Photon transport in a one-dimensional nanophotonic waveguide QED system

The waveguide quantum electrodynamics (QED) system may have important applications in quantum device and quantum information technology. In this article we review the methods being proposed to calculate photon transport in a one-dimensional (1D) waveguide coupled to quantum emitters. We first introduce the Bethe ansatz approach and the input-output formalism to calculate the stationary results of a single photon transport. Then we present a dynamical time-dependent theory to calculate the real-time evolution of the waveguide QED system. In the longtime limit, both the stationary theory and the dynamical calculation give the same results. Finally, we also briefly discuss the calculations of the multiphoton transport problems.