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arXiv:1506.01580 · Physical Review A

Simplified scheme for entanglement preparation with Rydberg pumping via dissipation

Shi‐Lei Su, Qi Guo, Hong‐Fu Wang, Shou Zhang

Published Aug 12, 2015• 62 citations
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Abstract

Inspired by recent work [Carr and Saffman, Phys. Rev. Lett. 111, 033607 (2013)], we propose a simplified scheme to prepare the two-atom maximally entangled states via dissipative Rydberg pumping. Compared with the former scheme, the simplified one involves fewer classical laser fields and Rydberg interactions, and the asymmetric Rydberg interactions are avoided. Master equation simulations demonstrate that the fidelity and the Clauser-Horne-Shimony-Holt correlation of the maximally entangled state could reach up to 0.999 and 2.821, respectively, under certain conditions. Furthermore, we extend the physical thoughts to prepare the three-dimensional entangled state, and the numerical simulations show that, in theory, both the fidelity and the negativity of the desired entanglement could be very close to unity under certain conditions.

DOI
10.1103/physreva.92.022328

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Inspired by recent work [Carr and Saffman, Phys. Rev. Lett. 111, 033607 (2013)], we propose a simplified scheme to prepare the two-atom maximally entangled states via dissipative Rydberg pumping. Compared with the former scheme, the simplified one involves fewer classical laser fields and Rydberg interactions, and the asymmetric Rydberg interactions are avoided. Master equation simulations demonstrate that the fidelity and the Clauser-Horne-Shimony-Holt correlation of the maximally entangled state could reach up to 0.999 and 2.821, respectively, under certain conditions. Furthermore, we extend the physical thoughts to prepare the three-dimensional entangled state, and the numerical simulations show that, in theory, both the fidelity and the negativity of the desired entanglement could be very close to unity under certain conditions.
We extend the recent result of a bipartite Bell singlet [A. W. Carr and M. Saffman, Phys. Rev. Lett. 111, 033607 (2013)] to a stationary three-dimensional entanglement between two-individual neutral Rydberg atoms. This proposal makes full use of the coherent dynamics provided by a Rydberg-mediated interaction and the dissipative factor originating from the spontaneous emission of a Rydberg state. The numerical simulation of the master equation reveals that both the target state negativity $\mathcal{N}({\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\ensuremath{\infty}})$ and fidelity $\mathcal{F}({\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\ensuremath{\infty}})$ can exceed 99.90%. Furthermore, a steady three-atom singlet state $|{S}_{3}\ensuremath{\rangle}$ is also achievable based on the same mechanism.
We propose and analyze an approach for preparation of high fidelity entanglement and antiferromagnetic states using Rydberg mediated interactions with dissipation. Using asymmetric Rydberg interactions the two-atom Bell singlet is a dark state of the Rydberg pumping process. Master equation simulations demonstrate Bell singlet preparation fidelity F=0.998. Antiferromagnetic states are generated on a four-spin plaquette in agreement with results found from diagonalization of the transverse field Ising Hamiltonian.
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.
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.
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.
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.