A simple model of the classicalZitterbewegung: Photon wave function

Nuri Ünal

Ashok Muthukrishnan, Marlan O. Scully, M Zubairy

Nuri

We propose a simple classical model the zitterbewegung. In this model spin is proportional to the velocity o f the particle, lhe component parallel to p is constant and the orthogonal components are oscillating with 2p frequency. The quantization o f the system gives wave equations for spin O, 1/2, 1, 3/2,..., etc. respectively. These equations are convenient for massless particles. The wave equation of the spin-l, massless free particle is equivalent to the Maxwell equations and the state functions have a probability interpretation and exhibit conserved current densities. The ground state has zero energy.

Iwo Białynicki‐Birula

Alexandr Petrovich Davydov, Tatiana Pavlovna Zlydneva

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.

Nuri Ünal