  Superconducting coplanar waveguide (CPW), resonators are powerful and
versatile tools used in areas ranging from radiation detection to circuit
quantum electrodynamics. Their potential for low intrinsic losses makes them
attractive as sensitive probes of electronic properties of bulk materials and
thin films. Here we use superconducting MoRe CPW resonators, to investigate the
high-frequency (up to 0.3 GHz) and low temperature (down to 3.5 K) permittivity
of SrTiO3, a non-linear dielectric on the verge of a ferroelectric transition
(quantum paraelectricity). We perform a quantitative analysis of its dielectric
properties as a function of external dc bias (up to +-15V), rf power and mode
number and discuss our results within the framework of the most recent
theoretical models. We also discuss the origin of a fatigue effect that reduces
the tunability of the dielectric constant of SrTiO3, which we relate to the
presence of oxygen vacancies.
