Cavity-based reservoir engineering for Floquet engineered superconducting circuits

By periodically driving a quantum system at a high frequency, it can acquire novel properties that are captured by an effective time-independent Hamiltonian. An important application of such Floquet engineering is, e.g., the realization of effective gauge fields for charge-neutral particles. Here we consider driven Bose-Hubbard systems, as they can be realized as arrays of artificial atoms in superconducting circuits, and show that the ground state of the effective Hamiltonian can be prepared with high fidelity using reservoir engineering. For this purpose, some artificial atoms are coupled to driven leaky cavities. We derive an effective description of the open system by employing degenerate perturbation theory in the extended Floquet space with respect to both the periodic drive and the system-cavity coupling. Applying this theory to different Floquet-engineered flux ladders, we find both that it allows to cool the systems and that it shows excellent agreement with the full driven-dissipative evolution of system and cavities.