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.

中文翻译：

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压电基板上超导谐振器的声子损耗

我们通过数值和实验研究了在压电基板上制造的超导谐振器的声子损耗。在有限元方法模拟的帮助下，我们计算了由于机电转换为体声波和表面声波而造成的能量损失。这为谐振器内部品质因数 $Q_i$ 设置了上限。为了验证模拟，我们在 GaAs 上制造四分之一波长共面波导谐振器，并测量 Q_i 作为频率、功率和温度的函数。我们观察到 $Q_i$ 随频率线性增加，正如对恒定机电耦合的模拟所预测的那样。此外，$Q_i$ 在 10$\,$mK 附近显示出微弱的功率依赖性和可忽略的温度依赖性，