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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-lightcoupling strength is in the deep-strong coupling regime. We show how thedressed photon appears in the ground state. We dedicate this paper to PavelExner and Herbert Spohn on the occasion of their 70th birthdays, and Klaus Heppon the occasion of his 80th birthday.

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