Capacity-time Trade-off in Highly Reliable Quantum Memory

Reliable optical quantum memory is limited by real-world imperfections such as disordered coupling and detuning. Existing studies mostly address these factors separately, while in practice their correlated effects set a fundamental limit on storage performance. We develop a comprehensive model that simultaneously incorporates disordered coupling and detuning. It is shown that these disorders induce a random Berry's phase in the stored states, while decoherence from disordered coupling stems from correlations with detuning rather than individual imperfections. This mechanism imposes a fundamental trade-off among storage capacity, storage time, and driving time, setting a universal limit for reliable storage. Extending the analysis to memory based devices operating with multiple storage processes shows that enhancing parameter independence improves their reliability. We further provide a more precise relation for measuring and correcting global detuning, which is directly relevant to current experimental protocols.