# Steady three-dimensional dark state entanglement in dissipative Rydberg atoms

## TL;DR

This paper proposes a robust method to generate three-dimensional entangled states between Rydberg atoms using dissipative dynamics and EIT, effective regardless of initial states and interaction regimes.

## Contribution

It introduces a novel scheme for dark state entanglement in Rydberg atoms that is insensitive to initial state purity and does not require specific Rydberg interaction conditions.

## Key findings

- Feasible for arbitrary initial states and mixed states
- No precise timing or Rydberg interaction constraints needed
- Works in both blockade and intermediate regimes

## Abstract

Scheme to prepare three-dimensional entangled state between a pair of Rydberg atoms is proposed via dissipative dynamics and Electromagnetic Induced Transparency (EIT) associated with the single-atom dark state. The prepared entangled state is the dark state of the whole system. The schemes are feasible no matter the system initially in arbitrary purity or mixed states and do not have accurate requirements on evolution time. In contrast to most of the former Rydberg-atombased dissipative schemes, the Rydberg-Rydberg interaction (RRI) strength do not need to satisfy a certain relation with laser detuning since it works in the blockade as well as intermediate regimes.