Multilevel quantum routing of single photons with whispering-gallery resonators

Quantum routers determine the propagation of quantum signals in a quantum network. In a complex optical quantum network, the quantum signals should be routed to multilevel quantum channels, but how to modulate this quantum routing process is a challenge. We study the quantum routing of single photons with three-level quantum channels connected by two whispering-gallery resonators (WGRs). We find that single photons can be efficiently routed to a third level quantum channel, though the maximum probability is not higher than that to the second level quantum channel, which can reach $100%$. Moreover, we also investigate how the phase shift parameter and the dissipation rates influence the routing probability in a third level quantum channel. Our work provides a robust proposal for harvesting the potential of quantum networks in the future.