Coarse graining can beat the rotating-wave approximation in quantum Markovian master equations

We present a first-principles derivation of the Markovian semigroup master equation without invoking the rotating-wave approximation (RWA). Instead we use a time coarse-graining approach that leaves us with a free time-scale parameter, which we can optimize. Comparing this approach to the standard RWA-based Markovian master equation, we find that significantly better agreement is possible using the coarse-graining approach, for a three-levelmodelcoupledtoabathofoscillators,whoseexactdynamicswecansolveforatzerotemperature.The model has the important feature that the RWA has a nontrivial effect on the dynamics of the populations. We show that the two different master equations can exhibit strong qualitative differences for the population of the energy eigenstates even for such a simple model. The RWA-based master equation misses an important feature which the coarse-graining-based scheme does not. By optimizing the coarse-graining time scale the latter scheme can be made to approach the exact solution much more closely than the RWA-based master equation.