We employ a generalized approach to the master equation for driven open $N$-level ($N>2$) quantum systems using Lewis–Riesenfeld invariants, which avoids the driving-strength restrictions inherent to conventional approaches. We show that the invariant-based master equation provides a unifying generalized framework, which reduces to the frequently employed laboratory-frame master equations and the less frequently employed rotating-frame master equation framework under appropriate simplifications. Extending the prototypical two-level system, we show that the inclusion of another state coupled to the ground state via reservoir-induced dephasing gives rise to qualitatively new dissipative behaviors that are, in general, not captured by standard approximations. We also apply the invariant-based master-equation framework to a driven quantum dot coupled to a leaky cavity, demonstrating the framework's ability to capture relevant dissipative dynamics without additional assumptions. Our work paves the way for quantum-control applications in the presence of dissipation.

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• Hybrid quantum systems
• Quantum control
• Quantum engineering
• Quantum cavities
• Quantum dots
• Markovian processes
• Quantum master equation
• Rotating wave approximation