Multimer states in multilevel waveguide QED

We study theoretically the interplay of spontaneous emission and interactions for the multiple-excited quasistationary eigenstates in a finite periodic array of multilevel atoms coupled to the waveguide. We develop an analytical approach to calculate such eigenstates based on the subradiant dimer basis. Our calculations reveal the peculiar multimerization effect driven by the anharmonicity of the atomic potential: while a general eigenstate is an entangled one, there exist eigenstates that are products of dimers, trimers, or tetramers, depending on the size of the system and the fill factor. At half-filling, these product states acquire a periodic structure with all-to-all connections inside each multimer and become the most subradiant ones.