Abstract

Interference between two completely independent photons lies at the heart of many photonic quantum information applications such as quantum repeaters, teleportation, and quantum key distribution. Here, we report the observation of Hong–Ou–Mandel (HOM) interference with two independent continuous-wave coherent light sources that are neither synchronized nor share any common reference. To prepare indistinguishable photons from two independent laser sources, we employ high-precision frequency-stabilization techniques using the 5S1/2(F=3)5P1/2(F=3) transition line of Rb85 atoms. We successfully observe an HOM interference fringe with two independent continuous-wave coherent photons originating from either the frequency-locked or the frequency-modulated lasers. An interference fringe involving two-photon beating is also observed when the frequency difference between the two interfering photons is beyond the spectral bandwidth of the individual coherent photons. We carry out further experiments to verify the robustness of the source preparation regardless of the separation distance between the two independent photon sources.

© 2020 Chinese Laser Press

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. O. Carnal and J. Mlynek, “Young’s double-slit experiment with atoms: a simple atom interferometer,” Phys. Rev. Lett. 66, 2689–2692 (1991).
    [Crossref]
  2. A. Tonomura, J. Endo, T. Matsuda, and T. Kawasaki, “Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57, 117–120 (1989).
    [Crossref]
  3. A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, “Single and double-slit diffraction of neutrons,” Rev. Mod. Phys. 60, 1067–1073 (1988).
    [Crossref]
  4. M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw, and A. Zeilinger, “Wave-particle duality of C60 molecules,” Nature 401, 680–682 (1999).
    [Crossref]
  5. P. Grangier, G. Roger, and A. Aspect, “Evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences,” Europhys. Lett. 1, 173–179 (1986).
    [Crossref]
  6. P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Oxford University, 1958), p. 9.
  7. G. Magyar and L. Mandel, “Interference fringes produced by superposition of two independent maser light beams,” Nature 198, 255–256 (1963).
    [Crossref]
  8. M. S. Lipsett and L. Mandel, “Coherence time measurements of light from ruby optical masers,” Nature 199, 553–555 (1963).
    [Crossref]
  9. U. Fano, “Quantum theory of interference effects in the mixing of light from phase-independent sources,” Am. J. Phys. 29, 539–545 (1961).
    [Crossref]
  10. L. Mandel, “Quantum theory of interference effects produced by independent light beams,” Phys. Rev. 134, A10–A15 (1964).
    [Crossref]
  11. T. F. Jordan and F. Ghielmetti, “Quantum theory of interference of light from two lasers,” Phys. Rev. Lett. 12, 607–609 (1964).
    [Crossref]
  12. A. Javan, E. A. Ballik, and W. L. Bond, “Frequency characteristics of a continuous-wave He-Ne optical laser,” J. Opt. Soc. Am. 52, 96–98 (1962).
    [Crossref]
  13. H. E. J. Neugebauer, “Coherence time of a maser,” J. Opt. Soc. Am. 52, 470–471 (1962).
    [Crossref]
  14. L. Mandel, “Transient coherence in optics,” J. Opt. Soc. Am. 52, 1407–1408 (1962).
    [Crossref]
  15. R. L. Pfleegor and L. Mandel, “Interference of independent photon beams,” Phys. Rev. 159, 1084–1088 (1967).
    [Crossref]
  16. R. L. Pfleegor and L. Mandel, “Interference effects at the single photon level,” Phys. Lett. A 24, 766–767 (1967).
    [Crossref]
  17. R. L. Pfleegor and L. Mandel, “Further experiments on interference of independent photon beams at low light levels,” J. Opt. Soc. Am. 58, 946–950 (1968).
    [Crossref]
  18. R. J. Glauber, “Dirac’s famous dictum on interference: one photon or two?” Am. J. Phys. 63, 12 (1995).
    [Crossref]
  19. R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
    [Crossref]
  20. R. H. Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).
    [Crossref]
  21. R. H. Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 178, 1046–1048 (1956).
    [Crossref]
  22. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
    [Crossref]
  23. L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).
    [Crossref]
  24. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
    [Crossref]
  25. Z. S. Yuan, X. H. Bao, C. Y. Lu, J. Zhang, C. Z. Peng, and J. W. Pan, “Entangled photons and quantum communication,” Phys. Rep. 497, 1–40 (2010).
    [Crossref]
