Noise and instability of an optical lattice clock

We present an analysis of the different types of noise from the detection and interrogation laser in our strontium lattice clock. We develop a noise model showing that in our setup quantum projection noise--limited detection is possible if more than 130~atoms are interrogated. Adding information about the noise spectrum of our clock laser with sub-$10^{-16}$ fractional frequency instability allows to infer the clock stability for different modes of operation. Excellent agreement with experimental observations for the instability of the difference between two interleaved stabilizations is found. We infer a clock instability of $1.6 \times 10^{-16}/\sqrt{\tau / \mathrm{s}}$ as a function of averaging time $\tau$ for normal clock operation.