Davies-Morris-Shore Framework for Multilevel Quantum Batteries: Dark and Funnel States in Interacting Qutrit Systems

Dark and subradiant states have emerged as a promising resource for stabilizing open quantum batteries against dissipation, but existing studies are largely limited to qubit ensembles and symmetry-based constructions. Here we introduce a systematic, thermodynamically consistent framework for identifying long-lived energy storage states in interacting multilevel quantum batteries, combining the Davies master equation with a Morris-Shore (MS)-type decomposition of dissipative coupling blocks. Focusing on a minimal model of two interacting qutrits coupled to a common bath, we analytically construct dark, bright, and funnel states-excited states that decay exclusively into protected manifolds. We also derive quantitative robustness conditions governed by the ratio of interaction strength to anharmonicity. We show that multilevel ladder structure and exchange interactions enable energetic storage states beyond the qubit case. Numerical simulations confirm that these states exhibit long-lived energy storage under realistic dissipation. Finally, we show that high-energy funnel states provide a natural design target for multilevel quantum batteries, as their decay pathways are highly structured and directed toward protected manifolds. Knowledge of these pathways offers a principled basis for developing future protection and control strategies in superconducting multilevel platforms.