Polarization-Dependent Behavior of Entangled Two-Photon States

We modeled the detection rate for a polarization-entangled two-photon state traveling through a unitary device of two input and two output paths, where output photons emerge along separate paths. We considered polarization-entangled states created via spontaneous parametric down-conversion, with variable relative amplitude and phase between horizontally and vertically polarized pairs. We investigated the detection rate as a function of relative time delay when one input photon encountered a phase retarder of arbitrary orientation. Applying polarization entanglement to a rotated half-waveplate and a beamsplitter, we replicated the Hong-Ou-Mandel dip at zero time delay and observed polarization entanglement-induced modifications to this destructive interference. As the relative amplitude of horizontally versus vertically polarized pairs becomes equal, increasing their relative phase difference from 0 to 90° washes out and inverts the dip. At its peak, constructive interference occurs and output photons are always detected along separate output paths. This model provides a foundation for future work into polarization-entangled photons through different phase retarders and unitary devices.