  Hyperentangled swapping is a quantum communication technique that involves
the exchange of hyperentangled states, which are quantum states entangled in
multiple degrees of freedom, to enable secure and efficient quantum information
transfer. In this paper, we demonstrate schematics for the hyperentanglement
swapping between separate pairs of neutral atoms through the mathematical
framework of atomic Bragg diffraction, which is efficient and resistant to
decoherence, yielding deterministic results with superior overall fidelity. The
utilized cavities are in superposition state and interact with the incoming
atoms off-resonantly. Quantum information carried by the cavities is swapped
through resonant interactions with two-level auxiliary atoms. We also discuss
entanglement swapping under a delayed-choice scenario and provide a schematic
generalization covering multiple-qubit scenarios. Finally, we introduce
specific experimental parameters to demonstrate the experimental feasibility of
the scheme.
