DFG-NSF: Demonstration of position and speed measurements in the quantum non-demolition regime towards a new gravitational-wave detector topology

重力改变了质量的位置和速度。最精确的引力测量设备是激光干涉仪，它能感知作为测试质量的反射镜的运动，特别是那些为探测引力波而建造的反射镜。量子计量学的理论研究预测了通过实现位置和速度的量子不破坏(QND)方案来改进力测量的可能性。这样的方案超过了所谓的标准量子极限(SQL)，标准量子极限是海森伯格测不准关系的直接结果，也是引力波探测器的一个基本但不是最终的极限。到目前为止，还没有超过SQL的位置和速度测量噪声谱密度的证明。该项目的目标是理论分析和构建一种新型的腔增强型光机械干涉仪；将速度的干涉测量表征为QND变量；以及利用新装置的独特特性来演示超出SQL的噪声谱密度。新的装置将是桌面式的，并将首次在环形腔内包含膜。与之前研究的中间带有薄膜的耦合腔相比，新的设置避免了光机械不稳定性，并将允许更高的腔内光功率。此外，新的设置有两个输出端口，这两个端口的组合使膜位置和膜速度能够同时监控。这一独特的功能将用于直接比较受量子反作用影响的位置测量和QND速度测量。高的腔内光功率，加上新系统的反向作用回避特性，以及压缩光态的注入，将使在5K以上的温度下达到甚至超过SQL。本项目计划的QND技术的第一次演示和验证将伴随着关于检测频率和测试质量大小的可扩展性的详细分析。这将是一种新的干涉仪拓扑结构的发展，具有前所未有的灵敏度，用于探测引力波。

Gravitational forces change the position and speed of a mass. The most precise measurement devices for gravitational forces are laser interferometers sensing the motion of mirrors acting as test masses, in particular those built for the detection of gravitational waves. Theoretical research in quantum metrology has predicted the possibility to improve force measurements by realising a quantum non-demolition (QND) scheme for position and speed. Such a scheme surpasses the so-called standard quantum limit (SQL), which is a direct consequence of Heisenberg's uncertainty relation and a fundamental, yet not ultimate, limit in gravitational-wave detectors. Up to now, neither a position nor a speed measurement noise spectral density beyond the SQL has been demonstrated. The aims of this project are the theoretical analysis and the construction of a new type of a cavity-enhanced optomechanical interferometer; the characterization of the interferometric measurement of speed as a QND variable; and the employment of the new setup's unique properties for demonstrating a noise spectral density beyond the SQL. The new setup will be table-top and will comprise for the first time a membrane inside a ring cavity. In contrast to previously investigated coupled cavities with a membrane in the middle, the new setup avoids optomechanical instabilities and will allow for much higher intra-cavity light powers. Furthermore, the new setup has two output ports, whose combination enables the simultaneous monitoring of membrane position and membrane speed. This unique feature will be used for a direct comparison between position measurements that are affected by quantum back-action and QND speed measurements. The high intra-cavity light powers, together with the back-action evading property of the new system and the injection of squeezed states of light will enable reaching and even surpassing the SQL at temperatures above 5K. The first demonstration and verification of QND techniques as planned in this project will be accompanied by a detailed analysis of scalability with regard to detection frequency and test mass size. This would be development towards a new interferometer topology with unprecedented sensitivity for the detection of gravitational waves.