Time-dependent Maxwell field operators and field energy density for an atom near a conducting wall

TL;DR

This paper analyzes the time evolution of electromagnetic field operators near a conducting wall, deriving energy densities and interactions, including the dynamical Casimir-Polder effect, with a focus on causality and boundary effects.

Contribution

It provides a detailed, iterative solution for time-dependent field operators near a conducting boundary, extending understanding of dynamical Casimir-Polder interactions and magnetic contributions.

Findings

Field energy densities can be interpreted as superpositions of direct and reflected fields.

Relativistic causality is maintained in the propagation of fields.

Large-time behavior recovers known stationary Casimir-Polder results.

Abstract

We consider the time evolution of the electric and magnetic field operators for a two-level atom, interacting with the electromagnetic field, placed near an infinite perfectly conducting wall. We solve iteratively the Heisenberg equations for the field operators and obtain the electric and magnetic energy density operators around the atom (valid for any initial state). Then we explicitly evaluate them for an initial state with the atom in its bare ground state and the field in the vacuum state. We show that the results can be physically interpreted as the superposition of the fields propagating directly from the atom and the fields reflected on the wall. Relativistic causality in the field propagation is discussed. Finally we apply these results to the calculation of the dynamical Casimir-Polder interaction energy in the far zone between two atoms when a boundary condition such as a conducting wall is present. Magnetic contributions to the interatomic Casimir-Polder interaction in the presence of the wall are also considered. We show that, in the limit of large times, the known results of the stationary case are recovered.