  26. F. Flamini, N. Spagnolo, and F. Sciarrino, “Photonic quantum information processing: a review,” Rep. Prog. Phys. 82, 016001 (2019).
    [Crossref]
  27. H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, “Quantum interference with photon pairs created in spatially separated sources,” Phys. Rev. A 67, 022301 (2003).
    [Crossref]
  28. R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett. 96, 240502 (2006).
    [Crossref]
  29. M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692–695 (2007).
    [Crossref]
  30. P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117, 013602 (2016).
    [Crossref]
  31. T. Jung, Y.-S. Lee, J. Park, H. Kim, and H. S. Moon, “Quantum interference between autonomous single-photon sources from Doppler-broadened atomic ensemble,” Optica 4, 1167–1170 (2017).
    [Crossref]
  32. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
    [Crossref]
  33. J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
    [Crossref]
  34. 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]
  35. Y. Miyamoto, T. Kuga, M. Baba, and M. Matsuoka, “Measurement of ultrafast optical pulses with two-photon interference,” Opt. Lett. 18, 900–902 (1993).
    [Crossref]
  36. 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]
  37. J. B. Liu, H. Zheng, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The first- and second-order temporal interference between thermal and laser light,” Opt. Express 23, 11868–11878 (2015).
    [Crossref]
  38. J. B. Liu, M. Le, B. Bai, W. Wang, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference of two independent single-mode He-Ne lasers,” Opt. Commun. 350, 196–201 (2015).
    [Crossref]
  39. J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
    [Crossref]
  40. H. K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).
    [Crossref]
  41. Z. L. Yuan, M. Lucamarini, J. F. Dynes, B. Fröhlich, M. B. Ward, and A. J. Shields, “Interference of short optical pulses from independent gain-switched laser diodes for quantum secure communications,” Phys. Rev. Appl. 2, 064006 (2014).
    [Crossref]
  42. C. Agnesi, B. Da Lio, D. Cozzolino, L. Cardi, B. B. Bakir, K. Hassan, A. D. Frera, A. Ruggeri, A. Giudice, G. Vallone, P. Villoresi, A. Tosi, K. Rottwitt, Y. Ding, and D. Bacco, “Hong-Ou-Mandel interference between independent III-V on silicon waveguide integrated lasers,” Opt. Lett. 44, 271–274 (2019).
    [Crossref]
  43. H. Semenenko, P. Sibson, M. G. Thompson, and C. Erven, “Interference between independent photonic integrated devices for quantum key distribution,” Opt. Lett. 44, 275–278 (2019).
    [Crossref]
  44. T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. C. do Amaral, G. P. Temporão, and J. P. von der Weid, “Proof-of–principle demonstration of measurement-device–independent quantum key distribution using polarization qubits,” Phys. Rev. A 88, 052303 (2013).
    [Crossref]
  45. E. Moschandreou, J. I. Garcia, B. J. Rollick, B. Qi, R. Pooser, and G. Siopsis, “Experimental study of Hong–Ou–Mandel interference using independent phase randomized weak coherent states,” J. Lightwave Technol. 36, 3752–3759 (2018).
    [Crossref]
  46. T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. P. Temporão, and J. P. von der Weid, “Long-distance Bell-state analysis of fully Independent polarization weak coherent states,” J. Lightwave Technol. 31, 2881–2887 (2013).
    [Crossref]
  47. T. F. da Silva, G. C. do Amaral, D. Vitoreti, G. P. Temporão, and J. P. von der Weid, “Spectral characterization of weak coherent state sources based on two-photon interference,” J. Opt. Soc. Am. B 32, 545–549 (2015).
    [Crossref]
  48. G. C. Amaral, T. F. da Silva, G. P. Temporão, and J. P. von der Weid, “Few-photon heterodyne spectroscopy,” Opt. Lett. 41, 1502–1505 (2016).
    [Crossref]
  49. T. Legero, T. Wilk, A. Kuhn, and G. Rempe, “Time-resolved two-photon quantum interference,” Appl. Phys. B 77, 797–802 (2003).
    [Crossref]
  50. T. Legero, T. Wilk, M. Hennrich, G. Rempe, and A. Kuhn, “Quantum beat of two single photons,” Phys. Rev. Lett. 93, 070503 (2004).
    [Crossref]
  51. 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]

2019 (3)

2018 (1)

2017 (1)

2016 (3)

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117, 013602 (2016).
[Crossref]

J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
[Crossref]

G. C. Amaral, T. F. da Silva, G. P. Temporão, and J. P. von der Weid, “Few-photon heterodyne spectroscopy,” Opt. Lett. 41, 1502–1505 (2016).
[Crossref]

2015 (3)

