva, “Interpretation of a Recent Experiment on Interference of Photon Beams,” Phys. Rev. 172, 1284–1285 (1968).
[CrossRef]

Slattery, O.

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

Sun, X.-J.

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, K. Wang, “Experimental observation of classical sub wavelength interference with a pseudo thermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef]

Tang, X.

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

Tapster, P.R.

J.G. Rarity, P.R. Tapster, R. Loudon, “Non-classical interference between independent sources,” J. Opt. B: Quantum Semiclass. Opt. 7, S171–S175 (2005).
[CrossRef]

Wang, K.

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, K. Wang, “Experimental observation of classical sub wavelength interference with a pseudo thermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef]

K. Wang, D.-Z. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70, 041801 (2004).
[CrossRef]

Wang, L.J.

X.Y. Zou, L.J. Wang, L. Mandel, “Induced coherence and indistinguishability in optical interference,” Phys. Rev. Lett. 67, 318–321 (1991).
[CrossRef] [PubMed]

Wilk, T.

T. Legero, T. Wilk, A. Kuhn, G. Rempe, “Characterization of single photons using two-photon interference,” Adv. Atom. Atom. Mol. Opt. Phys. 53, 253–289 (2006).
[CrossRef]

T. Legero, T. Wilk, M. Hennrich, G. Rempe, A. Kuhn, “Quantum beat of two single photons,” Phys. Rev. Lett. 93, 070503 (2004).
[CrossRef] [PubMed]

T. Legero, T. Wilk, A. Kuhn, G. Rempe, “Time-resolved two-photon quantum interference,” Appl. Phys. B 77, 797–802 (2003).
[CrossRef]

Wu, L.-A.

Y.H. Zhai, X.-H. Chen, D. Zhang, L.-A. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (2005).
[CrossRef]

Xiong, J.

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, K. Wang, “Experimental observation of classical sub wavelength interference with a pseudo thermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef]

Young, T.

T. Young, Lectures on Natural Philosophy, Vol. I, p. 464 (Johnson, London, 1807).

Zhai, Y.H.

Y.H. Zhai, X.-H. Chen, D. Zhang, L.-A. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (2005).
[CrossRef]

Zhang, D.

Y.H. Zhai, X.-H. Chen, D. Zhang, L.-A. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (2005).
[CrossRef]

Zou, X.Y.

X.Y. Zou, L.J. Wang, L. Mandel, “Induced coherence and indistinguishability in optical interference,” Phys. Rev. Lett. 67, 318–321 (1991).
[CrossRef] [PubMed]

Adv. Atom. Atom. Mol. Opt. Phys. (1)

T. Legero, T. Wilk, A. Kuhn, G. Rempe, “Characterization of single photons using two-photon interference,” Adv. Atom. Atom. Mol. Opt. Phys. 53, 253–289 (2006).
[CrossRef]

Appl. Phys. B (1)

T. Legero, T. Wilk, A. Kuhn, G. Rempe, “Time-resolved two-photon quantum interference,” Appl. Phys. B 77, 797–802 (2003).
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Figures (5)

Fig. 1
Fig. 1

(a) The schematic of two-photon interference with CW coherent light. (b) Experimental setup of two-photon interference with CW coherent light with a single laser. The degree of first-order coherence |γt)| can be maintained to be nonzero while the phases between two inputs are randomized by two independent acousto-optic modulators, AOM1 and AOM2.

Fig. 2
Fig. 2

Simulations of two-photon interference. Gaussian distributions of |γt)| and |Γ(ΔT)| with the full width at half maximums of 0.67 ps and 1.18 μs, respectively, are assumed. The periodic first-order coherence function for a diode laser with period of Tp = 10.57 ps is also assumed. (a) For Δω = 0, HOM dips with visibility of 0.5 can be shown when ΔT = 0 and Δt = nLp, where n = 0, ±1, ±2, ···. (b) For Δω = 2π × 3 MHz, the coincidence shows the sinusoidal two-photon beating with respect to ΔT with envelopes defined by the two coherence functions.

Fig. 3
Fig. 3

(a) The spectrum of CW multi-mode diode laser. (b) Single-photon interference registered at D1 with synchronized AOMs.

Fig. 4
Fig. 4

Two-photon coincidences as a function of the detection-time difference ΔT. The optical path length difference Δt = 0 during the measurement. (a) Δω = 0, (b) Δω = 2π × 3 MHz. (a) and (b) are measured at the various FM noises for RF signal of AOM1 that introduces limited |Γ(ΔT)|. Error bars denote the experimental standard deviations.

Fig. 5
Fig. 5

Two-photon coincidences as a function of the optical path difference, Δt for various detection-time differences (a) ΔT = 0, (b) ΔT = 0.16 μs, (c) ΔT = 0.32 μs, and (d) ΔT = 1.49 μs. HOM dips/peaks are measured depending on the conditions. The dips/peaks are repeated every Tp = 10.60 ± 0.10 ps which is the same for the single-photon interference repeating period.

Equations (7)

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E j ( t ) = | E 0 | e i ( ω j t + ϕ j ) ,
E 3 ( t ) = 1 2 [ E 1 ( t t 1 ) + i E 2 ( t t 2 ) ] , E 4 ( t ) = 1 2 [ E 2 ( t t 2 ) + i E 1 ( t t 1 ) ] ,
I 3 ( t ) = E 3 * ( t ) E 3 ( t ) = | E 0 | 2 { 1 + | γ ( Δ t ) | sin [ ω 2 t 2 ω 1 t 1 Δ ω t Δ ϕ ] } , I 4 ( t ) = E 4 * ( t ) E 4 ( t ) = | E 0 | 2 { 1 | γ ( Δ t ) | sin [ ω 2 t 2 ω 1 t 1 Δ ω t Δ ϕ ] } ,
I 3 ( t ) = | E 0 | 2 { 1 + | γ ( Δ t ) | sin ( ω 0 Δ t Δ ϕ ) } , I 4 ( t ) = | E 0 | 2 { 1 | γ ( Δ t ) sin [ ω 0 Δ t Δ ϕ ] | } .
I 3 ( T 1 ) I 4 ( T 2 ) = | E 0 | 4 { 1 + | γ ( Δ t ) | sin [ 𝒜 Δ ω T 1 ] | γ ( Δ t ) | sin [ 𝒜 Δ ω T 2 ] | γ ( Δ t ) | 2 sin [ 𝒜 Δ ω T 1 ] sin [ 𝒜 Δ ω T 2 ] } .
I 3 ( T 1 ) I 4 ( T 2 ) ~ 1 1 2 | γ ( Δ t ) | 2 cos [ Δ ω Δ T ] .
I 3 I 4 ( Δ t , Δ T ) ~ 1 1 2 | γ ( Δ t ) | 2 | Γ ( Δ T ) | cos [ Δ ω Δ T ] .

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