Bridging between laboratory and rotating-frame master equations for open quantum systems

The problem of a driven quantum system coupled to a bath and coherently driven is usually treated using either of two approaches: Employing the common secular approximation in the laboratory frame (as usually done in the context of atomic physics) or in the rotating frame (prevailing in, e.g., the treatment of solid-state qubits). These approaches are applicable in different parts of the parameter space and yield different results. We show how to bridge between these two approaches by working in the rotating frame without employing the secular approximation with respect to the driving amplitude. This allows us to uncover unusual behaviors in regimes which were previously inaccessible or inadequately treated. Exceptional features such as the qualitative different evolution of the coherence, population inversion at a lower driving amplitude, and unique structure in the resonance fluorescence spectrum of the system are found. We argue that this generalized approach is essential for analyzing hybrid systems, with components that come from distinctly different regimes which can now be treated simultaneously, giving specific examples from recent experiments on quantum dots coupled to optical cavities, and single-spin electron paramagnetic resonance.