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While the Rydberg-blockade regime provides the natural setting for creating$W$-type entanglement with cold neutral atoms, it is demonstrated here that ascalable entanglement resource of this type can even be obtained undercompletely different physical circumstances. To be more precise, a specialinstance of twisted $W$ states -- namely, $\pi$-twisted ones -- can beengineered in one-dimensional arrays of cold neutral atoms with Rydberg-dressedresonant dipole-dipole interaction. In particular, it is shown here that thisis possible even when a (dressed) Rydberg excitation is coupled to the motionaldegrees of freedom of atoms in their respective, nearly-harmonic optical-dipolemicrotraps, which are quantized into dispersionless (zero-dimensional) bosons.For a specially chosen ("sweet-spot") detuning of the off-resonant dressinglasers from the relevant internal atomic transitions, the desired $\pi$-twisted$W$ state of Rydberg-dressed qubits is the ground state of the effectiveexcitation -- boson Hamiltonian of the system in a broad window of the relevantparameters. Being at the same time separated from the other eigenstates by agap equal to the single-boson energy, this $W$ state can be prepared using aRabi-type driving protocol. The corresponding preparation times are independentof the system size and several orders of magnitude shorter than the effectivelifetimes of the relevant atomic states.

Scalable $W$-type entanglement resource in neutral-atom arrays with Rydberg-dressed resonant dipole-dipole interaction