On numerical and approximate analytical modeling of single- and two-photon Young's experiment using the photon coordinate wave function

Abstract

In modern areas of photonics, the physical description of the interaction of photons with matter in the control, transmission and registration of single-photon and two-photon states implemented in practice is of great importance. An appropriate acceptable description may be faced with the need to take into account various kinds of interference effects associated with these states. Meanwhile, even the most “simple” case of single-photon interference in Young's experiment requires the use of a rather complex apparatus of quantum electrodynamics. This article explains one- and two-photon interference in Young's thought experiment based on the photon wave function (PWF) in coordinate representation. This explanation is illustrated by two examples of wavelengths: 10.6 μm and 1.5 cm. For both examples, two approaches to PWF modeling are used: “purely quantum-mechanical” and “quasi-classical”. In the first approach, a 6-component coordinate PWF is constructed using a spherically symmetric momentum distribution in a wave packet, followed by numerical and approximate analytical calculations. In the second approach, a one-component “quasi-classical” PWF is constructed, which corresponds to either electric dipole radiation or simulated spherically symmetric radiation. In all cases, the same pronounced interference pattern was obtained, which allows us to conclude that not only the quantum-mechanical coordinate PWF is able to explain the phenomena of one- and two-photon interference, but also a much simpler “quasi-classical” PWF. This conclusion sheds light on the theoretical interpretation of the measurement of the coordinate PWF in some recent experiments.