非移动介质球体的量子电动力学：洛伦兹-米散射的量子化
Quantum Electrodynamics with a Nonmoving Dielectric Sphere: Quantizing Lorenz-Mie Scattering
AI总结：
本文量子化真空中非移动介质球体周围的电磁场，推导平面波与归一化本征模式的正则变换，并用于分析单光子、压缩光及双光子散射，揭示三维分束器的洪-欧-曼德尔干涉角分布，为光与介质球体机械自由度量子相互作用奠定理论。
摘要：
我们在真空中存在非移动介质球体的情形下对电磁场进行量子化。该球体被假定为无损耗、无色散、各向同性且均匀的。量子化过程使用归一化本征模式以及平面波模式进行。我们指定了两种有用的归一化本征模式替代基：球面本征模式和散射本征模式。推导了平面波模式与归一化本征模式之间的正则变换。该形式体系被用于研究单个光子、相干压缩光以及双光子态在介质球体上的散射。在后一种情形中，我们计算了散射场的二阶关联函数，从而揭示了介质球体作为三维分束器时洪-欧-曼德尔干涉的角分布。我们的结果针对任意尺寸的介质球体解析推导，并特别强调了小粒子极限。这项工作为描述光与介质球体的运动、旋转和振动自由度之间的量子相互作用奠定了理论基础。
英文摘要：
We quantize the electromagnetic field in the presence of a nonmoving dielectric sphere in vacuum. The sphere is assumed to be lossless, dispersionless, isotropic, and homogeneous. The quantization is performed using normalized eigenmodes as well as plane-wave modes. We specify two useful alternative bases of normalized eigenmodes: spherical eigenmodes and scattering eigenmodes. A canonical transformation between plane-wave modes and normalized eigenmodes is derived. This formalism is employed to study the scattering of a single photon, coherent squeezed light, and two-photon states off a dielectric sphere. In the latter case we calculate the second-order correlation function of the scattered field, thereby unveiling the angular distribution of the Hong-Ou-Mandel interference for a dielectric sphere acting as a three-dimensional beam splitter. Our results are analytically derived for an arbitrary size of the dielectric sphere with a particular emphasis on the small-particle limit. This work sets the theoretical foundation for describing the quantum interaction between light and the motional, rotational and vibrational degrees of freedom of a dielectric sphere.
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