We investigate the optical response of a linear waveguide quantum electrodynamics (QED) system, namely, a bosonic oscillator coupled to a waveguide. Our analysis is based on exact diagonalization of the overall Hamiltonian and is therefore rigorous even in the ultrastrong-coupling regime of waveguide QED. Owing to the counter-rotating terms in the oscillator-waveguide coupling, the phase-space motion of the oscillator is elliptical in general, and this becomes remarkable in the ultrastrong-coupling regime. We also reveal that such elliptical motion does not propagate into the output field and present an analytic form of the reflection coefficient that is asymmetric with respect to the resonance frequency.

中文翻译：

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超强波导QED中玻色子振荡器的椭圆旋转

我们研究线性波导量子电动力学（QED）系统的光学响应，即耦合到波导的Bosonic振荡器。我们的分析基于整个哈密顿量的精确对角线化，因此即使在波导QED的超强耦合状态下也很严格。由于振荡器-波导耦合中的反向旋转项，振荡器的相空间运动通常是椭圆形的，这在超强耦合状态下变得非常明显。我们还揭示了这种椭圆运动不会传播到输出场中，并且呈现出相对于共振频率不对称的反射系数的解析形式。