Recoil Error Correction for Remote Entanglement of Trapped Ions Based on a Single-Excitation Scheme

Scaling quantum processors will depend on fast, high-fidelity interconnects between spatially separate nodes. Heralded photon-mediated entanglement (PME) offers a natural approach toward such interconnects in trapped-ion systems, but the achievable rate is often limited by the low photon collection efficiency. Most PME schemes herald entanglement on the coincidence of photon-detection events from two ions and thus entanglement rates scale quadratically with the collection efficiency. In contrast, in single-excitation schemes, a single detection event heralds entanglement at a rate scaling linearly with detection probability. In this scheme, only one atom receives a momentum kick from absorbing and emitting a photon. The resulting unwanted spin-motion entanglement degrades the ion-ion entanglement fidelity when the motion is traced out. However, recent theoretical work proposes a method for coherent spin-motion disentanglement via spin-dependent displacements. We present a scheme for applying this motional correction procedure to a pair of barium ions using a bichromatic laser drive. Coherently correcting the recoil-induced error inherent in the single-excitation scheme would be a significant step toward fast, high-fidelity remote entanglement between trapped-ion modules.