Real-time milli-Kelvin thermometry in a semiconductor qubit architecture

We report local time-resolved thermometry in a silicon nanowire quantum dot device designed to host a linear array of spin qubits. Using two alternative measurement schemes based on rf reflectometry, we are able to probe either local electron or phonon temperatures with $\mu$s-scale time resolution and a noise equivalent temperature of $3$ $\rm mK/\sqrt{\rm Hz}$. Following the application of short microwave pulses, causing local periodic heating, time-dependent thermometry can track the dynamics of thermal excitation and relaxation, revealing clearly different characteristic time scales. This work opens important prospects to investigate the out-of-equilibrium thermal properties of semiconductor quantum electronic devices operating at very low temperature. In particular, it may provide a powerful handle to understand heating effects recently observed in semiconductor spin-qubit systems.