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2020-08-20
Classical and Quantum Electromagnetic Interferences: What Is the Difference?
By
Progress In Electromagnetics Research, Vol. 168, 1-13, 2020
Abstract
The zeroing of second order correlation functions between output fields after interferences in a 50/50 beam splitter has been accepted decades-long in the quantum optics community as an indicator of the quantum nature of lights. But, a recent work [1] presented some notable discussions and experiments that classical electromagnetic fields can still exhibit the zero correlation under specific conditions. Here, we examine analytically classical and quantum electromagnetic field interferences in a 50/50 beam splitter in the context of the second order correlation function for various input conditions. Adopting the Heisenberg picture in quantum electromagnetics, we examine components of four-term interference terms in the numerator of second order correlation functions and elucidate their physical significance. As such, we reveal the fundamental difference between the classical and quantum interference as illustrated by the Hong-Ou-Mandel (HOM) effect. The quantum HOM effect is strongly associated with: (1) the commutator relation that does not have a classical analogue; (2) the property of Fock states needed to stipulate the one-photon quantum state of the system; and (3) a destructive wave interference effect. Here, (1) and (2) imply the indivisibility of a photon. On the contrary, the classical HOM effect requires the presence of two destructive wave interferences without the need to stipulate a quantum state.
Citation
Dong-Yeop Na Weng Cho Chew , "Classical and Quantum Electromagnetic Interferences: What Is the Difference?," Progress In Electromagnetics Research, Vol. 168, 1-13, 2020.
doi:10.2528/PIER20060301
http://www.jpier.org/PIER/pier.php?paper=20060301
References

1. Sadana, S., D. Ghosh, K. Joarder, A. N. Lakshmi, B. C. Sanders, and U. Sinha, "Near-100% two-photon-like coincidence-visibility dip with classical light and the role of complementarity," Phys. Rev. A, Vol. 100, 013839, 2019.
doi:10.1103/PhysRevA.100.013839

2. Wikipedia, Newton’s rings, https://en.wikipedia.org/wiki/Newton's_rings.

3. Phase-locked loop, https://en.wikipedia.org/wiki/Phase-locked_loop.

4. Goodman, J. W., Statistical Optics, Wiley-Interscience, New York, 1985.

5. Loudon, R., "The Quantum Theory of Light," OUP Oxford, 2000.

6. Mandel, L. and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press, Cambridge, UK, 1995.
doi:10.1017/CBO9781139644105

7. Gerry, C. and P. Knight, Introductory Quantum Optics, Cambridge University Press, Cambridge, UK, 2004.
doi:10.1017/CBO9780511791239

8. Fox, M., Quantum Optics: An Introduction, Vol. 15, OUP Oxford, Oxford, UK, 2006.

9. Hanbury Brown, R. and R. Q. Twiss, "Correlation between photons in two coherent beams of light," Nature, Vol. 177, No. 4497, 27-29, 1956.
doi:10.1038/177027a0

10. Hong, C. K., Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett., Vol. 59, 2044-2046, Nov. 1987.

11. Fearn, H. and R. Loudon, "Quantum theory of the lossless beam splitter," Optics Communications, Vol. 64, 485-490, 1987.
doi:10.1016/0030-4018(87)90275-6

12. Kaltenbaek, R., B. Blauensteiner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, "Experimental interference of independent photons," Phys. Rev. Lett., Vol. 96, 240502, Jun. 2006.
doi:10.1103/PhysRevLett.96.240502

13. Prasad, S., M. O. Scully, and W. Martienssen, "A quantum description of the beam splitter," Optics Communications, Vol. 62, No. 3, 139-145, 1987.
doi:10.1016/0030-4018(87)90015-0

14. Ou, Z. Y., "Quantum theory of fourth-order interference," Phys. Rev. A, Vol. 37, 1607-1619, 1988.
doi:10.1103/PhysRevA.37.1607

15. Ham, B. S., "The origin of anticorrelation for photon bunching on a beam splitter," Scientific Reports, Vol. 10, 7309, 2020.
doi:10.1038/s41598-020-64441-2

16. Branczyk, A. M., "Hong-Ou-Mandel interference,", arXiv:1711.00080, 2017.

17. Di Martino, G., Y. Sonnefraud, M. S. Tame, S. Kena-Cohen, F. Dieleman, K. Ozdemir, M. S. Kim, and S. A. Maier, "Observation of quantum interference in the plasmonic Hong-Ou-Mandel effect," Phys. Rev. Applied, Vol. 1, 034004, 2014.
doi:10.1103/PhysRevApplied.1.034004

18. Longo, P., J. H. Cole, and K. Busch, "The Hong-Ou-Mandel effect in the context of few-photon scattering," Opt. Express, Vol. 20, 12 326-12 340, 2012.
doi:10.1364/OE.20.012326

19. Lang, C., C. Eichler, L. Steffen, J. M. Fink, M. J. Woolley, A. Blais, and A. Wallraff, "Correlations, indistinguishability and entanglement in Hong-Ou-Mandel experiments at microwave frequencies," Nature Physics, Vol. 9, 345-348, 2013.
doi:10.1038/nphys2612

20. Lopes, R., A. Imanaliev, A. Aspect, M. Cheneau, D. Boiron, and C. I. Westbrook, "Atomic Hong-Ou-Mandel experiment," Nature, Vol. 520, 66-68, 2015.
doi:10.1038/nature14331

21. Kobayashi, T., R. Ikuta, S. Yasui, S. Miki, T. Yamashita, H. Terai, T. Yamamoto, M. Koashi, and N. Imoto, "Frequency-domain Hong-Ou-Mandel interference," Nature Photonics, Vol. 10, 441-444, 2016.
doi:10.1038/nphoton.2016.74

