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Inspired by a recent work [Reiter, Reeb, and S{\o}rensen, Phys. Rev. Lett.{\bf117}, 040501 (2016)], we present a simplified proposal for dissipativelypreparing a Greenberger-Horne-Zeilinger (GHZ) state of three Rydberg atoms in acavity. The $Z$ pumping is implemented under the action of the spontaneousemission of $\Lambda$-type atoms and the quantum Zeno dynamics induced bystrong continuous coupling. In the meantime, a dissipative Rydberg pumpingbreaks up the stability of the state $|{\rm GHZ}_+\rangle$ in the process of$Z$ pumping, making $|{\rm GHZ}_-\rangle$ be the unique steady state of system.Compared with the former scheme, the number of driving fields acting on atomsis greatly reduced and only a single-mode cavity is required. The numericalsimulation of the full master equation reveals that a high fidelity $\sim98\%$can be obtained with the currently achievable parameters in theRydberg-atom-cavity system.

Dissipative preparation of steady Greenberger-Horne-Zeilinger states for Rydberg atoms with quantum Zeno dynamics