Laser spectral analysis using $^{87}$Sr atoms with a quantum projection limited noise floor

Ultra-stable lasers are essential tools in a variety of precision measurement experiments and their stability often dictates the performance of the experiments they serve. For example, a Sr clock recently demonstrated record clock stability by using a laser with $10^{-16}$ fractional stability[1]. Despite the importance of laser performance, evaluating noise spectra of state-of-the-art lasers remains challenging. Often, multiple lasers of similar performance are built for the sole purpose of evaluating laser noise [2]. We demonstrate a technique to measure the noise spectrum of a single ultra-stable laser using optical lattice-trapped $^{87}$Sr atoms as a quantum projection noise-limited reference. Using a simple theoretical framework, we deduce the laser spectrum from measured fluctuations in atomic excitation. Measurements using a variety of probe sequences are consistent with resonant features observed in an optical beat with a less stable laser. Furthermore, we use features from this beat to actively reduce resonant noise in our ultra-stable laser. Finally, we show how knowledge of our laser's spectrum informs the optimal conditions for clock operation.\\[4pt] [1] T. L. Nicholson et al., PRL 109, 23081 (2012).\\[0pt] [2] T. Kessler et al., Nature Photon. 6, 687-692 (2012).