How to reduce energy loss at the interface of superconducting devices

We present a quantum theory of dielectric energy loss due to the interaction of photons, tunneling two level systems (TTLSs), and phonons in superconducting devices. As each TTLS couple to photons and phonons, it induces a photon-phonon interaction that can be described as an effective piezoelectric effect. We show that most energy loss occurs at the interface, with phonon interference playing an important role, leading to several predictions that can be tested in current experiments. Explicit numerical calculations of the loss tangent in devices demonstrates that dielectric energy loss can be reduced by exploiting destructive interference of the phonon radiation emitted from different interfaces.