Phononic loss in superconducting resonators on piezoelectric substrates

We numerically and experimentally investigate the phononic loss for superconducting resonators fabricated on a piezoelectric substrate. With the help of finite element method simulations, we calculate the energy loss due to electromechanical conversion into bulk and surface acoustic waves. This sets an upper limit for the resonator internal quality factor Q_i. To validate the simulation, we fabricate quarter wavelength coplanar waveguide resonators on GaAs and measure Q_i as function of frequency, power and temperature. We observe a linear increase of Q_i with frequency, as predicted by the simulations for a constant electromechanical coupling. Additionally, Q_i shows a weak power dependence and a negligible temperature dependence around 10 mK, excluding two level systems and non-equilibrium quasiparticles as the main source of losses at that temperature.