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Laser Physics Letters

Fast dissipative preparation of three-dimensional entangled states for two Rydberg atoms via Lyapunov control

Zong-Xing Ding, Chang‐Sheng Hu, Li-Tuo Shen, Wan-Jun Su, Huai‐Zhi Wu, Shi‐Biao Zheng

Published Jan 25, 2021• 2 citations
Publisher

Abstract

Abstract 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.

DOI
10.1088/1612-202x/abd8d8

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Abstract 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.
Abstract Preparation of entangled steady states via dissipation and pumping in Rydberg atoms has been recently found to be useful for quantum information processing. The driven-dissipative dynamics is closely related to the natural linewidth of the Rydberg states and can be usually modulated by engineering the thermal reservior. Instead of modifying the effectively radiative decay, we propose an alternatively optimized scheme, which combines the resonant Rydberg antiblockade excitation and the Lyapunov control of the ground states to speed up the prepration of the singlet state for two interacting Rydberg atoms. The acceleration process strongly depends on the initial state of the system with respect to the initial coherence between the singlet state and decoherence-sensitive bright state. We study the optimal parameter regime for fast entanglement preparation and the robustness of the fidelity against random noises. The numerical results show that a fidelity above 0.99 can be achieved around 0.4 ms with the current experimental parameters. The scheme may be generalized for preparation of more complicate multi-atom entangled states.
Based on Lyapunov control, a scheme is proposed to accelerate dissipation dynamics for the generation of high-fidelity entanglement between two Rydberg atoms in the context of cavity QED. We first use quantum Zeno dynamics and the Rydberg antiblockade to find a unique steady state (two-atom singlet state) for the system. Then, we apply additional coherent control (ACC) fields to improve the evolution speed of the dissipative system. The ACC fields are designed based on the target state and they vanish gradually along with increasing of the fidelity; thus, the system is guaranteed to be finally stable. Additionally, the current accelerated scheme is checked to be robust against systematic and amplitude-noise errors.
Scheme to prepare three-dimensional entangled state between a pair of Rydberg atoms is proposed via dissipative dynamics and Electromagnetic Induced Transparency (EIT) associated with the single-atom dark state. The prepared entangled state is the dark state of the whole system. The schemes are feasible no matter the system initially in arbitrary purity or mixed states and do not have accurate requirements on evolution time. In contrast to most of the former Rydberg-atombased dissipative schemes, the Rydberg-Rydberg interaction (RRI) strength do not need to satisfy a certain relation with laser detuning since it works in the blockade as well as intermediate regimes.
Multiparticle singlet states are special quantum entangled states that have been shown to have many interesting applications. We develop a simple scheme to prepare a steady three-atom singlet state with a dissipative Rydberg pumping process, which combines dissipative dynamics and Rydberg interactions. The numerical simulations show that the fidelity of the created three-atom singlet state can reach up to 0.9947 under certain conditions. The scheme does not require a cavity, initial-state preparation, and exact controlling of operation time, which reduces the difficulty of the experiment. Finally, the experimental feasibility of the scheme is discussed.
A scheme is proposed for dissipative generation of maximally entanglement between two Rydberg atoms in the context of cavity QED. The spontaneous emission of atoms combined with quantum Zeno dynamics and the Rydberg antiblockade guarantees a unique steady solution of the master equation of the system, which just corresponds to the antisymmetric Bell state $|S\ensuremath{\rangle}$. The convergence rate can be accelerated by the ground-state blockade mechanism of Rydberg atoms. Meanwhile the effect of cavity decay is suppressed by the Zeno requirement, leading to a steady-state fidelity about 9090%90 as the single-atom cooperativity parameter $C\ensuremath{\equiv}{g}^{2}/(\ensuremath{\kappa}\ensuremath{\gamma})=10$, and this restriction is further relaxed to C=5.2C=5.2C=5.2 once the quantum-jump-based feedback control is exploited.
Abstract A scheme to prepare a 3D entangled state between a pair of Rydberg atoms via dissipative dynamics and electromagnetic induced transparency associated with the single‐atom dark state is proposed. The prepared entangled state is the dark state of the whole system. The scheme is also feasible regardless of initial purity or mixed state. Since the proposed scheme is based on the Rydberg block regime, the Rydberg–Rydberg interaction strength does not need to satisfy a certain relation with laser detuning, which is very different to the Rydberg‐antiblock‐based dissipative schemes. One group of Rydberg states and corresponding parameters to simulate the fidelity are used, which verify the feasibility of the scheme.