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arXiv:1402.3760 · Physical Review A

Stationary three-dimensional entanglement via dissipative Rydberg pumping

Xiao‐Qiang Shao, Jia-Bin You, Tai-Yu Zheng, C. H. Oh, Shou Zhang

Published May 12, 2014• 68 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.89.052313

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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 N(\ensuremathρ\ifmmode^\elseˆ\fi\ensuremath∞)\mathcal{N}({\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\ensuremath{\infty}})N(\ensuremathρ\ifmmode^\elseˆ\fi​\ensuremath∞​) and fidelity F(\ensuremathρ\ifmmode^\elseˆ\fi\ensuremath∞)\mathcal{F}({\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\ensuremath{\infty}})F(\ensuremathρ\ifmmode^\elseˆ\fi​\ensuremath∞​) can exceed 99.90%. Furthermore, a steady three-atom singlet state ∣S3\ensuremath⟩|{S}_{3}\ensuremath{\rangle}∣S3​\ensuremath⟩ is also achievable based on the same mechanism.
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.
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.
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.
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.
We present a protocol to prepare rapidly a stationary three-atom singlet state with high fidelity, which takes advantage of the dissipative factor originating from the spontaneous emission of short-lived excited states and Rydberg blockade. The short lifetime of the excited states is an active ingredient in the state preparation, and the numerical simulation results of the master equation show that the fidelity of the created state can achieve 0.98 when the evolution time of the system is as short as 300 $\ensuremath{\mu}\mathrm{s}$ under certain reasonable conditions. Moreover, the protocol is only weakly dependent on the Rydberg interaction strength and needs no state initialization, optical cavity, feedback controls, and fine controlling of the system parameters, which can greatly reduce the experimental difficulty.