A mathematical analysis of dressed photon in ground state of generalized quantum Rabi model using pair theory

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. This regime is introduced by Casanova et al (2010 Phys. Rev. Lett. 105 263603) as the coupling regime exceeding the ultra-strong one. We show how the dressed photon appears in the ground state.