Exact quantum master equations serve as a fundamental tool for investigating quantum dissipative dynamics. However, deriving such equations—even when possible—is extremely tedious for multistate and multiatom systems. In this work, we focus exclusively on population dynamics of the extended Jaynes-Cummings model and develop a rigorous equation-of-motion approach for the double-excitation manifold. The resulting dynamical equations are simple and involve only two auxiliary functions. Numerical simulations confirm that the dynamics in the double-excitation manifold closely resembles that of the single-excitation manifold: both exhibit a quantum phase transition from a dissipative phase to a localized phase, with the double-excitation manifold showing a higher critical dissipation strength than its single-excitation counterpart.

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• Nonequilibrium statistical mechanics
• Open quantum systems
• Phase diagrams