Optical lever measurements with an imprecision below that at theStandard Quantum Limit*

An optical lever can be used to precisely monitor mechanical motion and is a natural choice for measuring tilt and rotation. It is relatively immune to technical noise sources such as laser intensity and frequency noise and does not require precise path length stability, unlike interferometric techniques. Here we report on optical lever readout of a strained Si3N4 nanobeam possessing ultra-high-Q torsional modes. We show that its sensitivity to angular displacement can be reduced more than an order of magnitude below the zero-point spectral

density of the beam's fundamental torsional mode (3 nrad/√Hz), in good agreement with a quantum noise model. To our knowledge, this constitutes the first non-interferometric displacement measurement with an imprecision below that at the Standard Quantum Limit, signaling the potential for a new class of cavity-free torsional quantum optomechanics.