The Rabi Hamiltonian in the dispersive regime

TL;DR

This paper analyzes the Rabi Hamiltonian in the dispersive and ultra-strong coupling regimes, deriving approximate solutions and eigenfunctions using a recent unitary transformation.

Contribution

It introduces a novel application of a recent unitary transformation to obtain approximate Hamiltonians, energy levels, and eigenfunctions in complex coupling regimes.

Findings

Derived approximate Hamiltonian and eigenfunctions

Connected the approximation to other regimes

Discussed the validity of the approximation

Abstract

The Rabi Hamiltonian is studied in the dispersive regime and ultra-strong coupling. We employ a recent unitary transformation to obtain not only the approximate Hamiltonian and its energy levels but also its eigenfunctions. The relationship of the approximation with other regimes and their approximations are also discussed.