Single-photon transport in an array of quantum emitters with long-range interactions

Abstract

We investigate photon transport in a waveguide coupled to two-level quantum emitters with long-range interactions. We derive an exact solution for transmission and reflection amplitudes in the framwork of real-space Hamiltonian. Our explicit formula allows for a complete description of photon transport in the presence of N quantum emitters with arbitrary non-local interactions. We apply this approach to single-photon transport in an one-dimensional waveguide coupled to two atoms with dipole-dipole interaction (DDI). Our numerical results confirm the Fano spectrum line shapes as a result of strong DDI, and demonstrate how the split of perfect reflection spectrum and the resonance transmission can be achieved by tuning the photon-atom and the atom-atom interactions.