We theoretically study a system composed by a waveguide and a quantum emitter moving in a one-dimensional potential along the waveguide axis. We focus on the single excitation subspace and treat the emitter motional degree of freedom full quantum mechanically. We first characterize single-photon scattering off a single moving quantum emitter, showing both direction-dependent transmission and recoil-induced reduction of the quantum emitter motional energy. We then characterize the bound states within the bandgap, which display a motion-induced asymmetric phase in real space. We also demonstrate how these bound states form a continuous band with exotic dispersion relations. Finally, we study the spontaneous emission of an initially excited quantum emitter with various initial momentum distributions, finding strong deviations with respect to the static emitter counterpart both in the occupation dynamics and in the spatial distribution of the emitted photons. Our work extends the waveguide-QED toolbox by including the quantum motional degree of freedom of emitters, whose impact in the few-photon dynamics could be harnessed for quantum technologies.

中文翻译：

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具有移动发射器的波导QED理论

我们从理论上研究了一个由波导和量子发射器组成的系统，该系统沿波导轴在一维电势中移动。我们专注于单个激发子空间，并以机械方式完全处理发射器的运动自由度。我们首先表征单个移动量子发射器的单光子散射，同时显示了与方向相关的传输和后坐力诱导的量子发射器运动能量的减少。然后，我们表征带隙内的束缚状态，这些束缚状态在真实空间中显示运动引起的不对称相位。我们还演示了这些束缚态如何形成具有奇异色散关系的连续谱带。最后，我们研究了具有各种初始动量分布的初始激发量子发射器的自发发射，相对于静态发射器在发射动力学和发射光子的空间分布方面都发现了很大的偏差。我们的工作通过包括发射器的量子运动自由度来扩展波导QED工具箱，可以将其对少数光子动力学的影响用于量子技术。