层状结构中的热平衡和光子数量子化
Thermal balance and photon-number quantization in layered structures
摘要：
有耗色散介质中电磁场的量子化在过去几十年中得到了广泛的研究。然而，能量转移的几个方面及其与在非平衡条件下一致地定义电磁场的位置相关的梯形算子的关系部分地逃脱了注意。在这项工作中，我们定义的位置相关的阶梯运营商和一个有效的本地光子数运营商，是符合规范的交换关系，并使用这些概念来描述分层几何的能量传递和热平衡。这种方法的结果在一个位置依赖的光子数的概念，是简单的，并与经典的能量守恒参数一致。该算子是通过首先使用格林函数形式主义和朗之万噪声源算子计算与介质及其温度相关的矢量势算子，然后定义相应的位置相关的湮灭算子来形成的，该湮灭算子是满足任意几何中的正则对易关系所需的。我们的研究结果表明，与电场的有效光子数通常是位置相关的，并使一个简单的方法来计算场和本地介质之间的能量转移率。特别是，我们的研究结果预测，在两个损耗材料层之间形成的真空腔中的有效光子数可以振荡的位置的函数，这表明也局部场温度振荡。预计这些振荡可以使用相对简单的实验装置直接观察到，其中场与物质的相互作用由与电场的耦合主导。
英文摘要：
The quantization of the electromagnetic field in lossy and dispersive dielectric media has been widely studied during the last few decades. However, several aspects of energy transfer and its relation to consistently defining position-dependent ladder operators for the electromagnetic field in nonequilibrium conditions have partly escaped the attention. In this work we define the position-dependent ladder operators and an effective local photon-number operator that are consistent with the canonical commutation relations and use these concepts to describe the energy transfer and thermal balance in layered geometries. This approach results in a position-dependent photon-number concept that is simple and consistent with classical energy conservation arguments. The operators are formed by first calculating the vector potential operator using Green's function formalism and Langevin noise source operators related to the medium and its temperature, and then defining the corresponding position-dependent annihilation operator that is required to satisfy the canonical commutation relations in arbitrary geometry. Our results suggest that the effective photon number associated with the electric field is generally position dependent and enables a straightforward method to calculate the energy transfer rate between the field and the local medium. In particular, our results predict that the effective photon number in a vacuum cavity formed between two lossy material layers can oscillate as a function of the position suggesting that also the local field temperature oscillates. These oscillations are expected to be directly observable using relatively straightforward experimental setups in which the field-matter interaction is dominated by the coupling to the electric field.
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