Quantum statistics of two identical particles and modified Hong-Ou-Mandel interferometer

We propose an experimental scheme to probe the quantum statistics of two identical particles. The transition from quantum to classical statistics of two identical particles can be described by introducing multiple identical internal energy levels for each particle. We show that as the thermal energy exceeds the level spacing, the particles acquire effective distinguishability. This gives rise to a mesoscopic regime that smoothly connects quantum indistinguishability and classical distinguishability. A realistic experimental approach is proposed using a two-particle interferometer, where the particles reach statistical equilibrium before the two-particle distribution is measured. The unitarity of the scattering and separation processes guarantees preservation of the equilibrium distribution, enabling a direct measurement of the two-particle statistical distribution. Our results show the transition between quantum and classical behavior of the two-particle distribution, which can be directly probed by a realistic experiment.