On-Demand Control of Input-State-Dependent Single-Photon Scattering in Multi-Mode Waveguides

Precise control of a single photon transport in broadband, multi-mode waveguides is a fundamental challenge for scalable quantum networks. We propose a theoretical scheme for on-demand control of single-photon scattering using a driven Λ-type emitter coupled to a rectangular waveguide. By employing the Lippmann-Schwinger formalism, we derive the exact analytical scattering matrix and reveal two key interference mechanisms: electromagnetically induced transparency for complete transmission and Fano resonance for complete reflection. We demonstrate that the single-photon scattering is dynamically engineered by the driving field, enabling a switch between complete transmission and dual-frequency complete reflection. Crucially, in the multi-mode regime, we show that the scattering is governed by quantum interference between modes, making it critically dependent on the input photonic state. By preparing the photon in a specific coherent superposition state, the multi-mode interference is harnessed to achieve Fano resonance-mediated complete reflection. Conversely, a single-mode input suppresses complete reflection. This input-state-dependent scattering establishes a general framework for multi-mode quantum photonics, paving the way for broadband dual-frequency filters, multi-mode quantum routers, and on-chip spectrometers.