Quantum bath engineering of a high impedance microwave mode through quasiparticle tunneling

In microwave quantum optics, dissipation usually corresponds to quantum jumps, where photons are lost one by one. Here we demonstrate a new approach to dissipation engineering. By coupling a high impedance microwave resonator to a tunnel junction, we use the photoassisted tunneling of quasiparticles as a tunable dissipative process. We are able to adjust the minimum number of lost photons per tunneling event to be one, two or more, through a dc voltage. Consequently, different Fock states of the resonator experience different loss processes. Causality then implies that each state experiences a different energy (Lamb) shift, as confirmed experimentally. This photoassisted tunneling process is analogous to a photoelectric effect, which requires a quantum description of light to be quantitatively understood. This work opens up new possibilities for quantum state manipulation in superconducting circuits, which do not rely on the Josephson effect.