Capturing non-Markovian dynamics with the reaction coordinate method

The reaction coordinate (RC) technique is emerging as a significant tool in the study of quantum dissipative dynamics and quantum thermodynamics. With the objective to further establish this tool, here we explore to what extent the method can capture non-Markovian dynamics of open quantum systems. As a case study, we focus on the pure decoherence model of a spin coupled to a harmonic reservoir. We compare the spin dynamics and measures for non-Markovianity from the exact analytical solution to simulations based on the RC method at the level of a second order quantum master equation. We find that the RC method can quantitatively capture non-Markovian effects at strong system-bath coupling and for structured baths. This is rationalized by the fact that the collective RC bath mode, which is made part of the system, maintains system-bath correlations. Lastly, we apply our RC method and study the spin-boson model in the non-Markovian regime.