Thermometry and Memcapacitance with a Qubit-Resonator System

We study theoretically the dynamics of a driven-dissipative qubit-resonator system. Specifically, a transmon qubit is coupled to a transmission-line resonator; this system is considered to be probed via a resonator, by means of either continuous or pulsed measurements. Analytic results obtained in the semiclassical approximation are compared with calculations in the semiquantum theory as well as with the previous experiments. We demonstrate that the temperature dependence of the resonator frequency shift can be used for the system thermometry and that the dynamics, which display a pinched-hysteretic curve, can be useful for realization of the memory devices termed quantum memcapacitors.