Cavity Quantum Electrodynamics in the Ultrastrong Coupling Regime

TL;DR

This paper analyzes the Jaynes-Cummings-Paul Hamiltonian in the ultrastrong coupling regime, revealing that traditional solutions are invalid and providing a new mathematical approach for accurate modeling.

Contribution

It rigorously demonstrates the breakdown of standard solutions in the ultrastrong coupling regime and offers a corrected mathematical formulation.

Findings

Standard solutions fail in the ultrastrong coupling regime

Bosonic field operators exhibit non-sinusoidal time variations

A new mathematical solution is proposed for accurate modeling

Abstract

We revisit the mathematical formulation of the famous Jaynes-Cummings-Paul Hamiltonian, which describes the interaction of a two-level atom with a single mode of an electromagnetic cavity reservoir. We rigorously show that under the condition of Ultrastrong coupling between the atom and cavity, in which the transition frequency is comparable to the coupling frequency, the bosonic field operators undergo non-sinusoidal time variations. As a result, the well-known solutions to the Jaynes-Cummings-Paul model are no longer valid, even when the rotating wave approximation is not used. We show how a correct mathematical solution could be found instead.