Three-Photon and Hybrid Coherent-Fock Interference in a Two-Phase Six-Port Mach-Zehnder Interferometer

Abstract

We present a unified theoretical analysis of three-photon quantum interference in a Six-Port Mach-Zehnder Interferometer (6p-MZI) constructed from two cascaded tritters, with two independent phase modulators placed between the tritter arms. We analytically derive the transfer matrix of the 6p-MZI and show how they organize into three symmetry classes, governed by the discrete Fourier transform (DFT) structure of the tritter and the conjugate relations. Furthermore, we analyze two input regimes: First, three indistinguishable single photons are injected into the tritter, and the output probability distributions $P_{[111]}$, $P_{[\{300\}]}$, and $P_{[\{210\}]}$ are derived as functions of the two relative phases $(ϕ_1, ϕ_2)$. At $ϕ_2 = 0$, the single-phase limit is recovered, which confirms 100\% visibility of the even-distribution fringe. Second, a hybrid coherent-Fock input $|α\rangle_1|α\rangle_2|1\rangle_3$ is analyzed via the density matrix formalism. The average photon number at each output port exhibits amplitude-dependent phase shifts. Our results establish the 6p-MZI as a programmable platform for tripartite quantum state manipulation and coherent amplitude sensing.