Orthogonality Catastrophes in Quantum Electrodynamics

TL;DR

This paper demonstrates that inserting a polarizable particle into a large optical cavity causes a fundamental orthogonality in the quantum state of the electromagnetic field, leading to a divergence in low-energy photon generation.

Contribution

It establishes an exact mapping of the photon problem to a many-body fermionic system and predicts macroscopic photon generation due to particle motion or insertion/removal.

Findings

Photon ground states become orthogonal with particle insertion.

Motion of particles induces divergence in low-energy photons.

Results impact understanding of quantum measurement and Casimir effects.

Abstract

The insertion of a small polarizable particle in an arbitrarily large optical cavity significantly alters the quantum-mechanical state of the electromagnetic field in that the photon ground state of the empty cavity and that of the cavity with the particle become mutually orthogonal and, thus, cannot be connected adiabatically in the infinite limit. The photon problem can be mapped exactly onto that of a many-body system of fermions, which is known to exhibit an orthogonality catastrophe when a finite-range local potential is introduced. We predict that the motion of polarizable objects inside a cavity, no matter how slow, as well as their addition and removal from the cavity, will generate a macroscopic, diverging number of low-energy photons. The significance of these results in regard to the quantum measurement problem and the dynamical Casimir effect are also discussed.