Parametric Resonance in Quantum Electrodynamics Vacuum Birefringence

TL;DR

This paper investigates how an oscillating magnetic field can induce vacuum birefringence through parametric resonance in quantum electrodynamics, with potential observable effects in cavity and localized field setups.

Contribution

It provides analytical and numerical analysis of vacuum birefringence caused by parametric resonance in quantum electrodynamics, including effects in cavities and localized magnetic fields.

Findings

Parametric resonance enhances vacuum birefringence when external field frequency matches wave frequency.

Different growth rates for normal and parallel wave components lead to birefringence.

Rotation of the polarization ellipse occurs in both cavity and localized field scenarios.

Abstract

Vacuum magnetic birefringence is one of the most interesting non-linear phenomena in quantum electrodynamics because it is a pure photon-photon result of the theory and it directly signalizes the violation of the classical superposition principle of electromagnetic fields in the full quantum theory. We perform analytical and numerical calculations when an electromagnetic wave interacts with an oscillating external magnetic field. We find that in an ideal cavity, when the external field frequency is around the electromagnetic wave frequency, the normal and parallel components of the wave suffer parametric resonance at different rates, producing a vacuum birefringence effect growing in time. We also study the case where there is no cavity and the oscillating magnetic field is spatially localized in a region of length $L$. In both cases we find also a rotation of the elliptical axis.