  The superb precision of an atomic clock is derived from its stability. Atomic
clocks based on optical (rather than microwave) frequencies are attractive
because of their potential for high stability, which scales with operational
frequency. Nevertheless, optical clocks have not yet realized this vast
potential, due in large part to limitations of the laser used to excite the
atomic resonance. To address this problem, we demonstrate a cavity-stabilized
laser system with a reduced thermal noise floor, exhibiting a fractional
frequency instability of $2 \times 10^{-16}$. We use this laser as a stable
optical source in a Yb optical lattice clock to resolve an ultranarrow 1 Hz
transition linewidth. With the stable laser source and the signal to noise
ratio (S/N) afforded by the Yb optical clock, we dramatically reduce key
stability limitations of the clock, and make measurements consistent with a
clock instability of $5 \times 10^{-16} / \sqrt{\tau}$.
