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Physical Review A

Fast creation of a three-atom singlet state with a dissipative mechanism and Rydberg blockade

Xiang Chen, Gongwei Lin, Hong Xie, Xiao Shang, Ming-Yong Ye, Xiu‐Min Lin

Published Oct 29, 2018• 9 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.98.042335

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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 \ensuremathμs\ensuremath{\mu}\mathrm{s}\ensuremathμs 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.
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.
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.
Quantum entanglement is a basic resource of quantum information processing and quantum computation. The simple and efficient generation of entangled states is always one of the hot research topics. As one of the ideal carriers of quantum information encoding, neutral Rydberg atom occupies a place in the field of generation of entangled state with its unique advantages. For example, Rydberg atom has a large volume and is easily ionized by an external electric field, so it is very sensitive to the change in the external electric field. Therefore, the interaction strength between Rydberg atoms can be changed by altering the external electric field. Rydberg state is a highly excited state, but its radiation attenuation is very small: the radiation lifetime can reach a millisecond level or even longer. The distance between the atomic kernel and the outermost electron is relatively long, and the electric dipole moment is very large. In this paper, the four-level inverted “Y”-type Rydberg atomic system is introduced into the Rydberg blocking ball to form a superatom, and the quantum information is encoded on the effective energy level of the superatom under the condition of weak cavity field. We construct shortcuts to adiabatic passage in a three-superatom system. Combined with quantum Zeno dynamics and shortcuts to adiabatic passage, the three-particle singlet state is simply and effectively generated. In addition, the influence of decoherence factors (including cavity decay and spontaneous emission of superatoms) on the fidelity is considered in this scheme. Numerical simulation results show that the proposed scheme can obtain high fidelity without precisely controlling the evolution time, and the fidelity of singlet state is robust to decoherence factors, since no cavity-photon population is involved in the whole process because of the quantum Zeno dynamics.
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.
Abstract A protocol to generate atomic singlet state of three atoms is proposed. The strong Rydberg interactions between atoms mediate the multi‐qubit operations and help to simplify the dynamics of the system. The effective Hamiltonian is constructed in the regime of Rydberg blockade and the evolution path is built up from an initial state to the target singlet state via the Lie‐transform‐based pulse design. Numerical simulations show the protocol can produce atomic singlet state with high fidelity and holds robustness against several types of experimental imperfections. Therefore, it may provide some useful results for the generation of singlet states in atomic system.