2014 (3)

Z. L. Yuan, M. Lucamarini, J. F. Dynes, B. Fröhlich, M. B. Ward, and A. J. Shields, “Interference of short optical pulses from independent gain-switched laser diodes for quantum secure communications,” Phys. Rev. Appl. 2, 064006 (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]

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]

2013 (2)

T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. P. Temporão, and J. P. von der Weid, “Long-distance Bell-state analysis of fully Independent polarization weak coherent states,” J. Lightwave Technol. 31, 2881–2887 (2013).
[Crossref]

T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. C. do Amaral, G. P. Temporão, and J. P. von der Weid, “Proof-of–principle demonstration of measurement-device–independent quantum key distribution using polarization qubits,” Phys. Rev. A 88, 052303 (2013).
[Crossref]

2012 (1)

H. K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).
[Crossref]

2010 (1)

Z. S. Yuan, X. H. Bao, C. Y. Lu, J. Zhang, C. Z. Peng, and J. W. Pan, “Entangled photons and quantum communication,” Phys. Rep. 497, 1–40 (2010).
[Crossref]

2007 (2)

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

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692–695 (2007).
[Crossref]

2006 (1)

R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett. 96, 240502 (2006).
[Crossref]

2004 (1)

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

2003 (2)

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

H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, “Quantum interference with photon pairs created in spatially separated sources,” Phys. Rev. A 67, 022301 (2003).
[Crossref]

1999 (2)

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

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw, and A. Zeilinger, “Wave-particle duality of C60 molecules,” Nature 401, 680–682 (1999).
[Crossref]

1998 (1)

J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

1997 (1)

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

1995 (1)

R. J. Glauber, “Dirac’s famous dictum on interference: one photon or two?” Am. J. Phys. 63, 12 (1995).
[Crossref]

1993 (1)

1991 (1)

O. Carnal and J. Mlynek, “Young’s double-slit experiment with atoms: a simple atom interferometer,” Phys. Rev. Lett. 66, 2689–2692 (1991).
[Crossref]

1989 (2)

A. Tonomura, J. Endo, T. Matsuda, and T. Kawasaki, “Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57, 117–120 (1989).
[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]

1988 (1)

A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, “Single and double-slit diffraction of neutrons,” Rev. Mod. Phys. 60, 1067–1073 (1988).
[Crossref]

1987 (2)

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[Crossref]

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

1986 (1)

P. Grangier, G. Roger, and A. Aspect, “Evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences,” Europhys. Lett. 1, 173–179 (1986).
[Crossref]

1968 (1)

1967 (2)

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

R. L. Pfleegor and L. Mandel, “Interference effects at the single photon level,” Phys. Lett. A 24, 766–767 (1967).
[Crossref]

1964 (2)

L. Mandel, “Quantum theory of interference effects produced by independent light beams,” Phys. Rev. 134, A10–A15 (1964).
[Crossref]

T. F. Jordan and F. Ghielmetti, “Quantum theory of interference of light from two lasers,” Phys. Rev. Lett. 12, 607–609 (1964).
[Crossref]

1963 (2)

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

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

1962 (3)

1961 (1)

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

1956 (2)

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

R. H. Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 178, 1046–1048 (1956).
[Crossref]

Agnesi, C.

Amaral, G. C.

Arndt, M.

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw, and A. Zeilinger, “Wave-particle duality of C60 molecules,” Nature 401, 680–682 (1999).
[Crossref]

Aspect, A.

P. Grangier, G. Roger, and A. Aspect, “Evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences,” Europhys. Lett. 1, 173–179 (1986).
[Crossref]

Aspelmeyer, M.

R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett. 96, 240502 (2006).
[Crossref]

Baba, M.

Bacco, D.

Bai, B.

J. B. Liu, M. Le, B. Bai, W. Wang, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference of two independent single-mode He-Ne lasers,” Opt. Commun. 350, 196–201 (2015).
[Crossref]

Bakir, B. B.

Ballik, E. A.

Bao, X. H.

Z. S. Yuan, X. H. Bao, C. Y. Lu, J. Zhang, C. Z. Peng, and J. W. Pan, “Entangled photons and quantum communication,” Phys. Rep. 497, 1–40 (2010).
[Crossref]

Beveratos, A.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692–695 (2007).
[Crossref]

Blauensteiner, B.

R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett. 96, 240502 (2006).
[Crossref]

Bond, W. L.

Bouwmeester, D.

J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Brown, R. H.

