Correlated relaxation and emerging entanglement in arrays of $\mathrm{\Lambda }$-type atoms

We present a theoretical framework for investigating the non-classical collective relaxation in arrays of Λ-type three-level atoms, where the two optical transitions coupled to a pair of orthogonal chiral or achiral waveguide modes. We demonstrate that the atomic entanglement emerges in the course of relaxation and persists in the final steady state of the system. We also reveal the entanglement of among the emitted photons as well as between the atoms and the photons. The presence and the degree of the entanglement depends crucially on the interatomic distance and the chirality of the waveguide. Our findings open a new way to engineer dissipation-induced entanglement.