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

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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.