Singlet States Preparation for Three $\Lambda$-type Atoms with Rydberg Blockade Mechanism

A proposal for the generation of singlet states of three $\Lambda$-type Rydberg atoms is presented. The singlet state is prepared through the combination of a Rydberg state and an EPR pair, and the scheme relies on the Rydberg blockade effect which prevents the simultaneous excitation of the two atoms to a Rydberg state. In addition, some frequency detuning between lasers and atomic transitions is set to eliminate the degenerate of the two ground states. And finally, a series of numerical simulations are made to show the feasibility of the scheme.