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

R. H. Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 178, 1046–1048 (1956).
[Crossref]

Cao, R.

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117, 013602 (2016).
[Crossref]

Cardi, L.

Carnal, O.

O. Carnal and J. Mlynek, “Young’s double-slit experiment with atoms: a simple atom interferometer,” Phys. Rev. Lett. 66, 2689–2692 (1991).
[Crossref]

Chen, H.

J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
[Crossref]

J. B. Liu, M. Le, B. Bai, W. Wang, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference of two independent single-mode He-Ne lasers,” Opt. Commun. 350, 196–201 (2015).
[Crossref]

J. B. Liu, H. Zheng, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The first- and second-order temporal interference between thermal and laser light,” Opt. Express 23, 11868–11878 (2015).
[Crossref]

Chen, J. F.

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117, 013602 (2016).
[Crossref]

Cozzolino, D.

Curty, M.

H. K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).
[Crossref]

Da Lio, B.

da Silva, T. F.

de Riedmatten, H.

H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, “Quantum interference with photon pairs created in spatially separated sources,” Phys. Rev. A 67, 022301 (2003).
[Crossref]

Ding, Y.

Dirac, P. A. M.

P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Oxford University, 1958), p. 9.

do Amaral, G. C.

T. F. da Silva, G. C. do Amaral, D. Vitoreti, G. P. Temporão, and J. P. von der Weid, “Spectral characterization of weak coherent state sources based on two-photon interference,” J. Opt. Soc. Am. B 32, 545–549 (2015).
[Crossref]

T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. C. do Amaral, G. P. Temporão, and J. P. von der Weid, “Proof-of–principle demonstration of measurement-device–independent quantum key distribution using polarization qubits,” Phys. Rev. A 88, 052303 (2013).
[Crossref]

Dowling, J. P.

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

Dynes, J. F.

Z. L. Yuan, M. Lucamarini, J. F. Dynes, B. Fröhlich, M. B. Ward, and A. J. Shields, “Interference of short optical pulses from independent gain-switched laser diodes for quantum secure communications,” Phys. Rev. Appl. 2, 064006 (2014).
[Crossref]

Eibl, M.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Endo, J.

A. Tonomura, J. Endo, T. Matsuda, and T. Kawasaki, “Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57, 117–120 (1989).
[Crossref]

Erven, C.

Fano, U.

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

Ferreira da Silva, T.

T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. C. do Amaral, G. P. Temporão, and J. P. von der Weid, “Proof-of–principle demonstration of measurement-device–independent quantum key distribution using polarization qubits,” Phys. Rev. A 88, 052303 (2013).
[Crossref]

T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. P. Temporão, and J. P. von der Weid, “Long-distance Bell-state analysis of fully Independent polarization weak coherent states,” J. Lightwave Technol. 31, 2881–2887 (2013).
[Crossref]

Flamini, F.

F. Flamini, N. Spagnolo, and F. Sciarrino, “Photonic quantum information processing: a review,” Rep. Prog. Phys. 82, 016001 (2019).
[Crossref]

Frera, A. D.

Fröhlich, B.

Z. L. Yuan, M. Lucamarini, J. F. Dynes, B. Fröhlich, M. B. Ward, and A. J. Shields, “Interference of short optical pulses from independent gain-switched laser diodes for quantum secure communications,” Phys. Rev. Appl. 2, 064006 (2014).
[Crossref]

Gage, E. C.

Gähler, R.

A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, “Single and double-slit diffraction of neutrons,” Rev. Mod. Phys. 60, 1067–1073 (1988).
[Crossref]

Gao, H.

J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
[Crossref]

Garcia, J. I.

Ghielmetti, F.

T. F. Jordan and F. Ghielmetti, “Quantum theory of interference of light from two lasers,” Phys. Rev. Lett. 12, 607–609 (1964).
[Crossref]

Ghosh, R.

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[Crossref]

Gisin, N.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692–695 (2007).
[Crossref]

H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, “Quantum interference with photon pairs created in spatially separated sources,” Phys. Rev. A 67, 022301 (2003).
[Crossref]

Giudice, A.

Glauber, R. J.

R. J. Glauber, “Dirac’s famous dictum on interference: one photon or two?” Am. J. Phys. 63, 12 (1995).
[Crossref]

Grangier, P.

P. Grangier, G. Roger, and A. Aspect, “Evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences,” Europhys. Lett. 1, 173–179 (1986).
[Crossref]

Gu, Z.

