Nonreciprocal photon transport in indirectly coupled whispering-gallery mode resonators

We study the reflection and transmission properties of a system comprising two whispering-gallery mode resonators, each containing a Zeeman-split quantum dot and side-coupled to an optical fiber. Our results demonstrate that unidirectional reflection and transmission can be achieved by tuning the coupling strength between the resonators and the optical fiber. Furthermore, we establish a correspondence between quantum dot energy level resonance frequencies and the positions of low reflection (transmission) peaks at a phase shift of {\pi}. This research provides insights for the development of quantum optical devices like isolators, circulators, and routers.