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Motivated by the significantly improved scalability of optically-trappedneutral-atom systems, extensive efforts have been devoted in recent years toquantum-state engineering in Rydberg-atom ensembles. Here we investigate theproblem of engineering generalized (``twisted'') $W$ states, as well asGreenberger-Horne-Zeilinger (GHZ) states, in the strongly-interacting regime ofa neutral-atom system. We assume that each atom in the envisioned systeminitially resides in its ground state and is subject to several external laserpulses that are close to being resonant with the same internal atomictransition. In particular, in the special case of a three-atom system(Rydberg-atom trimer) we determine configurations of field alignments andatomic positions that enable the realization of chiral $W$ states -- a specialtype of twisted three-qubit $W$ states of interest for implementingnoiseless-subsystem qubit encoding. Using chiral W states as an example we alsoaddress the problem of deterministically converting twisted $W$ states intotheir GHZ counterparts in the same three-atom system, thus significantlygeneralizing recent works that involve only ordinary $W$ states. We show thatstarting from twisted -- rather than ordinary -- $W$ states is equivalent torenormalizing downwards the relevant Rabi frequencies. While this leads tosomewhat longer state-conversion times, we also demonstrate that those timesare at least two orders of magnitude shorter than typical lifetimes of relevantRydberg states.

Dynamical generation of chiral $W$ and Greenberger-Horne-Zeilinger states in laser-controlled Rydberg-atom trimers