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arXiv:1709.08327 · Physical Review A

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

Xiao‐Qiang Shao, Jin-Hui Wu, X. X. Yi, Gui‐Lu Long

Published Dec 15, 2017• 73 citations
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Abstract

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 $Z$ 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 $Z$ 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.

DOI
10.1103/physreva.96.062315

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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 \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ-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+\ensuremath⟩|{\mathrm{GHZ}}_{+}\ensuremath{\rangle}∣GHZ+​\ensuremath⟩ in the process of ZZZ pumping, making ∣GHZ\ensuremath−\ensuremath⟩|{\mathrm{GHZ}}_{\ensuremath{-}}\ensuremath{\rangle}∣GHZ\ensuremath−​\ensuremath⟩ 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∼98\ensuremath{\sim}98%\ensuremath∼98 can be obtained with the currently achievable parameters in the Rydberg-atom-cavity system.
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.
The multipartite Greenberger–Horne–Zeilinger (GHZ) states play an important role in large-scale quantum information processing. We utilize the polychromatic driving fields and the engineered spontaneous emissions of Rydberg states to dissipatively drive three- and four-partite neutral atom systems into the steady GHZ states, at the presence of the next-nearest neighbor interaction of excited Rydberg states. Furthermore, the introduction of quantum Lyapunov control can help us optimize the dissipative dynamics of the system so as to shorten the convergence time of the target state, improve the robustness against the spontaneous radiations of the excited Rydberg states, and release the limiting condition for the strengths of the polychromatic driving fields. Under the feasible experimental conditions, the fidelities of three- and four-partite GHZ states can be stabilized at 99.24 % and 98.76 %, respectively.
The multipartite Greenberger-Horne-Zeilinger (GHZ) states are indispensable elements for various quantum information processing tasks. Here we put forward two deterministic proposals to dissipatively prepare tripartite GHZ states in a neutral atom system. The first scheme can be considered as an extension of a recent work [T. M. Wintermantel, Y. Wang, G. Lochead, \textit{et al}, {Phys. Rev. Lett. \textbf{124}, 070503 (2020)}]. By virtue of the polychromatic driving fields and the engineered spontaneous emission, a multipartite GHZ state with odd numbers of atoms are generated with a high efficiency. This scheme effectively overcomes the problem of dependence on the initial state but sensitive to the decay of Rydberg state. In the second scenario, we exploit the spontaneous emission of the Rydberg states as a resource, thence a steady tripartite GHZ state with fidelity around 98%98\%98% can be obtained by simultaneously integrating the switching driving of unconventional Rydberg pumping and the Rydberg antiblockade effect.
The multipartite Greenberger–Horne–Zeilinger (GHZ) states are indispensable elements for various quantum information processing tasks. Here we put forward two deterministic proposals to dissipatively prepare tripartite GHZ states in a neutral atom system. The first scheme utilizes the polychromatic driving fields and the engineered spontaneous emission of Rydberg states to generate a tripartite GHZ state with a high efficiency, which is then optimized by introducing the Gaussian soft control pulse. In the second scenario, we exploit the natural spontaneous emission of the Rydberg states as a resource, thence a steady tripartite GHZ state with fidelity around 98% can be obtained by simultaneously integrating the switching driving of unconventional Rydberg pumping and the Rydberg antiblockade effect.
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.