Three methods for the single-photon transport in a chiral cavity quantum electrodynamics system

We investigate the single-photon transport problem in system of a Whispering-Gallery mode microresonator directionally coupled with two-level quantum emitter (QE). This QE-microresonator coupling can usually be studied by cavity electrodynamics and methods. However, we find that if treat QE as phase-amplitude modulator, also deal such systems using transfer matrix method. Further, theory, prove these three methods are equivalent. The corresponding relations respective parameters among approaches precisely deduced. Our work extended to multiple-resonator interacting QEs chiral way. Therefore, method may provide convenient intuitive form for exploring more complex QE-resonator interaction systems.