Asymptotics for Anisotropic Rabi Models

TL;DR

This paper rigorously analyzes the spectral transition of anisotropic Rabi models from the rotating-wave approximation to the full model as the coupling strength becomes infinitely large, bridging a gap in mathematical understanding.

Contribution

It provides a rigorous operator-theoretic analysis of the spectral limit of anisotropic Rabi models at strong coupling, connecting physical intuition with mathematical formalism.

Findings

Spectral evolution from the rotating-wave approximation to the full Rabi model clarified.

Operator limits characterized as coupling tends to infinity.

Mathematically rigorous treatment of anisotropic Rabi model interpolations.

Abstract

A one-parameter family of self-adjoint operators interpolating between the quantum Rabi Hamiltonian and its rotating-wave approximation is studied. A mathematically rigorous treatment of such interpolations has been lacking. Motivated by the physical claim that counter-rotating terms dominate at strong coupling, we analyze the limit in which the coupling constant of the anisotropic Rabi model tends to infinity. Our results provide an operator-theoretic description of this limit and clarify the spectral evolution from the rotating-wave approximation to the full Rabi model.