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W态作为一种具有鲁棒性的多体纠缠态, 在量子信息处理、量子网络构建以及量子计算等领域具有重要应用. 本文借助里德堡超级原子的有效能级进行编码, 运用超绝热迭代技术, 提出一种快速制备里德堡超级原子W态的方案. 该方案无需对实验参数和交互时间进行精确控制, 且其反绝热哈密顿量与有效哈密顿量形式相同. 数值模拟结果表明, 此方案不仅能够快速制备W态, 还具备较高的保真度和良好的实验可操作性. 进一步的数值模拟分析显示, 在面对原子自发辐射和光子泄漏引发的退相干问题时, 该方案展现出较强的鲁棒性. 此外, 该方案可扩展至 N 个里德堡超级原子的情况, 这展示了该技术在大规模多体纠缠态制备中的潜力.The W state, as a robust multipartite entangled state, plays an important role in quantum information processing, quantum network construction and quantum computing. In this paper, the three-level ladder-type Rydberg atomic system is put into the Rydberg blocking ball to form a superatom. Each superatom has many collective states including just one Rydberg excitation constrained by the Rydberg blockade effect. In the weak cavity field limit, at most one atom can be pumped into excited state, then we can describe the superatom by a three-level ladder-type system. Afterwards we encode quantum information on the effective energy levels of Rydberg superatoms and propose a fast scheme for preparing the Rydberg superatom W state based on the superadiabatic iterative technique and quantum Zeno dynamics, this scheme can be achieved in only one step by controlling the laser pulses. In the current scheme, the superatoms are trapped in spatially separated cavities connected by optical fibers, which significantly enhances the feasibility of experimental manipulation. A remarkable feature is that it does not require precise control of experimental parameters and interaction time. Meanwhile, the form of counterdiabatic Hamiltonian is the same as that of the effective Hamiltonian. Through numerical simulations, the fidelity of this scheme can reach 99.94%. Even considering decoherence effects, including atomic spontaneous emission and photon leakage, the fidelity can still exceed 97.5%, further demonstrating the strong robustness of the solution. In addition, the Rabi frequency can be characterized as a linear superposition of Gaussian functions, this representation significantly alleviates the complexity encountered in practical experiments. Futhermore, we also analyzed the impact of parameter fluctuations on the fidelity, the results show that this scheme is robust against parameter fluctuations. At last, the present scheme is extended to the cases of N Rydberg superatoms, which shows the scalability of our scheme.
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Keywords:
- Superadiabatic /
- W state /
- Rydberg superatoms
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图 1 (a)单个里德堡原子能级结构图; (b)里德堡超级原子的等效能级结构图
Fig. 1. (a) Energy level structure diagram of a single Rydberg atom; (b) The equivalent energy level structure diagram of Rydberg superatom.
图 2 里德堡超级原子与腔系统的示意图. SA是里德堡超级原子, $ \Omega_k $是第k个腔中经典场的拉比频率
Fig. 2. Schematic diagram of the structure of the Rydberg superatom-cavity system. SA denots the Rydberg superatom, and $ \Omega_k $ is the classical field Rabi frequency in the k-th cavity.
图 3 $ \theta_1(t) $随时间的变化关系. 选取的参数为 $ t_0 = 0.14 T $ 和 $ t_c = 0.19 T $
Fig. 3. The $ \theta_1(t) $ as a function of the time. The parameters $ t_0 = 0.14 T $ and $ t_c = 0.19 T $.
图 4 $ \theta_2(t) $ 随时间的变化关系. 选取的参数为$ t_0 = 0.14 T $ 和 $ t_c = 0.19 T $
Fig. 4. The $ \theta_2(t) $ as a function of the time. The parameters $ t_0 = 0.14 T $and $ t_c = 0.19 T $.
图 5 $ \Omega_0(T^{-1}) $对保真度$ F(T) $的影响图. 当$ \Omega_0 = 8 T^{-1} $时, 保真度$ F(T) = 0.9994 $
Fig. 5. The influence of $ \Omega_0(T^{-1}) $ on fidelity $ F(T) $. When $ \Omega_0 = 8 T^{-1} $, the fidelity $ F(T) = 0.9994 $.
图 6 (a)对比脉冲$ \Omega'_1(t) $和拟合的高斯脉冲$ \widetilde{\Omega}_1(t) $. (b)对比脉冲$ \Omega'_2(t) $和拟合的高斯脉冲$ \widetilde{\Omega}_2(t) $
Fig. 6. (a) Comparing the pulse $ \Omega '_1 (t) $ and the fitting of gaussian pulse $ \widetilde {\Omega} _1 (t) $. (b) Comparing the pulse $ \Omega '_2 (t) $ and the fitting of gaussian pulse $ \widetilde {\Omega} _2 (t) $.
图 7 W态的保真度在超绝热迭代$ T = 8/\Omega_0 $、绝热演化$ T = 8/\Omega_0 $、绝热演化$ T = 35/\Omega_0 $三种不同情况下随时间的变化
Fig. 7. Under the three different conditions: superadiabatic iteration $ T = 8/\Omega_0 $, adiabatic evolution $ T = 8/\Omega_0 $ and adiabatic evolution $ T = 35/\Omega_0 $, the fidelity of W state as a function of the time.
图 8 哈密顿量$ H_{tot} $的控制下的W态的保真度与$ \kappa/\lambda $和$ \gamma/\lambda $的关系. $ T = 8/\Omega_0, \Omega_0 = 0.1\lambda $
Fig. 8. The relationship between the fidelity of the W state and $ \kappa/\lambda $, $ \gamma/\lambda $ by the Hamiltonian $ H_{tot} $. $ T = 8 / \Omega_0, $$ \Omega_0 = 0.1\lambda $.
图 9 (a)保真度随$ \delta \widetilde{\Omega}_1 $ 和 $ \delta \widetilde{\Omega}_2 $的变化. (b)保真度随$ \delta \lambda $和$ \delta v $的变化
Fig. 9. (a)The fidelity versus $ \delta \widetilde{\Omega}_1 $ and $ \delta \widetilde{\Omega}_2 $. (b)The fidelity versus $ \delta \lambda $ and $ \delta v $.
图 10 N个里德堡超级原子-腔系统结构型的示意图. 每个里德堡超级原子被分别放置在不同的真空腔中, 第 2 到第 N 个腔均与第 1 个腔相连. $ \Omega_N $是第N个腔中经典场驱动的拉比频率
Fig. 10. A schematic diagram illustrating the structure of N-Rydberg superatom-cavity system. Each of the Rydberg superatom is placed in a separate vacuum cavity, with cavities 2 through N all connected to cavity 1. $ \Omega_N $ is the classical field-driven Rabi frequency in the N-th cavity.
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