Ultrasensitive Inverse Weak-Value Tilt Meter

We present an interferometric technique for measuring ultra-small tilts. The information of a tilt in one of the mirrors of a modified Sagnac interferometer is carried by the phase difference between the counter propagating laser beams. Using a small misalignment of the interferometer, orthogonal to the plane of the tilt, a bimodal (or two-fringe) pattern is induced in the beam's transverse power distribution. By tracking the mean of such a distribution, using a split detector, a sensitive measurement of the phase is performed. With 1.2 mW of continuous-wave laser power, the technique has a shot noise limited sensitivity of 56 frad/$\sqrt{\mbox{Hz}}$, and a measured noise floor of 200 frad/$\sqrt{\mbox{Hz}}$ for tilt frequencies above 2 Hz. A tilt of 200 frad corresponds to a differential displacement of 4.0 fm in our setup. The novelty of the protocol relies on signal amplification due to the misalignment, and on good performance at low frequencies. A noise floor of about 70 prad/$\sqrt{\mbox{Hz}}$ is observed between 2 and 100 mHz.