We study a superconducting artificial atom which is represented by a single Josephson junction or a Josephson junction chain, capacitively coupled to a coherently driven transmission line, and which contains exactly one residual quasiparticle (or up to one quasiparticle per island in a chain). We study the dissipation in the atom induced by the quasiparticle tunneling, taking into account the quasiparticle heating by the drive. We calculate the transmission coefficient in the transmission line for drive frequencies near resonance and show that, when the artificial atom spectrum is nearly harmonic, the intrinsic quality factor of the resonance increases with the drive power. This counterintuitive behavior is due to the energy dependence of the quasiparticle density of states.
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