Uniting Quantum Processing Nodes of Cavity-Coupled Ions with Rare-Earth Quantum Repeaters Using Single-Photon Pulse Shaping Based on Atomic Frequency Comb

We present an architecture for remotely connecting cavity-coupled trapped ions via a quantum repeater based on rare-earth-doped crystals. The main challenge for its realization lies in interfacing these two physical platforms, which produce photons with a typical temporal mismatch of one or two orders of magnitude. To address this, we propose an efficient protocol that enables custom temporal reshaping of single-photon pulses while preserving purity. Our approach is to modify a commonly used memory protocol, called atomic frequency comb, for systems exhibiting inhomogeneous broadening like rare-earth-doped crystals. Pertaining to a growing interest in hybrid quantum information systems designed to exploit the distinct advantages of diverse physical components, our results offer a viable solution for uniting quantum processing nodes with a quantum repeater backbone.