Extending the Hong-Ou-Mandel Effect: the power of nonclassicality

We show that the parity (evenness or oddness) of a nonclassical state of light has a dominant influence on the interference effects at a balanced beam splitter, irrespective of the state initially occupying the other input mode. Specifically, the parity of the nonclassical state gives rise to destructive interference effects that result in deep valleys in the output joint number distribution of which the Hong-Ou-Mandel (HOM) effect is a limiting case. The counter-intuitive influence of even a single photon to control the output of a beam splitter illuminated by any field, be it a coherent or even a noisy thermal field, demonstrates the extraordinary power of non-classicality. The canonical example of total destructive interference of quantum amplitudes leading to the absence of coincidence counts from a 50/50 beam splitter is the celebrated HOM effect, characterized by the vanishing of the joint probability of detecting singe photons in each of the output beams. We show that this is a limiting case of more general input states upon which a 50/50 BS can create total, or near total, destructive interference of quantum amplitudes. For odd photon number input Fock states of arbitrary value n>0 we show that the joint photon number probabilities vanish when detecting identical photon numbers in each output beams. We examine the mixing of photon number states of n = 1, 2, and 3 with a CV state, such as a coherent state of arbitrary amplitude, and a thermal state. These vanishing joint probabilities form what we call a central nodal line -- a contiguous set of zeros representing complete destructive interference of quantum amplitudes. For odd or even photon number Fock states with n>1 there will be additional off-diagonal pseudo-nodal curves along which the joint photon number probabilities are either zero, or near zero, which constitute a near, but not complete, destructive interference.
Comment: 27 pages, 13 figures; v2: minor editorial fixes (minor notational corrections in Appendix D), additional clarification comments at end of Appendix A