Surface acoustic wave resonators in the quantum regime

We present systematic measurements of the quality factors of surface acoustic wave (SAW) resonators on ST-X quartz in the gigahertz range at a temperature of $10\mathrm{mK}$. We demonstrate an internal quality factor $Q_{\mathrm{i}}$ approaching $0.5$ million at $0.5\text{GHz}$ and show that $Q_{\mathrm{i}}\ge 4.0\times {10}^4$ is achievable up to $4.4\text{GHz}$. We show evidence for a polynomial dependence of propagation loss on frequency, as well as a weak drive power dependence of $Q_{\mathrm{i}}$ that saturates at low power, the latter being consistent with coupling to a bath of two-level systems. Our results indicate that SAW resonators are promising devices for integration with superconducting quantum circuits.