Standard quantum limit of angular motion of a suspended mirror and homodyne detection of ponderomotively squeezed vacuum field

摘要

Compared to the quantum noise in the measurement of the translational motionof a suspended mirror using laser light, the quantum noise in the measurementof the angular motion of a suspended mirror has not been investigatedintensively despite its potential importance. In this article, an expressionfor the quantum noise in the angular motion measurement is explicitly derived.The expression indicates that one quadrature of the vacuum field of thefirst-order Hermite-Gaussian mode of light causes quantum sensing noise and theother causes quantum backaction noise, or in other words the first-order vacuumfield is ponderomotively squeezed. It is also shown that the Gouy phase shiftthe light acquires between the mirror and the position of detection of thelight corresponds to the homodyne angle. Therefore, the quantum backactionnoise can be cancelled and the standard quantum limit can be surpassed bychoosing the appropriate position of detection analogously to the cancellationof quantum radiation pressure noise by choosing an appropriate homodyne angle.