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117, 013602 (2016).
[Crossref]

Halder, M.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692–695 (2007).
[Crossref]

Hassan, K.

Hennrich, M.

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

Hong, C. K.

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

Javan, A.

Jordan, T. F.

T. F. Jordan and F. Ghielmetti, “Quantum theory of interference of light from two lasers,” Phys. Rev. Lett. 12, 607–609 (1964).
[Crossref]

Jung, T.

Kaltenbaek, R.

R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett. 96, 240502 (2006).
[Crossref]

Kawasaki, T.

A. Tonomura, J. Endo, T. Matsuda, and T. Kawasaki, “Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57, 117–120 (1989).
[Crossref]

Keller, C.

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw, and A. Zeilinger, “Wave-particle duality of C60 molecules,” Nature 401, 680–682 (1999).
[Crossref]

Kim, H.

Kim, Y. S.

Kok, P.

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

Kuga, T.

Kuhn, A.

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

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

Kuo, P. S.

Le, M.

J. B. Liu, M. Le, B. Bai, W. Wang, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference of two independent single-mode He-Ne lasers,” Opt. Commun. 350, 196–201 (2015).
[Crossref]

Lee, Y.-S.

Legero, T.

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

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

Li, F. L.

J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
[Crossref]

J. B. Liu, M. Le, B. Bai, W. Wang, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference of two independent single-mode He-Ne lasers,” Opt. Commun. 350, 196–201 (2015).
[Crossref]

J. B. Liu, H. Zheng, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The first- and second-order temporal interference between thermal and laser light,” Opt. Express 23, 11868–11878 (2015).
[Crossref]

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]

Lipsett, M. S.

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

Liu, J. B.

J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
[Crossref]

J. B. Liu, M. Le, B. Bai, W. Wang, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference of two independent single-mode He-Ne lasers,” Opt. Commun. 350, 196–201 (2015).
[Crossref]

J. B. Liu, H. Zheng, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The first- and second-order temporal interference between thermal and laser light,” Opt. Express 23, 11868–11878 (2015).
[Crossref]

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]

Lo, H. K.

H. K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).
[Crossref]

Lu, C. Y.

Z. S. Yuan, X. H. Bao, C. Y. Lu, J. Zhang, C. Z. Peng, and J. W. Pan, “Entangled photons and quantum communication,” Phys. Rep. 497, 1–40 (2010).
[Crossref]

Lucamarini, M.

Z. L. Yuan, M. Lucamarini, J. F. Dynes, B. Fröhlich, M. B. Ward, and A. J. Shields, “Interference of short optical pulses from independent gain-switched laser diodes for quantum secure communications,” Phys. Rev. Appl. 2, 064006 (2014).
[Crossref]

Magill, B. E.

Magyar, G.

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

Mampe, W.

A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, “Single and double-slit diffraction of neutrons,” Rev. Mod. Phys. 60, 1067–1073 (1988).
[Crossref]

Mandel, L.

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

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

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[Crossref]

R. L. Pfleegor and L. Mandel, “Further experiments on interference of independent photon beams at low light levels,” J. Opt. Soc. Am. 58, 946–950 (1968).
[Crossref]

R. L. Pfleegor and L. Mandel, “Interference effects at the single photon level,” Phys. Lett. A 24, 766–767 (1967).
[Crossref]

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

L. Mandel, “Quantum theory of interference effects produced by independent light beams,” Phys. Rev. 134, A10–A15 (1964).
[Crossref]

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

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

L. Mandel, “Transient coherence in optics,” J. Opt. Soc. Am. 52, 1407–1408 (1962).
[Crossref]

Marcikic, I.

H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, “Quantum interference with photon pairs created in spatially separated sources,” Phys. Rev. A 67, 022301 (2003).
[Crossref]

Matsuda, T.

A. Tonomura, J. Endo, T. Matsuda, and T. Kawasaki, “Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57, 117–120 (1989).
[Crossref]

Matsuoka, M.

Mattle, K.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Milburn, G. J.

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

Miyamoto, Y.

Mlynek, J.

O. Carnal and J. Mlynek, “Young’s double-slit experiment with atoms: a simple atom interferometer,” Phys. Rev. Lett. 66, 2689–2692 (1991).
[Crossref]

Moon, H. S.

Moschandreou, E.

Munro, W. J.

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

Nairz, O.

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw, and A. Zeilinger, “Wave-particle duality of C60 molecules,” Nature 401, 680–682 (1999).
[Crossref]

Nemoto, K.

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

Neugebauer, H. E. J.

Ou, Z. Y.

