Deterministic generation of high-dimensional entanglement between distant atomic memories via multiphoton exchange

Promising access to high-speed quantum networks relies on the creation of high-dimensional entangled memories that provide communication with higher capacity noisy channels, thereby reducing transmission time information. Yet, distribution multidimensional entanglement between remote memory nodes is still faintly investigated. We propose an experimentally feasible protocol deterministic generation distant multilevel atoms confined in high-finesse optical cavities and driven by laser pulses. Three-dimensional generated deterministically triggering a two-photon wave packet, which mediates superposition states chosen pulse parameters. The efficient transfer atomic allows construction three-dimensional repeater, where successful can be verified simple method for reliable measurement ground Zeeman states.