Quasiflat band enabling subradiant two-photon bound states

Abstract

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 $1/12\mathrm{th}$ of the light wavelength ${\ensuremath{\lambda}}_{0}$ [Phys. Rev. Research 2, 013173 (2020)]. 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 $d={\ensuremath{\lambda}}_{0}/12$, 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.