Photon Statistics for Fock and Coherent States Interfering in a Beamsplitter

Abstract

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 $|n⟩|\alpha ⟩$, and coherent states $|\alpha ⟩|\beta ⟩$. 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.

8 pages, 5 figures