  The Lindblad form of the master equation has proven to be one of the most
convenient ways to describe the impact of an environment interacting with a
quantum system of interest. For single systems the jump operators
characterizing these interactions usually take simple forms with a clear
interpretation. However, for coupled systems these operators take significantly
different forms and the full dynamics cannot be described by jump operators
acting on the individual subsystems only. In this work, we investigate the
differences between a common phenomenological model for the master equation and
the more rigorous dressed-state master equation for optomechanical systems. We
provide an analytical method to obtain the absorption spectrum of the system
for both models and show the breakdown of the phenomenological model in both
the bad cavity and the ultra-strong coupling limit. We present a careful
discussion of the indirect dephasing of the optical cavity in both models and
its role in the differences of their predicted absorption spectra. Our work
provides a simple experimental test to determine whether the simpler
phenomenological model can be used to describe the system and is a step forward
toward a better understanding of the role of the coupling between subsystems
for open-quantum-system dynamics.

Quantum Physics