Estimating the Energy Threshold of Phonon-mediated Superconducting Qubit Detectors Operated in an Energy-Relaxation Sensing Scheme

In recent years, the lack of a conclusive detection of WIMP dark matter at the 10 GeV/c$^{2}$ mass scale and above has encouraged development of low-threshold detector technology aimed at probing lighter dark matter candidates. Detectors based on Cooper-pair-breaking sensors have emerged as a promising avenue for this detection due to the low (meV-scale) energy required for breaking a Cooper pair in most superconductors. Among them, devices based on superconducting qubits are interesting candidates for sensing due to their observed sensitivity to broken Cooper pairs. We have developed an end-to-end G4CMP-based simulation framework and have used it to evaluate performance metrics of qubit-based devices operating in a gate-based "energy relaxation" readout scheme, akin to those used in recent studies of qubit sensitivity to ionizing radiation. We find that for this readout scheme, the qubit acts as a phonon sensor with an energy threshold ranging down to $\simeq$0.4 eV for near-term performance parameters.