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117, 013602 (2016).
[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]

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

Pan, J. W.

Z. S. Yuan, X. H. Bao, C. Y. Lu, J. Zhang, C. Z. Peng, and J. W. Pan, “Entangled photons and quantum communication,” Phys. Rep. 497, 1–40 (2010).
[Crossref]

J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Park, J.

Peng, C. Z.

Z. S. Yuan, X. H. Bao, C. Y. Lu, J. Zhang, C. Z. Peng, and J. W. Pan, “Entangled photons and quantum communication,” Phys. Rep. 497, 1–40 (2010).
[Crossref]

Pfleegor, R. L.

R. L. Pfleegor and L. Mandel, “Further experiments on interference of independent photon beams at low light levels,” J. Opt. Soc. Am. 58, 946–950 (1968).
[Crossref]

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

R. L. Pfleegor and L. Mandel, “Interference effects at the single photon level,” Phys. Lett. A 24, 766–767 (1967).
[Crossref]

Pooser, R.

Qi, B.

Qian, P.

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117, 013602 (2016).
[Crossref]

Ralph, T. C.

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

Rempe, G.

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

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

Roger, G.

P. Grangier, G. Roger, and A. Aspect, “Evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences,” Europhys. Lett. 1, 173–179 (1986).
[Crossref]

Rollick, B. J.

Rottwitt, K.

Ruggeri, A.

Scarani, V.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692–695 (2007).
[Crossref]

Sciarrino, F.

F. Flamini, N. Spagnolo, and F. Sciarrino, “Photonic quantum information processing: a review,” Rep. Prog. Phys. 82, 016001 (2019).
[Crossref]

Semenenko, H.

Shields, A. J.

Z. L. Yuan, M. Lucamarini, J. F. Dynes, B. Fröhlich, M. B. Ward, and A. J. Shields, “Interference of short optical pulses from independent gain-switched laser diodes for quantum secure communications,” Phys. Rev. Appl. 2, 064006 (2014).
[Crossref]

Shull, C. G.

A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, “Single and double-slit diffraction of neutrons,” Rev. Mod. Phys. 60, 1067–1073 (1988).
[Crossref]

Sibson, P.

Simon, C.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692–695 (2007).
[Crossref]

Siopsis, G.

Slattery, O.

Spagnolo, N.

F. Flamini, N. Spagnolo, and F. Sciarrino, “Photonic quantum information processing: a review,” Rep. Prog. Phys. 82, 016001 (2019).
[Crossref]

Tang, X.

Temporão, G. P.

Thompson, M. G.

Tittel, W.

H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, “Quantum interference with photon pairs created in spatially separated sources,” Phys. Rev. A 67, 022301 (2003).
[Crossref]

Tonomura, A.

A. Tonomura, J. Endo, T. Matsuda, and T. Kawasaki, “Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57, 117–120 (1989).
[Crossref]

Tosi, A.

Treimer, W.

A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, “Single and double-slit diffraction of neutrons,” Rev. Mod. Phys. 60, 1067–1073 (1988).
[Crossref]

Twiss, R. Q.

R. H. Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 178, 1046–1048 (1956).
[Crossref]

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

Vallone, G.

van der Zouw, G.

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw, and A. Zeilinger, “Wave-particle duality of C60 molecules,” Nature 401, 680–682 (1999).
[Crossref]

Villoresi, P.

Vitoreti, D.

von der Weid, J. P.

Vos-Andreae, J.

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw, and A. Zeilinger, “Wave-particle duality of C60 molecules,” Nature 401, 680–682 (1999).
[Crossref]

Wang, W.

J. B. Liu, M. Le, B. Bai, W. Wang, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference of two independent single-mode He-Ne lasers,” Opt. Commun. 350, 196–201 (2015).
[Crossref]

Ward, M. B.

Z. L. Yuan, M. Lucamarini, J. F. Dynes, B. Fröhlich, M. B. Ward, and A. J. Shields, “Interference of short optical pulses from independent gain-switched laser diodes for quantum secure communications,” Phys. Rev. Appl. 2, 064006 (2014).
[Crossref]

Wei, D.

J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
[Crossref]

Weinfurter, H.

J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Wen, R.

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117, 013602 (2016).
[Crossref]

Wilk, T.

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

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

Xavier, G. B.

