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arXiv quant-ph/0307031quant-ph
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原子与光子环境的多极相互作用

Multipole interaction between atoms and their photonic environment

Martijn Wubs, L. G. Suttorp, A. Lagendijk

备注：
17 pages, to be published in Physical Review A
发表信息：
Phys. Rev. A 68, 013822 (2003)
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摘要：

宏观场量子化的非色散光子介质环境中，无论是在存在和不存在的客体原子。从最小耦合拉格朗日量开始，仔细研究函数导数，展示了如何在选择合适的规范之前和之后获得麦克斯韦方程组。推导出了考虑客体原子与电磁场多极相互作用时的哈密顿量。正则变量和字段的确定，特别是正则共轭的矢量势的字段被确定为减去全位移场的功能微分。一个重要的结果是，在电介质内部，偶极耦合到既不是（横向）电场也不是宏观位移场的场。介电函数不同于偶极子位置处的体介电函数，因此必须考虑局部场效应。

英文摘要：

Macroscopic field quantization is presented for a nondispersive photonic dielectric environment, both in the absence and presence of guest atoms. Starting with a minimal-coupling Lagrangian, a careful look at functional derivatives shows how to obtain Maxwell's equations before and after choosing a suitable gauge. A Hamiltonian is derived with a multipolar interaction between the guest atoms and the electromagnetic field. Canonical variables and fields are determined and in particular the field canonically conjugate to the vector potential is identified by functional differentiation as minus the full displacement field. An important result is that inside the dielectric a dipole couples to a field that is neither the (transverse) electric nor the macroscopic displacement field. The dielectric function is different from the bulk dielectric function at the position of the dipole, so that local-field effects must be taken into account.

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