Single-photon scattering in waveguide-QED systems plays a pivotal role in quantum information processing and communication. We introduce a time-dependent variational approach employing a modified multiple Davydov Ansatz to simulate single-photon dynamics in one-dimensional waveguide-QED systems within the strong-coupling regime. The method is benchmarked across three configurations: a single qubit, two distant qubits, and a ladder-type qutrit coupled to the waveguide. For the single- and two-qubit cases, the variational results exhibit excellent agreement with those derived from a transformed rotating-wave approximation (TRWA). The accuracy of our approach is further verified by an analysis of the local-in-time error, which remains small even under strong coupling, indicating its potential superiority over TRWA in specific regimes. In addition, by contrasting our results with the rotating-wave approximation, we elucidate the significant influence of counter-rotating couplings on scattering dynamics. Our findings establish this variational method as a reliable and versatile tool for investigating single-photon scattering in diverse waveguide-QED systems, particularly in regimes where traditional approximations falter.

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• Quantum optics with artificial atoms
• Waveguide arrays
• Spin-boson model
• Variational approach