Simplified process of dissipation-based Greenberger–Horne–Zeilinger state generation with Lyapunov control

Abstract

In this paper, we propose a protocol to generate steady Greenberger–Horne–Zeilinger (GHZ) states of three Rydberg atoms with dissipation dynamics and simplified Lyapunov control. Firstly, combining with the dissipation dynamics and Rydberg antiblockade, a unique and steady solution of the master equation of the system is obtained. Furthermore, to polish the convergence rate, we add well-designed additional coherent control (ACC) fields with Lyapunov control into the traditional dissipation process and simplify the control fields with bang–bang design proposed in the Ref. (Hou et al., 2012) for better experimental feasibility. Numerical simulation reveals that the GHZ states generation is prominently accelerated and the simplified control fields have the similar efficiency with the traditional Lyapunov control fields but are easier to realize in realistic situations. We hope this work could provide an alternative way to polish the generation of entanglement.