  Inspired by recent work [A. W. Carr and M. 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 less 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, 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.

Quantum Physics