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

Abstract

Inspired by a recent work [Reiter, Reeb, and Sørensen, Phys. Rev. Lett. {\bf117}, 040501 (2016)], we present a simplified proposal for dissipatively preparing a Greenberger-Horne-Zeilinger (GHZ) state of three Rydberg atoms in a cavity. The $Z$ pumping is implemented under the action of the spontaneous emission of $\Lambda$-type atoms and the quantum Zeno dynamics induced by strong continuous coupling. In the meantime, a dissipative Rydberg pumping breaks up the stability of the state $|{\mathrm{GHZ}}_{+}⟩$ in the process of $Z$ pumping, making $|{\mathrm{GHZ}}_{-}⟩$ be the unique steady state of system. Compared with the former scheme, the number of driving fields acting on atoms is greatly reduced and only a single-mode cavity is required. The numerical simulation of the full master equation reveals that a high fidelity $\sim 98\%$ can be obtained with the currently achievable parameters in the Rydberg-atom-cavity system.

arXiv commentaccepted by PRA

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