Photon-number-dependent effective Lamb shift

The Lamb shift, an energy shift arising from the presence of electromagnetic vacuum, has been observed in various quantum systems and established as part independent environmental photon number. However, typical studies are based on simplistic bosonic models which may be challenged practical devices. We demonstrate a hybrid bosonic-fermionic environment for linear resonator mode observe that number can dramatically increase both dissipation effective mode. Our observations quantitatively described by first-principles model we develop here also to guide device design future quantum-technological applications. demonstrated utilized fully rf-operated quantum-circuit refrigerator quickly reset superconducting qubits.