Entangled States and Entropy Remnants of a Photon-Electron System

TL;DR

This paper analyzes entanglement between photons and electrons, solving the Schrödinger equation non-perturbatively to reveal persistent entropy remnants after interaction, influenced by how the interaction is initiated and terminated.

Contribution

It provides a non-perturbative analytical solution for photon-electron entanglement and demonstrates the dependence of entropy remnants on interaction switching.

Findings

Non-vanishing entropy remnants persist after interaction.

Entanglement dynamics depend on interaction switching.

Wave packet analysis describes subsystem separation.

Abstract

In the present paper an example of entanglement between two different kinds of interacting particles, photons and electrons is analysed. The initial-value problem of the Schroedinger equation is solved non-perturbatively for the system of a free electron interacting with a quantized mode of the electromagnetic radiation. Wave packets of the dressed states so obtained are constructed in order to describe the spatio-temporal separation of the subsystems before and after the interaction. The joint probability amplitudes are calculated for the detection of the electron at some space-time location and the detection of a definite number of photons. The analytical study of the time evolution of entanglement between the initially separated electron wave packet and the radiation mode leads to the conclusion that in general there are non-vanishing entropy remnants in the subsystems after the interaction. On the basis of the simple model to be presented here, the calculated values of the entropy remnants crucially depend on the character of the switching-on and off of the interaction.