We present an interferometric technique for measuring ultrasmall 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/Hz and a measured noise floor of 200 frad/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/Hz is observed between 2 and 100 mHz.
We create an optical frequency, polarization-independent, narrow bandpass filter of 1.3 GHz (3 dB bandwidth), using the steep dispersion near the rubidium D atomic transitions within a prism-shaped vapor cell. This enables us to clean the amplified spontaneous emission from a laser by more than 3 orders of magnitude. Such a filter could find uses in fields such as quantum information processing and Raman spectroscopy.
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