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.
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.
Low temperature microwave superconducting resonators (SRs) are attractive candidates for producing quantum-sensitive, arrayable energy or power detectors for astrophysical and other precision measurement applications. Their readout uses a microwave probe signal with quanta of energy well below the threshold for pair-breaking in the superconductor. We have calculated the non-equilibrium quasiparticle and phonon distributions generated by the photons of the probe signal of a resonator operating well below its superconducting transition temperature T c as the absorbed probe power was changed using the coupled kinetic equations described by Chang and Scalapino. The calculations give insight into a rate equation estimate which suggests that the quasiparticle distributions can be driven far from their thermal equilibrium value for typical readout powers. From the driven quasiparticle distribution functions, the driven quasiparticle number densities and lifetimes were calculated. An effective temperature to describe the driven quasiparticles was defined. The non-equilibrium lifetimes were compared to the distribution-averaged thermal lifetimes at the effective temperature and good agreement was found typically within a few per cent. We used the non-equilibrium quasiparticle distribution to model a representative SR. The complex conductivity and hence the frequency dependence of the experimentally measured forward scattering parameter S 21 of the SR as a function of absorbed power were found. The non-equilibrium S 21 cannot be accurately modeled by a thermal distribution even at its own elevated temperature, having a higher quality factor in all cases studied, although for low absorbed powers the two effective temperatures are similar. From the non-equilibrium lifetimes and number densities we determined the achievable noise equivalent power (NEP) of the resonator used as a power detector as a function of absorbed microwave power. Simpler expressions to evaluate the effective quasiparticle temperature as a function of absorbed power have also been derived. We conclude that multiple photon absorption from the microwave probe increases the quasiparticle number above the thermal background and ultimately limits the achievable NEP of the resonator at temperatures well below T c .
Measuring the internal quality factor of coplanar waveguide superconducting resonators is an established method of determining small losses in superconducting devices. Often, resonator losses are attributed to two-level system (TLS) defects using a power dependent model for the quality factor. However, excess non-equilibrium quasiparticles can also limit the quality factor of superconducting resonators. Here, a two-temperature, power and temperature dependent model is used to evaluate resonator losses for titanium nitride and aluminum coplanar waveguide resonators with loss tangents of 10−5–10−6. This model enables a set of parameters to describe both the internal quality factor and fractional frequency shift of the resonator across a broad range of average cavity photon numbers, from 1 to 106, and temperatures between those limited by the experimental apparatus near 50 mK and thermal quasiparticle dominated. The presented model also offers potential insight into observing the temperature and power dependence of TLS–TLS interactions in these resonators.
The presence of quasiparticles typically degrades the performance of superconducting microwave circuits. The readout signal can generate non-equilibrium quasiparticles, which lead to excess microwave loss and decoherence. To understand this effect quantitatively, we measure quasiparticle fluctuations and extract the quasiparticle density across different temperatures, readout powers, and resonator volumes. We find that microwave power generates a higher quasiparticle density as the active resonator volume is reduced and show that this effect sets a sensitivity limit on kinetic inductance detectors. We compare our results with theoretical models of direct microwave photon absorption by quasiparticles and conclude that an unknown, indirect mechanism plays a dominant role in quasiparticle generation. These results provide a route to mitigate quasiparticle generation due to readout power in superconducting devices.
The performance and scalability of superconducting quantum circuits are fundamentally constrained by non-equilibrium quasiparticles, which induce microwave losses that limit resonator quality factors and qubit coherence times. Understanding and mitigating these excitations is therefore central to advancing scalable quantum technologies. Here, we demonstrate on-chip microwave sensing of quasiparticles in high-Q α-tantalum coplanar waveguide resonators on silicon, operated in the single-photon regime. Temperature-dependent measurements reveal persistent non-equilibrium quasiparticles at millikelvin temperatures, producing a measurable suppression of the internal quality factor (Qi) relative to theoretical expectations. By benchmarking across materials, we find that the quasiparticle density in α-Ta is approximately one-third that of NbN at equivalent normalised temperatures (T/Tc), directly correlating with reduced microwave loss. Our methodology establishes a scalable platform for probing quasiparticle dynamics and points towards new routes for engineering superconducting circuits with improved coherence, with impact on qubit readout resonators, kinetic-inductance detectors, and emerging quantum processors and sensors.
We investigate the nonlinear behavior of a superconducting microwave resonator subjected to a dissipative mechanism where the associated quality factor (Q factor) decreases with increasing dissipated power, leading to a dissipative feedback effect. By modifying the Rothwarf-Taylor equations, we establish a macroscopic quasiparticle heating (QPH) model that directly links the quality factor to the microwave readout power. The key finding is the identification of a distinctive oval-shaped distortion in the resonance circle in the complex plane. This distortion serves as a practical experimental signature for identifying the readout power regime in which QPH dominates the loss, under conditions where other nonlinear mechanisms are sufficiently weak. To validate the model, we design and fabricate a niobium (Nb) half-wavelength coplanar waveguide (CPW) resonator and conduct systematic bath temperature and readout power sweeps. The model provides a well fit to the observed oval-shaped resonance circle distortion across a wide range of operating conditions, confirming the QPH mechanism as the primary source of the dissipative non-linearity in the parameter space investigated.
In this thesis I describe work on developing theoretical and numerical models of supercon- ducting thin-film microwave resonators. Superconducting resonators are used in a variety of applications, one of which is as kinetic inductance detectors (KIDs). KIDs are ultra-low noise, highly sensitive, multiplexable detectors, with uses in a wide variety of fields including astrophysics, medical imaging, and particle physics. Resonators are also crucial for supercon- ducting qubit readout, superconducting mixers and parametric amplifiers, and as multiplexers for other devices. The results described in this thesis apply to all thin film resonators, but are primarily described in the context of KIDs. I develop models of how constant absorbed power affects superconducting thin films, driving them out of thermal equilibrium with the bath. Using the Chang & Scalapino equations, I calculate numerically the steady-state quasiparticle and phonon distributions for various sources of power (sub-gap and above-gap photons and phonons, single frequency and broadband). Many new results emerge, a few of which are: the quasiparticle heating effects of microwave power, explaining the experimentally measured saturation of resonator performance; the frequency dependence of the quasiparticle generation efficiency in the sub-mm wavelength range; and the importance of phonon trapping in thin films at low temperatures. I then use these nonequilibrium results in higher-level device models. Starting from a generic framework for resonators, I present and implement a model of a KID with variable thermal isolation. I calculate the effects of quasiparticle heating on both the large-signal and small-signal behaviour, highlighting the effects of electrothermal feedback caused by readout power. Electrothermal feedback is shown to be able to increase or decrease the magnitude and bandwidth of the responsivity and noise, depending on the operating point. Finally, I propose an experimental measurement of quasiparticle heating effects in a new device – a four-port ring resonator. In such a device, unlike in the standard two-port resonator, the device can be heated and read out independently. I develop detailed models for the thermal and electrical behaviour of these devices, and suggest a scheme by which the quasiparticle heating effects of microwave power, predicted in this thesis, can be measured.