By using the Lyapunov control approach—an optimization algorithm, we propose a dissipative scheme for efficiently preparing the three-dimensional entangled state of two Rydberg atoms, which subject to Rydberg–Rydberg interactions at the antiblockade regime. The steady target state is the unique dark state of the two-atom system, and is achieved with high fidelity under the Rydberg pumping and the atomic spontaneous emission. The time required to settle into the high-fidelity steady state is greatly accelerated by the help of Lyapunov control, which takes effects while the system is initially prepared in the states containing coherence between the dark state and decoherence-sensitive bright states. The numerical results show that a fidelity of the steady three-dimensional entangled state above 0.99 can be achieved around 2.2 ms with the current experimental conditions. We study in detail the optimal control parameters and show the robustness of the scheme against random noises. The scheme may be generalized for preparation of more complicate multi-atom entangled states.

通过使用Lyapunov控制方法（一种优化算法），我们提出了一种耗散方案，可以有效地准备两个Rydberg原子的三维纠缠态，在反封锁体制下，这些原子受Rydberg-Rydberg相互作用。稳态目标状态是双原子系统独特的暗状态，并且在里德堡泵浦和原子自发发射下以高保真度实现。借助Lyapunov控制，可以大大加快稳定至高保真稳态所需的时间，该控制在系统最初准备处于包含暗态和对退相干敏感的亮态之间的相干状态时生效。数值结果表明，在2附近可以实现0.99以上的稳定三维纠缠态的保真度。以目前的实验条件为2 ms。我们详细研究了最优控制参数，并显示了该方案对随机噪声的鲁棒性。该方案可以被概括用于制备更复杂的多原子纠缠态。