We investigate the quantum dynamics of a transmon qubit embedded in a high-impedance circuit. The transmon undergoes a charge-localization (Schmid) transition upon the impedance reaching a critical value. Due to the unique level structure of a transmon its microwave fluorescence spectrum carries a signature of the transition. The integrated intensity of the fluorescence spectrum yields the total cross-section of inelastic photon scattering. Our theory of the inelastic cross-section explains the recently measured quality factors of devices consisting of a transmon in a galvanic connection with a high-impedance array of Josephson junctions.
