Existence of an independent phonon bath in a quantum device

At low temperatures, the thermal wavelength of acoustic phonons in a metallic thin film on a substrate can widely exceed the film thickness. It is thus generally believed that a mesoscopic device operating at low temperature does not carry an individual phonon population. In this work, we provide direct experimental evidence for the thermal decoupling of phonons in a mesoscopic quantum device from its substrate phonon heat bath at a sub-Kelvin temperature. A simple heat balance model assuming an independent phonon bath following the usual electron-phonon and Kapitza coupling laws can account for all experimental observations.