Quantum Statistics of Two Identical Particles and Modified Hong-Ou-Mandel Interferometer

TL;DR

This paper proposes an experimental scheme using a modified Hong-Ou-Mandel interferometer to observe the transition from quantum to classical statistics in two identical particles by varying thermal energy and internal energy levels.

Contribution

It introduces a realistic experimental approach to probe the quantum-classical transition in two-particle statistics through a mesoscopic interferometer setup.

Findings

Demonstrates the emergence of effective distinguishability with increasing thermal energy.

Shows the transition between quantum indistinguishability and classical distinguishability.

Ensures preservation of equilibrium distribution via unitarity of scattering process.

Abstract

We propose an experimental scheme to probe the quantum statistics of two identical particles. The transition between the quantum and classical statistics of two identical particles is described by the particles having identical multiple internal energy levels. We show that effective distinguishability emerges as the thermal energy increases with respect to the energy level spacing, and the mesoscopic regime bridges 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/separation process ensures the preservation of the equilibrium distribution and allows 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.