The physics of superconducting microwave resonators

Over the past decade, low temperature detectors have brought astronomers revolutionary new observational capabilities and led to many great discoveries. Although a single low temperature detector has very impressive sensitivity, a large detector array would be much more powerful and are highly demanded for the study of more difficult and fundamental problems in astronomy. However, current detector technologies, such as transition edge sensors and superconducting tunnel junction detectors, are difficult to integrate into a large array. The microwave kinetic inductance detector (MKID)is a promising new detector technology invented at Caltech and JPL which provides both high sensitivity and an easy solution to the detector integration. It senses the change in the surface impedance of a superconductor as incoming photons break Cooper pairs, by using high-Q superconducting microwave resonators capacitively coupled to a common feedline. This architecture allows thousands of detectors to be easily integrated through passive frequency domain multiplexing. In this thesis, we explore the rich and interesting physics behind these superconducting microwave resonators. The first part of the thesis discusses the surface impedance of a superconductor, the kinetic inductance of a superconducting coplanar waveguide, and the circuit response of a resonator. These topics are related with the responsivity of MKIDs. The second part presents the study of the excess frequency noise that is universally observed in these resonators. The properties of the excess noise, including power, temperature, material, and geometry dependence, have been quantified. The noise source has been identified to be the two-level systems in the dielectric material on the surface of the resonator. A semi-empirical noise model has been developed to explain the power and geometry dependence of the noise, which is useful to predict the noise for a specified resonator geometry. The detailed physical noise mechanism, however, is still not clear. With the theoretical results of the responsivity and the semi-empirical noise model established in this thesis, a prediction of the detector sensitivity (noise equivalent power) and an optimization of the detector design are now possible.