Controllable Single Photon Scattering via Coupling of Driven $Λ$ System with Topological Waveguide

Abstract: We investigate the coherent single photon scattering process in a topological waveguide coupled with a driven $\Lambda$ system. We derive an analytical expression for transmittance by using the scattering formalism for three different sublattice sites (A, B, and AB), which couples to the $\Lambda$ system. We have demonstrated that the system's response is topology-independent for A and B sublattice-site coupling and becomes topology-dependent for AB sublattice-site coupling. In a weak control field regime, the system behaves as a perfect mirror in all of these configurations. Upon the control field strength enhancement, the transmission spectrum evolves from Electromagnetically Induced Transparency (EIT) to Autler-Townes splitting (ATS) in A and B sublattice-site coupling. The manipulation of transmission from opaque to transparent holds the key mechanism of a single photon switch. Further, the topology-dependent AB sublattice configuration allows the sharper Fano line shape that is absent in topology-independent A and B sublattice configurations. This characteristic of the Fano line can be used as a tunable single-photon switch and for sensing external perturbations. Furthermore, our study paves the way for the robustness and tunability of systems with applications in quantum technologies such as quantum switches, sensors, and communication devices.