  Open-system dynamics play a key role in the experimental and theoretical
study of cavity optomechanical systems. In many cases, the quantum Langevin
equations have enabled excellent models for optical decoherence, yet a
master-equation approach to the fully nonlinear optomechanical Hamiltonian has
thus far proven more elusive. To address this outstanding question and broaden
the mathematical tool set available, we derive a solution to the Lindblad
master equation that models optical decoherence for a system evolving with the
nonlinear optomechanical Hamiltonian. The method combines a Lie-algebra
solution to the unitary dynamics with a vectorization of the Lindblad equation,
and we demonstrate its applicability by considering the preparation of optical
cat states via the optomechanical nonlinearity in the presence of optical loss.
Our results provide a direct way of analytically assessing the impact of
optical decoherence on the optomechanical intracavity state.
