From quantum storage to amplification: the effect of unwanted couplings and an additional level in cavity-based ensemble quantum memories

Quantum-memory models often reduce complex level structures to an idealized $\Lambda$ system, potentially missing nearby levels and unwanted couplings that can qualitatively alter the predicted performance. Here, we study an extension of a cavity-based $\Lambda$-type ensemble memory, a four-level model with unwanted couplings from both the control field and signal, using a fully quantum treatment. We derive explicit expressions for the single-photon storage efficiency, retrieval efficiency, and fidelity, and on this basis identify three distinct dynamical regimes: stable, threshold, and unstable. Within the stable regime, we additionally discriminate between two qualitatively different sub-regimes. Applying the theory to warm-vapor-inspired parameters, we determine the conditions under which the system can still operate as a high-quality quantum memory. More generally, our results provide a practical framework for distinguishing genuine memory operation from amplification and for optimizing realistic quantum memories beyond idealized models.