Approximate controllability of the Jaynes-Cummings dynamics

TL;DR

This paper proves approximate controllability of the Jaynes-Cummings model in quantum optics for most coupling strengths, using spectral analysis to handle different control operators acting on the bosonic component.

Contribution

It establishes approximate controllability of the Jaynes-Cummings dynamics for all but a countable set of coupling constants, explicitly characterizing this set and analyzing spectral properties.

Findings

Approximate controllability holds for all coupling constants except a countable set.

Spectral analysis shows non-resonance conditions are satisfied for most coupling values.

Control operators acting on the bosonic part enable controllability in the model.

Abstract

We investigate the controllability of the Jaynes-Cummings dynamics in the resonant and nearly resonant regime. We analyze two different types of control operators acting on the bosonic part, corresponding - in the application to cavity QED - to an external electric and magnetic field, respectively. We prove approximate controllability for these models, for all values of the coupling constant g except those in a countable set S which is explicitly characterized in the statement. The proof relies on a spectral analysis which yields the non-resonance of the spectrum for every real g which is not in S.