DFG/NSF: Demonstration of Position and Speed Measurements in the Quantum Non-Demolition Regime Towards a New Gravitational-Wave Detector Topology

该奖项支持汉堡大学的Roman Schnabel和加州理工学院（Caltech）的Yanbei Chen的合作，由物理部的引力物理项目和国际科学与工程办公室的全球风险基金资助。重力改变物体的位置和速度。最精确的重力测量设备是激光干涉仪，它可以感应充当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拆除（QND）方案来改进力测量的可能性。这种方案超越了所谓的标准量子极限（SQL），这是海森堡不确定性关系的直接结果，也是引力波探测器的基本极限，但不是最终极限。到目前为止，位置和速度测量噪声谱密度都没有超出SQL的证明。这个项目研究并演示了在这个极限上提高未来引力波探测器灵敏度的策略。Schnabel领导的汉堡大学负责实验部分，Chen领导的加州理工学院负责理论部分。该项目将成为年轻科学家的培训基地，特别是教授博士生如何在实验和理论研究小组之间的密切合作中进行研究。在这里进行的研究将有利于更广泛的量子光力学社区，为制备、操纵和观察机械物体的量子态增加新的工具。本项目开发的技术也将适用于其他精密测量系统。本课题的目的是对一种新型腔增强光机械干涉仪进行理论分析和构造；作为QND变量的干涉测量速度的表征；以及利用新设置的独特属性来演示SQL之外的噪声谱密度。新的装置将是桌面式的，并将首次包括环形腔内的膜。与之前研究的中间有膜的耦合腔相比，新的设置避免了光力学不稳定性，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，其组合可以同时监测膜位置和膜速度。这一独特的特性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。高腔内光功率，加上新系统的反作用力规避特性和压缩态光的注入，将使在5K以上的温度下达到甚至超过SQL。在本项目中计划的QND技术的首次演示和验证将伴随着对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，它具有探测引力波的前所未有的灵敏度。

This award supports a collaboration between Roman Schnabel at University of Hamburg and Yanbei Chen at the California Institute of Technology (Caltech) and is funded by the Gravitational Physics program from Physics Division and the Global Venture Fund from the Office of International Science and Engineering. 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 realizing 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. This project studies and demonstrate strategies toward improving the sensitivity of future gravitational-wave detectors upon this limit. It has an experimental component at the University of Hamburg, led by Schnabel, and a theoretical component at Caltech, led by Chen. This project will serve as a training ground for young scientists, in particular teaching Ph.D. students how to conduct research within a close collaboration between experimental and theoretical research groups. Research carried out here will benefit the broader community of quantum optomechanics, adding new tools for preparing, manipulating and observing the quantum states of mechanical objects. Techniques developed in this project will also be applicable to other precision measurement systems.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.