Kinetic Inductance Detectors (KIDs) consist of thinfilm superconducting resonators. An incoming photon breaks Cooper pairs, and causes the surface impedance of the resonator to change. The resonant frequency shifts, and the absorption event is recorded by monitoring the change in microwave transmission amplitude and phase. In this paper, we show that the power deposited by the microwave readout signal can cause the temperature of the quasipartieles in the superconducting film to switch between well-defined states. Experimentally, the effect appears as a discontinuity in the resonance curve, but is actually a hysteretic switching between thermal states as the readout frequency is swept up and down. We present numerical simulations that predict, quite clearly, the existence of hysteretic switching in low Tc superconducting resonators. The switching occurs as a direct consequence of the relationship between the readout power absorbed by the resonator as a function of temperature, and the finite thermal impedance of the quasiparticle-phonon coupling. This work may lead to an improvement of the power handling in KIDs, which is the easiest way of noise reduction in these devices, and to a better understanding of electron-phonon coupling in superconductors.
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