High-Frequency Gravitational-Wave Detection Using a Chiral Resonant Mechanical Element and a Short Unstable Optical Cavity

Present gravitational wave detectors are based on the measurement of linear displacement in stable optical cavities. Here, we instead suggest the measurement of the twist of a chiral mechanical element induced by a gravitational wave. The induced twist rotates a flat optical mirror on top of this chiral element, leading to the deflection of an incident laser beam. This angle change is enhanced by multiple bounces of light between the rotating mirror and an originally parallel nearby fixed flat mirror. Based on detailed continuum-mechanics calculations, we present a feasible design for the chiral mechanical element including the rotating mirror. Our approach is most useful for signals in the frequency band 1 -- 100 kHz where we show that fundamental metrological limits would allow for smaller shot noise in this setup in comparison to the detection of linear displacement. We estimate a gravitational wave strain sensitivity between $10^{-21}/\sqrt{Hz}$ and $10^{-23}/\sqrt{Hz}$ at around 10 kHz frequency. When appropriately scaling the involved geometrical parameters, the strain sensitivity is proportional to frequency.