T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. P. Temporão, and J. P. von der Weid, “Long-distance Bell-state analysis of fully Independent polarization weak coherent states,” J. Lightwave Technol. 31, 2881–2887 (2013).
[Crossref]

T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. C. do Amaral, G. P. Temporão, and J. P. von der Weid, “Proof-of–principle demonstration of measurement-device–independent quantum key distribution using polarization qubits,” Phys. Rev. A 88, 052303 (2013).
[Crossref]

Xu, Z.

J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
[Crossref]

J. B. Liu, M. Le, B. Bai, W. Wang, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference of two independent single-mode He-Ne lasers,” Opt. Commun. 350, 196–201 (2015).
[Crossref]

J. B. Liu, H. Zheng, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The first- and second-order temporal interference between thermal and laser light,” Opt. Express 23, 11868–11878 (2015).
[Crossref]

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]

Yuan, Z. L.

Z. L. Yuan, M. Lucamarini, J. F. Dynes, B. Fröhlich, M. B. Ward, and A. J. Shields, “Interference of short optical pulses from independent gain-switched laser diodes for quantum secure communications,” Phys. Rev. Appl. 2, 064006 (2014).
[Crossref]

Yuan, Z. S.

Z. S. Yuan, X. H. Bao, C. Y. Lu, J. Zhang, C. Z. Peng, and J. W. Pan, “Entangled photons and quantum communication,” Phys. Rep. 497, 1–40 (2010).
[Crossref]

Zbinden, H.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692–695 (2007).
[Crossref]

H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, “Quantum interference with photon pairs created in spatially separated sources,” Phys. Rev. A 67, 022301 (2003).
[Crossref]

Zeilinger, A.

R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett. 96, 240502 (2006).
[Crossref]

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw, and A. Zeilinger, “Wave-particle duality of C60 molecules,” Nature 401, 680–682 (1999).
[Crossref]

J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, “Single and double-slit diffraction of neutrons,” Rev. Mod. Phys. 60, 1067–1073 (1988).
[Crossref]

Zhang, J.

Z. S. Yuan, X. H. Bao, C. Y. Lu, J. Zhang, C. Z. Peng, and J. W. Pan, “Entangled photons and quantum communication,” Phys. Rep. 497, 1–40 (2010).
[Crossref]

Zhang, W.

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117, 013602 (2016).
[Crossref]

Zheng, H.

Zheng, H. B.

J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
[Crossref]

Zhou, Y.

J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
[Crossref]

J. B. Liu, M. Le, B. Bai, W. Wang, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference of two independent single-mode He-Ne lasers,” Opt. Commun. 350, 196–201 (2015).
[Crossref]

J. B. Liu, H. Zheng, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The first- and second-order temporal interference between thermal and laser light,” Opt. Express 23, 11868–11878 (2015).
[Crossref]

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]

Zukowski, M.

R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett. 96, 240502 (2006).
[Crossref]

Am. J. Phys. (3)

A. Tonomura, J. Endo, T. Matsuda, and T. Kawasaki, “Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57, 117–120 (1989).
[Crossref]

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

R. J. Glauber, “Dirac’s famous dictum on interference: one photon or two?” Am. J. Phys. 63, 12 (1995).
[Crossref]

Appl. Phys. B (1)

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

Chin. Phys. B (1)

J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
[Crossref]

Europhys. Lett. (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]

P. Grangier, G. Roger, and A. Aspect, “Evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences,” Europhys. Lett. 1, 173–179 (1986).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. B (2)

Nat. Phys. (1)

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692–695 (2007).
[Crossref]

Nature (6)

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

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

R. H. Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 178, 1046–1048 (1956).
[Crossref]

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

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

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw, and A. Zeilinger, “Wave-particle duality of C60 molecules,” Nature 401, 680–682 (1999).
[Crossref]

Opt. Commun. (1)

J. B. Liu, M. Le, B. Bai, W. Wang, H. Chen, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference of two independent single-mode He-Ne lasers,” Opt. Commun. 350, 196–201 (2015).
[Crossref]

Opt. Express (2)

Opt. Lett. (4)

Optica (1)

Phys. Lett. A (1)

R. L. Pfleegor and L. Mandel, “Interference effects at the single photon level,” Phys. Lett. A 24, 766–767 (1967).
[Crossref]

Phys. Rep. (1)

Z. S. Yuan, X. H. Bao, C. Y. Lu, J. Zhang, C. Z. Peng, and J. W. Pan, “Entangled photons and quantum communication,” Phys. Rep. 497, 1–40 (2010).
[Crossref]

Phys. Rev. (2)

L. Mandel, “Quantum theory of interference effects produced by independent light beams,” Phys. Rev. 134, A10–A15 (1964).
[Crossref]

