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arXiv:1705.03614 · Physical Review A

Dissipation-based entanglement via quantum Zeno dynamics and Rydberg antiblockade

Xiao‐Qiang Shao, Jin-Hui Wu, X. X. Yi

Published Jun 29, 2017• 52 citations
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Abstract

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 $90%$ as the single-atom cooperativity parameter $C\ensuremath{\equiv}{g}^{2}/(\ensuremath{\kappa}\ensuremath{\gamma})=10$, and this restriction is further relaxed to $C=5.2$ once the quantum-jump-based feedback control is exploited.

DOI
10.1103/physreva.95.062339

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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⟩|S\ensuremath{\rangle}∣S\ensuremath⟩. 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≡g2/(\ensuremathκ\ensuremathγ)=10C\ensuremath{\equiv}{g}^{2}/(\ensuremath{\kappa}\ensuremath{\gamma})=10C\ensuremath≡g2/(\ensuremathκ\ensuremathγ)=10, and this restriction is further relaxed to C=5.2C=5.2C=5.2 once the quantum-jump-based feedback control is exploited.
A new mechanism is proposed for dissipatively preparing maximal Bell entangled state of two atoms in an optical cavity. This scheme integrates the spontaneous emission, the light shift of atoms in the presence of dispersive microwave field, and the quantum Zeno dynamics induced by continuous coupling, to obtain a unique steady state irrespective of initial state. Even for a large cavity decay, a high-fidelity entangled state is achievable at a short convergence time, since the occupation of the cavity mode is inhibited by the Zeno requirement. Therefore, a low single-atom cooperativity C=g2/(κγ) is good enough for realizing a high fidelity of entanglement in a wide range of decoherence parameters. As a straightforward extension, the feasibility for preparation of two-atom Knill–Laflamme–Milburn state with the same mechanism is also discussed.
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.
Inspired by a recent work [Reiter, Reeb, and Sorensen, 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 ZZZ pumping is implemented under the action of the spontaneous emission of Λ\LambdaΛ-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 ∣GHZ+⟩|{\rm GHZ}_+\rangle∣GHZ+​⟩ in the process of ZZZ pumping, making ∣GHZ−⟩|{\rm GHZ}_-\rangle∣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 ∼98%\sim98\%∼98% can be obtained with the currently achievable parameters in the Rydberg-atom-cavity system.
Inspired by a recent work [F. Reiter, D. Reeb, and A. S. S\o{}rensen, Phys. Rev. Lett. 117, 040501 (2016)], we present a simplified proposal for dissipatively preparing a Greenberger-Horne-Zeilinger (GHZ) state of three Rydberg atoms in a cavity. The ZZZ pumping is implemented under the action of the spontaneous emission of $\mathrm{\ensuremath{\Lambda}}$-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 $|{\mathrm{GHZ}}_{+}\ensuremath{\rangle}$ in the process of ZZZ pumping, making $|{\mathrm{GHZ}}_{\ensuremath{-}}\ensuremath{\rangle}$ the unique steady state of the 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 $\ensuremath{\sim}98%$ can be obtained with the currently achievable parameters in the Rydberg-atom-cavity system.
We propose a mechanism of ground-state blockade between two NNN-type Rydberg atoms by virtue of the Rydberg-antiblockade effect and the Raman transition. Inspired by the quantum Zeno effect, the strong Rydberg antiblockade interaction plays a role in frequently measuring one ground state of two, leading to a blockade effect for double occupation of the corresponding quantum state. By encoding the logic qubits into the ground states, we efficiently avoid the spontaneous emission of the excited Rydberg state and maintain the nonlinear Rydberg-Rydberg interaction at the same time. As applications, we discuss in detail the feasibility of preparing two-atom and three-atom entanglement with ground-state blockade in closed and open systems, respectively, which shows that a high fidelity of the entangled state can be obtained with current experimental parameters.