Microwave multimode memory with an erbium spin ensemble

Hybrid quantum systems combining circuit QED with spin-doped solids are an attractive platform for distributed quantum information processing. There, the magnetic ions serve as coherent memory elements and reversible conversion elements of microwave to optical qubits. Among many possible spin-doped solids, erbium ions offer the unique opportunity for a coherent conversion of microwave photons into the telecom C band at 1.540.28em0exμm employed for long distance communication. In our work, we perform a time-resolved electron spin resonance study of an Er³⁺:Y₂SiO₅ spin ensemble at millidegrees Kelvin temperatures and demonstrate multimode storage and retrieval of up to 16 coherent microwave pulses. The memory efficiency is measured to be 10^-4 at a coherence time of T₂=5.60.28em0exμs. We observe a saturation of the spin coherence time below 50 mK due to full polarization of the surrounding electronic spin bath.