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

Phys. Rev. A (2)

H. de Riedmatten, I. Marcikic, W. Tittel, H. Zbinden, and N. Gisin, “Quantum interference with photon pairs created in spatially separated sources,” Phys. Rev. A 67, 022301 (2003).
[Crossref]

T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. C. do Amaral, G. P. Temporão, and J. P. von der Weid, “Proof-of–principle demonstration of measurement-device–independent quantum key distribution using polarization qubits,” Phys. Rev. A 88, 052303 (2013).
[Crossref]

Phys. Rev. Appl. (1)

Z. L. Yuan, M. Lucamarini, J. F. Dynes, B. Fröhlich, M. B. Ward, and A. J. Shields, “Interference of short optical pulses from independent gain-switched laser diodes for quantum secure communications,” Phys. Rev. Appl. 2, 064006 (2014).
[Crossref]

Phys. Rev. Lett. (9)

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

H. K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).
[Crossref]

R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett. 96, 240502 (2006).
[Crossref]

P. Qian, Z. Gu, R. Cao, R. Wen, Z. Y. Ou, J. F. Chen, and W. Zhang, “Temporal purity and quantum interference of single photons from two independent cold atomic ensembles,” Phys. Rev. Lett. 117, 013602 (2016).
[Crossref]

J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[Crossref]

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

T. F. Jordan and F. Ghielmetti, “Quantum theory of interference of light from two lasers,” Phys. Rev. Lett. 12, 607–609 (1964).
[Crossref]

O. Carnal and J. Mlynek, “Young’s double-slit experiment with atoms: a simple atom interferometer,” Phys. Rev. Lett. 66, 2689–2692 (1991).
[Crossref]

Rep. Prog. Phys. (1)

F. Flamini, N. Spagnolo, and F. Sciarrino, “Photonic quantum information processing: a review,” Rep. Prog. Phys. 82, 016001 (2019).
[Crossref]

Rev. Mod. Phys. (3)

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

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

A. Zeilinger, R. Gähler, C. G. Shull, W. Treimer, and W. Mampe, “Single and double-slit diffraction of neutrons,” Rev. Mod. Phys. 60, 1067–1073 (1988).
[Crossref]

Other (1)

P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Oxford University, 1958), p. 9.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1. Experimental setup for observation of Hong–Ou–Mandel (HOM) interference with two completely independent continuous-wave coherent photons (CWCPs). (a) Schematic of the experimental setup for HOM interference between two independent CWCPs (P, polarizer; H, half-wave plate; Q, quarter-wave plate; BS, beam splitter; SPDs, single-photon detectors; TCSPC, time-correlated single-photon counter; Rb, atomic vapor cell of Rb85; SAS, saturated absorption spectroscopy; PS, polarization spectroscopy). (b) SAS spectrum (blue curve) of ECDL1 and (c) PS spectrum (red curve) of ECDL2 for the 5S1/2(F=3)5P1/2(F=2,3) transition of Rb85.
Fig. 2.
Fig. 2. Spectral properties of two independent continuous-wave coherent photons. Spectral density spectrum of (a) frequency-stabilized ECDL1 upon error-signal locking of the SAS with frequency modulation and (b) frequency-stabilized ECDL2 obtained by offset locking of the PS.
Fig. 3.
Fig. 3. Hong–Ou–Mandel interference fringe with two independent continuous-wave coherent photons. Experimental result and theoretical curve fitting under the conditions of a bandwidth of 3.3 MHz and Δω=0.
Fig. 4.
Fig. 4. Two-photon beat fringes for different offset frequencies. (a) PS spectra (blue: Δω/2π=+3.5MHz; black: Δω=0; and red: Δω/2π=3.5MHz) of ECDL2 frequency-stabilized to the 5S1/2(F=3)5P1/2(F=3) transition of Rb85; the horizontal dashed line (gray) indicates the DC-offset reference. (b)–(d) The HOM-type two-photon beating fringes are measured for different offset frequencies.
Fig. 5.
Fig. 5. Hong–Ou–Mandel interference fringes with arbitrary time delay between two independent CWCP sources. Three single-mode fiber (SMF) spools are employed as relative optical delay lines (ODLs). (a) SMFof0m (black curve), (b) SMFof200m (red curve), (c) SMFof400m (green curve), and (d) SMFof600m (blue curve).

Equations (1)

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

Pcoin.(ΔT)=1VΓ12(ΔT)cos(ΔωΔT),