Heating Dynamics of Mesoscopic Electron Baths at High Magnetic Field
Quantum thermodynamics addresses the dynamics of heat flow in quantum devices driven out of equilibrium. Although mesoscopic circuits at low temperatures provide a flexible platform to explore this dynamics, experimental studies are wanting because thermal timescales in nanodevices are often too fast. Here we engineer and investigate with noise thermometry a mesoscopic thermal circuit where heat flows between electron, phonon and nuclear systems can occur on slower timescales. The central constituent of this device is a micrometer-scale metallic island electrically connected to large cold electron reservoirs through two to four ballistic quantum Hall channels, a component frequently used for exploring stationary thermal currents. We uncover a two-step thermalization process specific to the mesoscopic scale, involving a fast initial temperature step followed by a much slower rise extending over minutes. This observation is quantitatively accounted for by the balance between heat flows through electronic quantum channels, to cold phonons, and to the nuclear spins in the metallic island. The disclosed mesoscopic thermalization takes a step into the field of quantum thermo-\emph{dynamical} phenomena, highlighting their distinctive nature on a central constituent of quantum circuits. The implications for the thermal engineering of nanodevices include the thermal characterization of exotic states at high magnetic field.