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.
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