We consider the effects of quasiparticle heating on the dynamical behaviour of superconducting microresonators operating with high readout powers. It is seen that resonance-curve distortion and hysteretic switching are an inevitable consequence of the forms of the quasiparticle heating and cooling functions. The model uses a diagrammatic representation of dynamical behaviour to gain an insight into how the instantaneous operating point moves in response to step changes in readout power, signal power, bath temperature, and frequency. The coupling quality factor has a marked effect on non-linear behaviour. The model is used to calculate the waveforms generated when a device switches between hysteretic states. The work suggests that measured response times need not be representative of intrinsic quasiparticle relaxation rates.
We consider the effects of quasiparticle heating on the dynamical behaviour of superconducting microresonators operating with high readout powers. It is seen that resonance-curve distortion and hysteretic switching are an inevitable consequence of the forms of the quasiparticle heating and cooling functions. The model uses a diagrammatic representation of dynamical behaviour to gain an insight into how the instantaneous operating point moves in response to step changes in readout power, signal power, bath temperature, and frequency. The coupling quality factor has a marked effect on non-linear behaviour. The model is used to calculate the waveforms generated when a device switches between hysteretic states. The work suggests that measured response times need not be representative of intrinsic quasiparticle relaxation rates.
The sensitivities, saturation powers, and response times of Kinetic Inductance Detectors depend on the degree to which the quasiparticle and phonon temperatures differ when readout and signal power are applied. Previously, we proposed a model for saturation in KIDs, and found that hysteretic switching, which is seen experimentally, emerges from the model in a natural way. Here we extend our work, and show through a diagrammatic rep- resentation of operating-point trajectories that output pulse shapes can be calculated for non-hysteretic and hysteretic changes of state driven by readout-frequency, readout-power, and signal-power pulses. The work has several applications: (i) Understanding quasiparticle and phonon relaxation, and their dependence on film and substrate thickness. (ii) Recovering quasiparticle cooling functions from measurements. (iii) Understanding the relationship between optimum readout power and device and material parameters. (iv) Characterising the time-dependent behaviour of photon-counting KIDs, including nonlinearity and pile up.
A model is presented for readout-power heating in kinetic inductance detectors. It is shown that the power dissipated by the readout signal can cause the temperature of the quasiparticle system in the superconducting resonator to switch between well-defined states. At low readout powers, only a single solution to the heat balance equation exists, and the resonance curve merely distorts as the readout power is increased. At high readout powers, three states exist, two of which are stable, and the resonance curve shows hysteretic switching. The power threshold for switching depends on the geometry and material used but is typically around −70 dBm for Aluminum resonators. A comprehensive set of simulations is reported, and a detailed account of the switching process is given. Experimental results are also shown, which are in strong qualitative agreement with the simulations. The general features of the model are independent of the precise cooling function, and are even applicable for resonators on suspended, thermally isolated, dielectric membranes, where an increase in quasiparticle lifetime is expected. We discuss various extensions to the technique, including the possibility of recovering the cooling function from large-signal measurements of the resonance curve.
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 quasiparticles 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.
Abstract In kinetic inductance detectors (KIDs) and other similar applications of superconducting microresonators, both the large and small-signal behaviour of the device may be affected by electrothermal feedback. Microwave power applied to read out the device is absorbed by and heats the superconductor quasiparticles, changing the superconductor conductivity and hence the readout power absorbed in a positive or negative feedback loop. In this work, we explore numerically the implications of an extensible theoretical model of a generic superconducting microresonator device for a typical KID, incorporating recent work on the power flow between superconductor quasiparticles and phonons. This model calculates the large-signal (changes in operating point) and small-signal behaviour of a device, allowing us to determine the effect of electrothermal feedback on device responsivity and noise characteristics under various operating conditions. We also investigate how thermally isolating the device from the bath, for example by designing the device on a membrane only connected to the bulk substrate by thin legs, affects device performance. We find that at a typical device operating point, positive electrothermal feedback reduces the effective thermal conductance from the superconductor quasiparticles to the bath, and so increases responsivity to signal (pair-breaking) power, increases noise from temperature fluctuations, and decreases the noise equivalent power (NEP). Similarly, increasing the thermal isolation of the device while keeping the quasiparticle temperature constant decreases the NEP, but also decreases the device response bandwidth.
Abstract The performance of superconducting resonators underpins a wide range of modern quantum technologies, yet their quality factor often deviates at low temperatures from standard Mattis-Bardeen predictions. This discrepancy is often attributed to nonthermal quasiparticles generated by microwave readout power, which limits the sensitivity of superconducting devices. We present a macroscopic model based on modified Rothwarf-Taylor equations that incorporates a power-dependent phonon generation term, providing an explicit relationship between quality factor, bath temperature and readout power. The model shows excellent agreement with temperature sweep measurements of NbN microstrip resonators with β-Ta terminations over a wide dynamic range of readout power levels, accurately capturing the transition between thermally-dominated and microwave-induced loss regimes. This framework provides a predictive tool for optimizing superconducting resonators and advancing the design of high-Q devices for quantum sensing and quantum information processing.
In kinetic inductance detectors (KIDs) and other similar applications of superconducting microresonators, both the large and small-signal behaviour of the device may be affected by electrothermal feedback. Microwave power applied to read out the device is absorbed by and heats the superconductor quasiparticles, changing the superconductor conductivity and hence the readout power absorbed in a positive or negative feedback loop. In this work, we explore numerically the implications of an extensible theoretical model of a generic superconducting microresonator device for a typical KID, incorporating recent work on the power flow between superconductor quasiparticles and phonons. This model calculates the large-signal (changes in operating point) and small-signal behaviour of a device, allowing us to determine the effect of electrothermal feedback on device responsivity and noise characteristics under various operating conditions. We also investigate how thermally isolating the device from the bath, for example by designing the device on a membrane only connected to the bulk substrate by thin legs, affects device performance. We find that at a typical device operating point, positive electrothermal feedback reduces the effective thermal conductance from the superconductor quasiparticles to the bath, and so increases responsivity to signal (pair-breaking) power, increases noise from temperature fluctuations, and decreases the noise equivalent power (NEP). Similarly, increasing the thermal isolation of the device while keeping the quasiparticle temperature constant decreases the NEP, but also decreases the device response bandwidth.