The modified Langevin noise formalism has been proposed for the correct charaterization of quantum electromagnetic fields in the presence of finite-sized lossy dielectric objects in free space. The main modification to the original one (also known as the Green's function approach available only for bulk inhomogeneous lossy dielectric medium) was to add fluctuating sources in reaction to the radiation loss. Consequently, a resulting electric field operator is now determined by (i) boundary-assisted and (ii) medium-assisted fields on an equal footing, which are fluctuating sources due to radiation and medium losses, respectively. However, due to the lengthy mathematical manipulation and complicated concepts, the validity of the modified Langevin noise formalism has not been clearly checked yet.
In this work, we propose and develop a novel numerical framework for the modified Langevin noise formalism by exploiting computational electromagnetic methods (CEM). Specifically, we utilize the finite-element method to numerically solve plane-wave-scattering and point-source-radiation problems whose solutions are boundary-assisted and medium-assisted fields, respectively. Based on the developed numerical framework, we calculate the Purcell factor of a two-level atom inside or outside a lossy dielectric slab. It is numerically proved, for the first time, that one can retrieve the conventional expression of the spontaneous emission rate, viz., the imaginary part of the Green's function.
The proposed numerical framework is particularly useful for estimating the dynamics of multi-level atoms near practical plasmonic structures or metasurfaces.
Equivalence between the Hamiltonian and Langevin noise description of plasmon-polaritons in a dispersive and lossy inhomogeneous medium
我们证明了存在于非均匀、有耗和色散介质中的量子电动力学的两种不同描述之间的基本联系，这两种描述基于极化激元的Huttner-Barnett形式[B]。Huttner和S. M. Barnett，Phys.Rev. A 46，4306（1992）]或使用波动电流的朗之万噪声方法[T. Gruner和D.- G. Welsch，Phys.Rev.A53，1818（1996）]。在这项工作中，我们证明了这两种描述的实际等价性，通过引入有效光子态的概念与一些特定的噪声电流分布。我们研究这些结果的计算和解释的量子观测，如波动，相关性和卡西米尔力的影响。
Simulating lossy and partially distinguishable quantum optical circuits: theory, algorithms and applications to experiment validation and state preparation
Electrical Noise Produced by Micron-Sized Particles above a Surface Paul Trap
University of California, Berkeley（加州大学伯克利分校）；Challenge Institute for Quantum Computation, University of California, Berkeley（加州大学伯克利分校量子计算挑战研究所）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
