We have illuminated a thin-film superconducting Al lumped-element microwave resonator with 780 nm light and observed the resonator quality factor and resonance frequency as a function of illumination and microwave power in the 20 to 300 mK temperature range. The optically induced microwave loss increases with increasing illumination but decreases with increasing microwave power. Although this behavior may suggest the presence of optically activated two-level systems, we find that the loss is better explained by the presence of nonequilibrium quasiparticles generated by the illumination and excited by the microwave drive. We model the system by assuming that the illumination creates an effective source of phonons with energy higher than double the superconducting gap and solve the coupled quasiparticle-phonon rate equations. We fit the simulation results to our measurements and find good agreement with the observed dependence of the resonator quality factor and frequency shift on temperature, microwave power, and optical illumination. Examination of the model reveals approaches to reducing optically induced loss and improving the relaxation time of superconducting quantum devices.
We have illuminated a thin-film superconducting Al lumped-element microwave resonator with 780 nm light and observed the resonator quality factor and resonance frequency as a function of illumination and microwave power in the 20 to 300 mK temperature range. The optically induced microwave loss increases with increasing illumination but decreases with increasing microwave power. Although this behavior may suggest the presence of optically activated two-level systems, we find that the loss is better explained by the presence of nonequilibrium quasiparticles generated by the illumination and excited by the microwave drive. We model the system by assuming that the illumination creates an effective source of phonons with energy higher than double the superconducting gap and solve the coupled quasiparticle-phonon rate equations. We fit the simulation results to our measurements and find good agreement with the observed dependence of the resonator quality factor and frequency shift on temperature, microwave power, and optical illumination. Examination of the model reveals approaches to reducing optically induced loss and improving the relaxation time of superconducting quantum devices.
I report measurements of two different types of superconducting devices illuminated by 780 nm light, one of the wavelengths needed in a proposed atom-superconductor hybrid quantum system. I illuminated a thin-film Al lumped-element resonator and observed the resonator quality factor and resonance frequency as a function of illumination intensity, microwave power, and temperature. The resonator was mounted in a 3d aluminum cavity. The variation in optically-induced loss due to microwave power was similar to the behavior expected for loss from a distribution of two-level systems. Although this behavior may suggest the presence of optically activated two-level systems, I found that the loss is better explained by the presence of nonequilibrium quasiparticles generated by the illumination and excited by the microwave drive. I described a model of the system where optical absorption creates an effective source of phonons and solved the coupled quasiparticle-phonon rate equations. I found good agreement between the simulation and the measured resonator quality factor and frequency shift as a function of temperature, microwave power, and optical illumination. I fabricated a transmon qubit and studied the qubit transition frequency and relaxation time as a function of illumination intensity and temperature. The qubit was mounted in a 3d aluminum cavity and coupled to the cavity forming a Jaynes-Cummings system. Qubit relaxation showed non-exponential behavior that I fit to a quasiparticle fluctuation model with two characteristic times. The transition frequency and both characteristic times decreased with increasing illumination intensity. For comparison, I described a nonequilibrium quasiparticle model for the expected frequency shift and relaxation time due to quasiparticle tunneling through the Josephson junction. While the quasiparticle simulation predicted the general qualitative behavior of the frequency shift and relaxation time, there were some significant discrepancies with the data. This suggests the model needs to be extended, for example by including a different gap in the two superconductor layers forming the junction, and by taking into account other possible sources of loss and decoherence.
We have coupled a tapered optical microfiber to a translatable thin-film lumped-element superconducting Al microwave resonator that is cooled to 15 mK. The thin-film resonator has a resonance frequency of 6.14 GHz, a quality factor of Q = 2.59 × 105, and is mounted inside a 3-D Al microwave cavity that provides a well-isolated electromagnetic environment. The microfiber is held fixed while the cavity is mounted on an x-z translation stage that allows the lumped-element resonator and the optical fiber to be brought close to each other (less than 1 mm). When 780-nm light is sent through the fiber, Rayleigh scattering in the fiber causes a weak position-dependent nonuniform illumination of the thin-film resonator, exciting quasiparticles in the superconducting film and thereby affecting its resonance frequency foand Q. We report on the response of the resonator to both the scattered optical power and the presence of the fiber's dielectric, as the thin-film resonator is moved in situ with respect to the fiber.
In a superconductor, absorption of photons with an energy below the superconducting gap leads to redistribution of quasiparticles over energy and thus induces a strong nonequilibrium quasiparticle energy distribution. We have measured the electrodynamic response, quality factor, and resonant frequency of a superconducting aluminium microwave resonator as a function of microwave power and temperature. Below 200 mK, both the quality factor and resonant frequency decrease with increasing microwave power, consistent with the creation of excess quasiparticles due to microwave absorption. Counterintuitively, above 200 mK, the quality factor and resonant frequency increase with increasing power. We demonstrate that the effect can only be understood by a nonthermal quasiparticle distribution.
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.
This dissertation describes energy dissipation and microwave loss due to non-equilibrium quasiparticles in superconducting transmon qubits and titanium nitride coplanar waveguide resonators. During the measurements of transmon T1 relaxation time and resonator quality factor QI, I observed reduced microwave loss as the temperature increased from 20 mK to approximately Tc/10 at which the loss takes on a minimum value. I argue that this effect is due to non-equilibrium quasiparticles. I measured the temperature dependence of the relaxation time T1 of the excited state of an Al/AlOx/Al transmon and found that, in some cases, T1 increased by almost a factor of two as the temperature increased from 30 mK to 100 mK with a best T1 of 0.2 ms. I present an argument showing this unexpected temperature dependence occurs due to the behavior of non-equilibrium quasiparticles in devices in which one electrode in the tunnel junction has a smaller volume, and slightly smaller superconducting energy gap, than the other electrode. At sufficiently low temperatures, non-equilibrium quasiparticles accumulate in the electrode with the smaller gap, leading to a relatively high density of quasiparticles at the junction and a short T1. Increasing the temperature gives the quasiparticles enough thermal energy to occupy the higher gap electrode, reducing the density at the junction and increasing T1. I present a model of this effect, extract the density of quasiparticles and the two superconducting energy gaps, and discuss implications for increasing the relaxation time of transmons. I also observed a similar phenomenon in low temperature microwave studies of titanium nitride coplanar waveguide resonators. I report on loss in a resonator at temperatures from 20 mK up to 1.1 K and with the application of infrared pair breaking radiation (λ=1.55 μm). With no applied IR light, the internal quality factor increased from QI = 800,000 at T < 70 mK up to QI=(2×10^6 ) at 600 mK. The resonant frequency f0 increased by 2 parts per million over the same temperature range. Above 600 mK both QI and f0 decreased rapidly, consistent with the increase in the density of thermally generated quasiparticles. With the application of IR light and for intensities below 1 aW μm^(-2) and T < 400 mK, QI increased in a similar way to increasing the temperature before beginning to decrease with larger intensities. I show that a model involving non-equilibrium quasiparticles and two regions of different superconducting gaps can explain this unexpected behavior.
We studied the effect of these quasiparticles on the temperature and microwave power dependence of the characteristics of superconducting thin-film resonator, assuming that there are a significant number of quasiparticles in the superconductor even atT≪Tc. It is demonstrated that the temperature dependence of both the internal quality factor and resonance frequency are well described by that of the normal conductivity of quasiparticles including the contributions from Kondo effect, phonon, and electron-electron scatterings. It also found that the readout microwave power dependence of the internal quality factor is well explained by the change of quasiparticle density due to the energy re-distribution of quasiparticles under microwave field in the resonator.