On the Interference of Coherent Photon States and Number Photon States

This study presents a theoretical analysis of three-photon interference in a six-port Mach-Zehnder Interferometer (6p-MZI) system, which incorporates two identical ideal six-port optical beam splitters (tritters) and phase modulators. We investigate interference patterns produced by hybrid input photon configurations that combine Fock state and coherent states, exploring the effects of both relative phase differences and average number of coherent photon state at the input ports. Our analysis demonstrates that the phase positions of constructive interference peaks systematically shift in response to the average number of coherent photons $\left(|\alpha|^{2}\right)$ at the input ports. When $|\alpha|^{2}$ increases from 0 to 0.5, the constructive interference peaks at output ports 2 and 3 undergo symmetric shifts of up to $\pi / 3$ radians relative to the extreme interference pattern of output port 3 at $5 \pi / 3$. The results highlight the high sensitivity of interference patterns to both relative phase differences and coherent state photon amplitudes. These findings suggest novel approaches for controlling three-photon interference patterns in 6p-MZI systems through precise manipulation of phase and low-amplitude coherent photon states. This work advances our understanding of multi-photon interference in the quantum regime, with potential applications in quantum information processing, metrology, and fundamental quantum optics studies.