Controllability of spin-boson systems

TL;DR

This paper investigates the controllability of spin-boson systems, specifically the Rabi model, demonstrating approximate controllability using geometric control and perturbation techniques for most interaction parameters.

Contribution

It introduces a novel control approach for the Rabi model, proving approximate controllability via geometric and spectral analysis methods.

Findings

Proves approximate controllability of the Rabi model.

Uses geometric control on Galerkin approximations.

Employs perturbation theory to ensure non-resonance.

Abstract

In this paper we study the so-called spin-boson system, namely {a two-level system} in interaction with a distinguished mode of a quantized bosonic field. We give a brief description of the controlled Rabi and Jaynes--Cummings models and we discuss their appearance in the mathematics and physics literature. We then study the controllability of the Rabi model when the control is an external field acting on the bosonic part. Applying geometric control techniques to the Galerkin approximation and using perturbation theory to guarantee non-resonance of the spectrum of the drift operator, we prove approximate controllability of the system, for almost every value of the interaction parameter.