We present a straightforward yet comprehensive theoretical study of different quantum states emerging from a bi-modal beamsplitter when various input states interfere. Specifically, we analyze the output states for different combinations of input fields, including Fock states ∣n⟩∣m⟩, hybrid states ∣n⟩∣α⟩, and coherent states ∣α⟩∣β⟩. We derive explicit expressions for the output state vectors, calculate the mean photon number, photon number variance, Mandel Q parameter, and secondorder coherence function to characterize the statistical properties of the output fields. Our results are intended as a pedagogical resource, serving as an introductory reference for students and researchers aiming to understand basic photon statistics using beamsplitters.
@article{arxiv.2508.08223,
title = {Photon Statistics for Fock and Coherent States Interfering in a Beamsplitter},
author = {Jhordan A. T. Santiago},
journal= {arXiv preprint arXiv:2508.08223},
year = {2026}
}