Qubit dynamics beyond Lindblad: Non-Markovianity versus rotating wave approximation

With increasing performance of actual qubit devices, even subtle effects in the interaction between qubits and environmental degrees of freedom become progressively relevant and experimentally visible. This applies particularly to the timescale separations that are at the basis of the most commonly used numerical simulation platform for qubit operations, namely, the conventional Lindblad master equation (LE): the Markov approximation and the rotating wave approximation (RWA). In this contribution, we shed light on the questions (i) to which extent it is possible to monitor violations of either of these timescale separations experimentally and (ii) which of them is the most severe to provide highly accurate predictions within (approximate) numerical schemes in relevant parameter ranges. For this purpose, we compare three simulation methods for the reduced density matrix with progressively growing accuracy. In particular, predictions for relaxation and decoherence of a qubit system in the presence of reservoirs with Ohmic and sub-Ohmic spectral densities are explored and, with the aid of proper protocols based on Ramsey experiments, the role of non-Markovianity and RWA are revealed. We discuss potential implications for future experiments and the design of approximate yet accurate numerical approaches.