A Mathematical Analysis of Dressed Photon in Ground State of Generalized Quantum Rabi Model Using Pair Theory

TL;DR

This paper provides a mathematical analysis of the dressed photon phenomenon in the ground state of a generalized quantum Rabi model with an $A^{2}$-term, focusing on the deep-strong coupling regime and quantum phase transitions.

Contribution

It introduces a novel mathematical framework to analyze dressed photons in the generalized quantum Rabi model including the $A^{2}$-term, highlighting their emergence in the ground state.

Findings

Dressed photons appear in the ground state under deep-strong coupling.

The $A^{2}$-term significantly influences the ground state properties.

The analysis connects dressed photons with quantum phase transitions.

Abstract

We consider the generalized quantum Rabi model with the so-called $A^{2}$-term in the light of the Hepp-Lieb-Preparata quantum phase transition. We investigate the dressed photon in its ground state when the atom-light coupling strength is in the deep-strong coupling regime. We show how the dressed photon appears in the ground state. We dedicate this paper to Pavel Exner and Herbert Spohn on the occasion of their 70th birthdays, and Klaus Hepp on the occasion of his 80th birthday.