Photon Statistics for Fock and Coherent States Interfering in a Beamsplitter

TL;DR

This paper provides a comprehensive theoretical analysis of photon statistics resulting from various quantum states interfering in a beamsplitter, including Fock, coherent, and hybrid states, with explicit formulas and statistical characterizations.

Contribution

It offers explicit expressions for output states and statistical measures for different input states, serving as an educational resource for understanding photon statistics in quantum optics.

Findings

Derived explicit output state vectors for various input states

Calculated mean photon number, variance, Mandel Q, and coherence functions

Provided a pedagogical framework for analyzing photon statistics in beamsplitters

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 $|n\rangle|m\rangle$, hybrid states $|n\rangle|\alpha\rangle$, and coherent states $|\alpha\rangle|\beta\rangle$. 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.