Quasiflat band enabling subradiant two-photon bound states

We study theoretically the radiative lifetime of bound two-particle excitations in a waveguide with an array of two-level atoms, realizing a one-dimensional Dicke-like model. Recently, Zhang et al. have numerically found an unexpected sharp maximum of the bound pair lifetime when the array period d is equal to 1/12th of the light wavelength λ0 [Phys. Rev. Research 2, 013173 (2020)10.1103/PhysRevResearch.2.013173]. We uncover a rigorous transformation from the non-Hermitian Hamiltonian with the long-range radiative coupling to the nearest-neighbor coupling model with the radiative losses only at the edges. This naturally explains the puzzle of long lifetime: The effective mass of the bound photon pair also diverges for d=λ0/12, hampering an escape of photons through the edges. We also link the oscillations of the lifetime with the number of atoms to the nonmonotonous quasi-flat-band dispersion of the bound pair.