Figure 4

(a) Internal quality factor and resonance frequency of the resonator at different values of the applied direct current (blue markers), from 0 A (highest values) to 0.35 μA (lowest values), and at different cryostat temperatures as indicated by the colors. The black solid line is obtained from the Mattis–Bardeen theory as described in “Methods”. (b) Temperature of the resonator as a function of the applied current. We find these data points by matching the the data for different bias currents in (a) with those recorded at different temperatures. (c) Effective inductance and resistance of the aluminium strip (markers) according to the lumped-element model at different perturbation currents, from the unperturbed state (bottom left) to the 0.35 μA perturbation (top right). The data has been extracted from (a) considering a constant effective impedance contribution of 1.5 nH and a negligible effective resistance for the bare resonator. The solid line provides the corresponding values from the results of the Mattis–Bardeen theory in (a). (d) Number of quasiparticles in the aluminum strip as a function of the temperature (top horizontal axis) and bias current (bottom horizontal axis). The blue solid line considers the temperature dependence (top horizontal axis) from the integral in Eq. (5) and the black dots correspond to the approximation provided at the end of Eq. (5). The red points show the number of quasiparticles as a function of the bias current (bottom horizontal axis) according to the integral form of Eq. (5) where the temperature at a given bias current is obtained from panel (b).