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固定边界的量子场的“模拟模型”的研究。这种模型通常是为了研究奇异的，实验上无法达到的效果（例如由于时空的曲率）在简单的系统上，具有完全的实验访问。在这个项目中，我们专注于旋转超流体作为旋转时空的模型，并在金属微腔中的量子电磁场作为强外部/引力场存在下的量子场模型。该项目的实验可行性基于旋转超流体（快速旋转的玻色-爱因斯坦凝聚体）物理学的最新成就和光电探测物理学的进展，包括近场增强高量子效率光电二极管的能力。在旋转超流体的情况下，我们在项目的第一部分中已经表明，当涡核的直径非常小时，存在背景涡流的声音表现出令人惊讶的现象。在这种情况下，存在丰富的束缚态族，尽管在声学时空中声音对应于无质量场（并且将光捕获在没有视界的有界区域中是违反直觉的）。我们已经证明了这种效应与对应的模拟（声学）时空中的能区的存在有关。在该项目的扩展部分，我们调查的核心大小的影响声散射截面，并对由于声散射的旋涡上的作用力。在该项目的第二个分支中，处理量子场，我们专注于研究在存在静态边界或量子流体流动的情况下量子涨落的减少。我们已经证明，这种环境的基态表现出量子涨落的减少（相对于没有边界的真空态中的这些涨落的水平）。在该项目的扩展部分，我们开发了一种探测器的详细设计，该探测器能够测量金属微腔中量子电磁场的波动减少（横截面仅略微超过相关波长的腔; Casimir设置）。我们专注于确定适当的设置，明智地采用与金属的边界相关联的表面等离子体激元的属性，以集中的光电探测过程。表面等离子体激元的贡献的频率位置相关的模式的波动在相关的设置将被确定的帮助下（适当适应）的数值代码（微元法）求解偏微分方程在非均匀域的任意几何形状。

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.