  Greenberger-Horne-Zeilinger and W states feature genuine tripartite
entanglement that cannot be converted into each other by local operations and
classical communication. Here, we present a dissipative protocol for
deterministic interconversion between Greenberger-Horne-Zeilinger and W states
of three neutral $^{87}$Rb atoms arranged in an equilateral triangle of a
two-dimensional array. With three atomic levels and diagonal van der Waals
interactions of Rydberg atoms, the interconversion between tripartite entangled
states can be efficiently accomplished in the Floquet-Lindblad framework
through the periodic optical pump and dissipation engineering. We evaluate the
feasibility of the existing methodology using the experimental parameters
accessible to current neutral-atom platforms. We find that our scheme is robust
against typical noises, such as laser phase noise and geometric imperfections
of the atom array. In addition, our scheme can integrate the Gaussian soft
quantum control technique, which further reduces the overall conversion time
and increases the resilience to timing errors and interatomic distance
fluctuations. The high-fidelity and robust tripartite entanglement
interconversion protocol provides a route to save physical resources and
enhance the computational efficiency of quantum networks formed by neutral-atom
arrays.
