Non-Markovian bath engineering of a superconducting qubit

The dynamics of open quantum systems are often described by a Markovian master equation in which correlations between the quantum system and the reservoir are short lived. This approximation is accurate for qubits coupled to lossy photonic baths, where the transit time of the photon is effectively instantaneous relative to the coherence time of the qubit. Here we introduce a novel hybrid quantum system for coupling a superconducting qubit to a phononic bath composed of surface acoustic wave (SAW) phonons. The presence of the SAW device introduces a tailored loss channel to the qubit and we engineer this phonon bath such that the transit time of a phonon is comparable to the lifetime of the qubit necessitating a non-Markovian treatment of the system.