Dynamics of a Single Spin in Markovian and non-Markovian Environments*

The spin-boson model, describing a two-level system strongly coupled to a thermal bath, is extensively well studied in the context of dissipative quantum systems. This model exhibits rich behavior and even a localization transition in the strong coupling regime. Here, we investigate the consequence of Markovian dissipation (on top of the non-Markovian bath) due to coupling to a noisy environment. For moderate values of coupling, we develop a non-perturbative method to characterize the dynamics of the spin. We show that the Markovian dissipation renormalizes the frequency and the decay rate of the spin evolution. Our findings are relevant to the strong coupling regime in circuit QED systems among others.