Intrinsic mechanisms for drive-dependent Purcell decay in superconducting quantum circuits

We develop an approach to understanding intrinsic mechanisms that cause the ${T}_{1}$-decay rate of a multilevel superconducting qubit to depend on the photonic population of a coupled, detuned cavity. Our method yields simple analytic expressions for both the coherently driven or thermally excited cases, which are in good agreement with full master equation numerics, and also facilitates direct physical intuition. It also predicts several interesting phenomena. In particular, we find that in a wide range of settings, the cavity-qubit detuning controls whether a nonzero photonic population increases or decreases qubit Purcell decay. Our method combines insights from a Keldysh treatment of the system, and Lindblad perturbation theory.