Drive-induced lifetime renormalization of superconducting qubits I: Effective Master Equations

We show that number non-conserving terms in the Josephson anharmonicity lead to a renormalization of the lifetime of microwave-driven superconducting qubits. Using a method of unitary transformations, we account for the frequently neglected number non-conserving terms in the Josephson potential, and show that they generate drive- and anharmonicity-dependent corrections of the qubit and readout resonator relaxation rates. Simultaneously, the number-conserving terms yield the known Kerr corrections to the eigenfrequencies of the system. We present our results in the form of effective master equations with renormalized Hamiltonian and collapse operators. Effective master equations provide an efficient tool to extract drive-, state- and anharmonicity-dependent relaxation rates.