Interactions between atoms and lasers provide the potential for unprecedentedcontrol of quantum states. Fulfilling this potential requires detailedknowledge of frequency noise in optical oscillators with state-of-the-artstability. We demonstrate a technique that precisely measures the noisespectrum of an ultrastable laser using optical lattice-trapped $^{87}$Sr atomsas a quantum projection noise-limited reference. We determine the laser noisespectrum from near DC to 100 Hz via the measured fluctuations in atomicexcitation, guided by a simple and robust theory model. The noise spectrumyields a 26(4) mHz linewidth at a central frequency of 429 THz, correspondingto an optical quality factor of $1.6\times10^{16}$. This approach improves uponoptical heterodyne beats between two similar laser systems by providinginformation unique to a single laser, and complements the traditionally usedAllan deviation which evaluates laser performance at relatively long timescales. We use this technique to verify the reduction of resonant noise in ourultrastable laser via feedback from an optical heterodyne beat. Finally, weshow that knowledge of our laser's spectrum allows us to accurately predict thelaser-limited stability for optical atomic clocks.
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