  The Hong-Ou-Mandel (HOM) effect is widely regarded as the quintessential
quantum interference phenomenon in optics. In this work we examine how
nonlinearity can smear statistical photon bunching in the HOM interferometer.
We model both the nonlinearity and a balanced beam splitter with a single
two-level system and calculate a finite probability of anti-bunching arising in
this geometry. We thus argue that the presence of such nonlinearity would
reduce the visibility in the standard HOM setup, offering some explanation for
the diminution of the HOM visibility observed in many experiments. We use the
same model to show that the nonlinearity affects a resonant two-photon
propagation through a two-level impurity in a waveguide due to a "weak photon
blockade" caused by the impossibility of double-occupancy and argue that this
effect might be stronger for multi-photon propagation.
