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arXiv:2511.22840 · Optics Express

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

Yan Liu, Qing-Ao Xiang, Xin-Yuan Yang, Ji-Bing Yuan, Shi-Qing Tang, Xin-Wen Wang, Ya-Ju Song

quant-phSubmitted Nov 28, 2025• Announced Dec 1, 2025• 1 citation• Revised Dec 18, 2025 (v2)
v1 · Nov 28, 2025v2 · Dec 18, 2025
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Abstract

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.

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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 ΛΛΛ-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.
The single-photon scattering by a V-type three-level emitter in a rectangular waveguide is studied. Here the frequency value of input photons can be large beyond the single-transverse-mode region. By using Green's function formalism, the necessary and sufficient conditions of complete transmission as well as complete reflection are derived analytically. In the region of single transverse mode, the physical mechanisms of complete transmission and complete reflection are electromagnetically induced transparency (EIT) and Fano resonance, respectively. In the region of multiple transverse modes, which are induced by the finite cross section, the quantum interference between multiple scattering pathways with different transverse modes can be used to manipulate the single-photon transport. We find that the emitter becomes transparent when the superposition of waveguide modes has zero amplitude at the position of emitter. And the perfect reflection is absent even under Fano resonance unless the input-state is in a coherent superposition state. These results may promote the development of single-photon devices with wide applicable frequency region.
We propose a single-photon router using a single atom with an inversion center coupled to quantum multichannels made of coupled-resonator waveguides. We show that the spontaneous emission of the atom can direct single photons from one quantum channel into another. The on-demand classical field perfectly switches off the single-photon routing due to the quantum interference in the atomic amplitudes of optical transitions. Total reflections in the incident channel are due to the photonic bound state in the continuum. Two virtual channels, named the scatter-free and controllable channels, are found, which are coherent superpositions of quantum channels. Any incident photon in the scatter-free channel is totally transmitted. The propagating states of the controllable channel are orthogonal to those of the scatter-free channel. Single photons in the controllable channel can be perfectly reflected or transmitted by the atom.
We investigate the coherent single-photon scattering process in a topological waveguide coupled to a driven three-level atom in the $\mathrm{\ensuremath{\Lambda}}$ configuration, where two ground states are optically connected to a common excited state. We derive an analytical expression for transmittance by using the scattering formalism for three distinct sublattice sites (A, B, and AB) of the waveguide, which couple to the $\mathrm{\ensuremath{\Lambda}}$ 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 control field strength enhancement, the transmission spectrum evolves from Electromagnetically Induced Transparency to Autler-Townes splitting in A and B sublattice-site coupling. The manipulation of transmission from opaque to transparent holds the key mechanism of a single-photon switching. Furthermore, the topology-dependent AB sublattice configuration allows multiple-path-induced quantum interference, resulting in the sharper Fano line shape. This topological Fano resonance is not only tunable via the control field and coupling strength but also robust against structural imperfections due to the topological nature of the waveguide. These combined features such as tunability and topological protection make our system a promising platform for next-generation quantum technologies, including single-photon switches, high-resolution sensors, and communication devices.
All-optical manipulation of a single-photon quantum transport is of fundamental importance in quantum nanophotonics. Here, a system consisting of a single-mode waveguide coupling with a V-type three-level atom is proposed, where two excited states of the atom are strongly driven by the external coherent field. Transmission and reflection spectra for the output photon at different frequency components, including virtual transitions induced by the ultrastrong driving, are calculated. The interaction between the waveguide photon and the driven atom experiences quantum interferences, which leads to a variety of capabilities for manipulating the single-photon transport in the spectral domain. We perform simulations to demonstrate the possibilities of achieving desired frequency conversions as well as generating different correlated single-photon states by using external drive field at chosen strength. Our work therefore studies the single-photon transport in a strongly driven atom–waveguide system and shows applications for all-optically manipulating the single photon in the field of quantum information processing.
Abstract We present a theoretical study of controlled single-photon routing in a cavity-quantum electrodynamics system coupled to dual waveguides, where each cavity embedding with a two-level atom mediates photon transport between two channels. The proposed system achieves enhanced routing performance through tailored phase-dependent cavity–waveguide couplings that generate optimized quantum interference patterns. Using a real-space formalism, we derive analytical expressions for single-photon scattering amplitudes and identify optimal conditions for maximum routing efficiency. Our analysis shows that targeted routing with near-unity efficiency can be realized by precisely manipulating both the accumulated phase and differential phase shift, while the atom–cavity coupling strength enables frequency-selective tunability. Furthermore, we demonstrate engineered nonreciprocal transmission and chiral scattering, enabling deterministic control over photonic propagation direction. This phase-tunable protocol establishes a scalable platform for quantum network implementation and enables novel functionalities in photonic quantum information processing.
We study the transverse-size effect of a quasi-one-dimensional rectangular waveguide on the single-photon scattering on a two-level system. We calculate the transmission and reflection coefficients for single incident photons using the scattering formalism based on the Lippmann-Schwinger equation. When the transverse size of the waveguide is larger than a critical size, we find that the transverse mode will be involved in the single-photon scattering. Including the coupling to a higher traverse mode, we find that the photon in the lowest channel will be lost into the other channel, corresponding to the other transverse modes, when the input energy is larger than the maximum bound-state energy. Three kinds of resonance phenomena are predicted: single-photon resonance, photonic Feshbach resonance, and cutoff (minimum) frequency resonance. At these resonances, the input photon is completely reflected.