Optimal absorption and emission of itinerant fields into a spin-ensemble memory

Quantum memories integrated in a modular quantum processing architecture can rationalize the resources required for quantum computation. This work focuses on spin-based quantum memories, where itinerant electromagnetic fields are stored in large ensembles of effective two-level systems, such as atomic or solid-state spin ensembles, embedded in a cavity. Using a mean-field framework, we model the ensemble as an effective spin communication channel and describe both absorption and emission processes using a cascaded quantum model. We derive optimal time-dependent modulations of the cavity linewidth that maximize storage and retrieval efficiency for fast incoming pulses. Our analysis yields an upper bound on efficiency, which can be met in the narrow bandwidth regime. It also shows the existence of a critical bandwidth above which the efficiency severely decreases. Numerical simulations are presented in the context of microwave-frequency quantum memories interfaced with superconducting quantum processors, highlighting the protocol's relevance for modular quantum architectures.