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arXiv:1304.6374 · Physical Review Letters

Preparation of Entangled and Antiferromagnetic States by Dissipative Rydberg Pumping

Alex Carr, Mark E. Saffman

Published Jul 17, 2013• 146 citations
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Abstract

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.

DOI
10.1103/physrevlett.111.033607

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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.
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.
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 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.
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.
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 a scheme for rapid generation of high fidelity steady-state entanglement between a pair of atoms. A two-photon excitation process toward long-lived Rydberg states with finite pairwise interaction, a dark-state interference effect in the individual atoms, and spontaneous emission from their short-lived excited states lead to rapid, dissipative formation of an entangled steady state. We show that for a wide range of physical parameters, this entangled state is formed on a time scale given by the strengths of coherent Raman and Rabi fields applied to the atoms, while it is only weakly dependent on the Rydberg interaction strength.