22. Imany, P., O. D. Odele, M. S. Alshaykh, H.-H. Lu, D. E. Leaird, and A. M. Weiner, "Frequency-domain Hong-Ou-Mandel interference with linear optics," Opt. Lett., Vol. 43, No. 12, 2760-2763, 2018.
doi:10.1364/OL.43.002760

23. Rohde, P. P. and T. C. Ralph, "Frequency and temporal effects in linear optical quantum computing," Phys. Rev. A, Vol. 71, 032320, 2005.
doi:10.1103/PhysRevA.71.032320

24. Rohde, P. P., T. C. Ralph, and M. A. Nielsen, "Optimal photons for quantum-information processing," Phys. Rev. A, Vol. 72, 052332, 2005.
doi:10.1103/PhysRevA.72.052332

25. Mahrlein, S., S. Oppel, R. Wiegner, and J. von Zanthier, "Hong-Ou-Mandel interference without beam splitters," Journal of Modern Optics, Vol. 64, 921-929, 2017.
doi:10.1080/09500340.2016.1242790

26. Kim, M. S., W. Son, V. Buzek, and P. L. Knight, "Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement," Phys. Rev. A, Vol. 65, 032323, 2002.
doi:10.1103/PhysRevA.65.032323

27. Walschaers, M., "Signatures of many-particle interference," Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 53, 043001, 2020.
doi:10.1088/1361-6455/ab5c30

28. Deng, Y.-H., H. Wang, X. Ding, Z.-C. Duan, J. Qin, M.-C. Chen, Y. He, Y.-M. He, J.-P. Li, Y.- H. Li, L.-C. Peng, E. S. Matekole, T. Byrnes, C. Schneider, M. Kamp, D.-W. Wang, J. P. Dowling, S. Hofling, C.-Y. Lu, M. O. Scully, and J.-W. Pan, "Quantum interference between light sources separated by 150 million kilometers," Phys. Rev. Lett., Vol. 123, 080401, 2019.
doi:10.1103/PhysRevLett.123.080401

29. Chew, W. C., Waves and Fields in Inhomogeneous Media, Van Nostrand, 1990.

30. Electromagnetic field theory, Lecture Notes for ECE 604 at Purdue U, 2020, https://engineering.purdue.edu/wcchew/ece604s20/EMFTAll.pdf.

31. Na, D.-Y., J. Zhu, F. L. Teixeira, and W. C. Chew, "Quantum information propagation preserving computational electromagnetics,", arXiv preprint arXiv:1911.00947, 2019.

32. Na, D.-Y., J. Zhu, W. C. Chew, and F. L. Teixeira, "Quantum information preserving computational electromagnetics," Phys. Rev. A, Vol. 102, No. 1, 013711, Jul. 2020.
doi:10.1103/PhysRevA.102.013711

33. Chew, W. C., A. Y. Liu, C. Salazar-Lazaro, and W. E. I. Sha, "Quantum electromagnetics: A new look — Part I and Part II," J. Multiscale and Multiphys. Comput. Techn., Vol. 1, 73-97, 2016.
doi:10.1109/JMMCT.2016.2617018

34. Kirk, D. E., Optimal Control Theory: An Introduction, Courier Corporation, 2004.

35. Schrodinger, E., "An undulatory theory of the mechanics of atoms and molecules," Phys. Rev., Vol. 28, No. 6, 1049, 1926.
doi:10.1103/PhysRev.28.1049

36. Chew, W., A. Liu, C. Salazar-Lazaro, D.-Y. Na, and W. Sha, "Hamilton equations, commutator, and energy conservation," Quantum Reports, Vol. 1, 295-303, 2019.
doi:10.3390/quantum1020027

37. Louisell, W. H. and W. H. Louisell, Quantum Statistical Properties of Radiation, Vol. 7, Wiley, New York, 1973.

38. Haken, H., Quantum Field Theory of Solids, an Introduction, North-Holland, 1976.

39. Cohen-Tannoudji, C., J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications, Wiley-VCH, New York, NY, USA, 1988.

40. Vogel, W. and D.-G. Welsch, "Quantum Optics," John Wiley & Sons, 2006.

41. Walls, D. F. and G. J. Milburn, Quantum Optics, Springer Science & Business Media, 2007.

42. Scheel, S. and S. Y. Buhmann, "Macroscopic quantum electrodynamics," Acta Physica Slovaca, Vol. 58, 675-809, 2008.

43. Garrison, J. and R. Chiao, Quantum Optics, Oxford University Press, Oxford, UK, 2008.
doi:10.1093/acprof:oso/9780198508861.001.0001

44. Gottfried, K. and T.-M. Yan, Quantum Mechanics: Fundamentals, CRC Press, Boca Raton, FL, USA, 2018.
doi:10.4324/9780429493225

45. Milonni, P., An Introduction to Quantum Optics and Quantum Fluctuations, Oxford University Press, 2019.
doi:10.1093/oso/9780199215614.001.0001

46. Miller, D. A., Quantum Mechanics for Scientists and Engineers, Cambridge University Press, Cambridge, UK, 2008.
doi:10.1017/CBO9780511813962

47. Chew, W. C., "Quantum mechanics made simple: Lecture notes for ECE 487 at UIUC,", 2016, http://wcchew.ece.illinois.edu/chew/course/QMAll20161206.pdf.

48. Gerry, C. C. and K. M. Bruno, The Quantum Divide: Why Schrodinger's Cat is Either Dead or Alive, Oxford University Press, Oxford, UK, 2013.
doi:10.1093/acprof:oso/9780199666560.001.0001

49. Glauber, R. J., "The quantum theory of optical coherence," Phys. Rev., Vol. 130, 2529-2539, 1963.
doi:10.1103/PhysRev.130.2529