Exploring the driven open multi-level system using Lewis-Riesenfeld invariants

We explore a generalized approach to the master equation for driven open quantum systems using Lewis-Riesenfeld invariants (LRI). In many cases, the derivation of master equations for such systems either completely neglects the driving field (laboratory frame) or makes secular approximations based on the driving field strengths (rotating frame). Since both approaches impose constraints on the driving strengths and protocols, these methods tend to be particularly effective for systems with comparatively simple time dependence but face limitations when dealing with more complex time-dependent drives, which are crucial for quantum control and engineering. For the two-level system, our LRI-based master equation formulation (Phys. Rev. A 106, 052217, 2022; arXiv:2401.11659), coincides with a generalized master equation put forward in the literature (Phys. Rev. B 100, 195436, 2019). We present extensions to multi-level systems and identify scenarios where the LRI-based master equation offers significant improvements. This work lays the groundwork for developing robust control protocols that are resilient to environmental noise and dissipation in quantum systems.