Decoherence of surface phonons in the weak dispersive regime of circuit quantum acoustodynamics*

Circuit quantum acoustodynamic (cQAD) systems are ideal for investigating the quantum properties of mechanical resonators by leveraging the intrinsic nonlinearity of superconducting qubits. Here we describe an experiment in which the electro-mechanical response of a surface acoustic wave (SAW) device enables the realization of an open cQAD system. The hybrid system is implemented via capacitive coupling between a 3D transmon qubit and a custom-designed SAW device. This device architecture allows for the transmon to simultaneously couple strongly to a resonant SAW mode and also weakly with non-resonant, lossy surface phonon modes. By populating the SAW device with phonons and then dispersively reading out its state via the qubit, we are able to measure the dynamics and decoherence of the surface phonon states in the resonator. In this fashion, with a single device, we can measure the decoherence of phonons in the resonant mode, and use the broader SAW phonon spectrum to investigate the decoherence of the hybrid system.