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Abstract: Quantum fluctuations in the radiation pressure of light can excite stochasticmotions of mechanical oscillators thereby realizing a linear quantumopto-mechanical coupling. When performing a precise measurement of the positionof an oscillator, this coupling results in quantum radiation pressure noise. Upto now this effect has not been observed yet. Generally speaking, the strengthof radiation pressure noise increases when the effective mass of the oscillatoris decreased or when the power of the reflected light is increased. Recently,extremely light SiN membranes with high mechanical Q-values at room temperaturehave attracted attention as low thermal noise mechanical oscillators. However,the power reflectance of these membranes is much lower than unity which makesthe use of advanced interferometer recycling techniques to amplify theradiation pressure noise in a standard Michelson interferometer inefficient.Here, we propose and theoretically analyze a Michelson-Sagnac interferometerthat includes the membrane as a common end mirror for the Michelsoninterferometer part. In this new topology, both, power- and signal-recyclingcan be used even if the reflectance of the membrane is much lower than unity.In particular, signal-recycling is a useful tool because it does not involve apower increase at the membrane. We derive the formulas for the quantumradiation pressure noise and the shot-noise of an oscillator positionmeasurement and compare them with theoretical models of the thermal noise of aSiN membrane with a fundamental resonant frequency of 75 kHz and an effectivemass of 125 ng. We find that quantum radiation pressure noise should beobservable with a power of 1 W at the central beam splitter of theinterferometer and a membrane temperature of 1 K.

Author: Kazuhiro Yamamoto, Daniel Friedrich, Tobias Westphal, Stefan Gossler, Karsten Danzmann, Roman Schnabel, Kentaro Somiya, Stefan L.

Source: https://arxiv.org/

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