Fluid analog models for classical and quantum field theory in curved spacetimes

DFG项目的这一扩展的目的是深化旋转环境中的经典场和存在静止边界的量子场的“模拟模型”的研究。这类模型的开发通常是为了研究在更简单的系统上的奇异的、实验上无法达到的效应(例如，由于时空的弯曲)，并具有完全的实验访问权限。在这个项目中，我们主要关注旋转超流体作为旋转时空的模型，以及金属微腔中的量子电磁场作为存在强外部/引力场存在的量子场的模型。该项目的实验可行性基于旋转超流体物理学(快速旋转的玻色-爱因斯坦凝聚体)的最新成就和光探测物理学的进展，包括高量子效率光电二极管能力的近场增强。在旋转超流体的情况下，我们已经在项目的第一部分展示了在背景涡流存在的情况下，当涡核直径非常小时，声音表现出令人惊讶的现象。在这种情况下，尽管在声学时空中，声音对应于无质量场(在没有视界的有界区域中囚禁光是违反直觉的)，但仍存在丰富的束缚态族。我们已经证明这种效应与相应的模拟(声学)时空中的遍历区的存在有关。在项目的扩展部分，我们研究了核心尺寸对声散射截面的影响，以及对由于声散射而作用在涡旋上的力的影响。在该项目的第二个分支，处理量子场，我们重点研究在存在静止的边界或量子流体流动的情况下减少量子涨落。我们已经证明，这种环境的基态表现出量子涨落的减少(相对于在没有边界的真空态中这些涨落的水平)。在项目的扩展部分，我们开发了一个能够测量金属微腔(截面仅略超过相关波长的腔；Casimir装置)中量子电磁场的起伏减少的探测器的详细设计。我们的重点是确定适当的设置，明智地利用与金属边界相关联的表面等离子激元的性质，以便聚焦于光检测过程。表面等离子体激元对相关装置中随频率变化的涨落模式的贡献将通过(适当调整的)数值程序(有限元方法)在任意几何形状的非均匀区域中求解偏微分方程组来确定。

The aim of this extension of the DFG project is to deepen the study of ``analog models'' for classical fields in rotating environments and quantum fields in the presence of stationary bounaries. Such models are typically developed in order to investigate exotic, experimentally inaccessible effects (e.g. due to curvature of spacetime) on simpler systems, with full experimental access. In this project we focus on rotating superfluids as models of rotating spacetimes, and on quantum electromagnetic fields in metallic microcavities as models of quantum fields in the presence of strong external/gravitational fields. Experimental feasibility of the project is based on recent achievements in physics of rotating superfluids (rapidly rotating Bose-Einstein condensates) and on progress in physics of photodetection including near-field enhancements of capabilities of high quantum-efficiency photodiodes. In the case of rotating superfluids we have shown in the first part of the project that sound in the presence of a background vortex flow exhibits surprising phenomena when the diameter of the vortex core is very small. In this case rich families of bound states are present even though in the acoustic spacetime sound corresponds to massless fields (and it is counterintuitive to trap light in a bounded region without a horizon). We have shown this effect to be related to the presence of an ergoregion in the corresponding analog (acoustic) spacetime. In the extended part of the project we investigate the influence of the core size on the sound-scattering cross section, and on the force acting on the vortex due to sound-scattering. In the second branch of the project, dealing with quantum fields, we focus on the study of the reduction of quantum fluctuations in the presence of stationary boundaries or flows of quantum fluids. We have shown, that ground states for such environments exhibit a reduction of quantum fluctuations (with respect to the level of these fluctuations in the vacuum state in the absence of boundaries). In the extended part of the project we develop a detailed design of a detector capable of measuring the fluctuation-reduction for quantum electomagnetic fields in metallic micro-cavities (cavities of cross-section only slightly exceeding the relevant wavelengths; Casimir setups). We focus on determination of the appropriate setup employing judiciously the properties of surface plasmons associated with the boundary of the metal in order to focus the photodetection process. The surface-plasmon contribution to the frequency-position-dependent pattern of fluctuations in relevant setups will be determined with the help of (properly adapted) numerical codes (Finite-Element-Methods) for solving partial-differential-equations in inhomogeneous domains of arbitrary geometry.