Preparation of Steady 3D Dark State Entanglement in Dissipative Rydberg Atoms via Electromagnetic Induced Transparency

A scheme to prepare a 3D entangled state between a pair of Rydberg atoms via dissipative dynamics and electromagnetic induced transparency associated with the single-atom dark state is proposed. The prepared entangled state is the dark state of the whole system. The scheme is also feasible regardless of initial purity or mixed state. Since the proposed scheme is based on the Rydberg block regime, the Rydberg-Rydberg interaction strength does not need to satisfy a certain relation with laser detuning, which is very different to the Rydberg-antiblock-based dissipative schemes. One group of Rydberg states and corresponding parameters to simulate the fidelity are used, which verify the feasibility of the scheme.