Invariant-Based Master Equation Approach for a Driven Atom-Cavity System

We apply a dynamical invariant-based master equation framework to a driven three-level Λ system that is coupled to a single-mode optical cavity and an external dissipative bath. The dynamical invariant-based approach provides a unified description of open quantum system dynamics across parameter regimes where commonly used Redfield master equations are valid only in restricted limits. While previous work has demonstrated the consistency of the invariant-based framework for two- and multilevel atoms with a leaky cavity that can be treated classically, here we extend the approach to treat the three-level system and the cavity quantum mechanically. We analyze the resulting dynamics and benchmark the invariant-based master equation against standard laboratory-frame and rotating-frame Redfield master equation treatments in their respective regimes of validity. Our framework allows us to investigate parameter regimes in which the cavity cannot be traced out, such as low-loss cavities or nonclassical initial cavity states. Our results clarify the applicability and limitations of semiclassical descriptions and provide a pathway toward a unified treatment of driven atom-cavity systems across weak, intermediate, and strong driving regimes.