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Laser decoherence limits the stability of optical clocks by broadening theobservable resonance linewidths and adding noise during the dead time betweenclock probes. Correlation spectroscopy avoids these limitations by measuringcorrelated atomic transitions between two ensembles, which provides a frequencydifference measurement independent of laser noise. Here, we apply thistechnique to perform stability measurements between two independent clocksbased on the $^1S_0\leftrightarrow{}^3P_0$ transition in $^{27}$Al$^+$. Bystabilizing the dominant sources of differential phase noise between the twoclocks, we observe coherence between them during synchronous Ramseyinterrogations as long as 8 s at a frequency of $1.12\times10^{15}$ Hz. Theobserved contrast in the correlation spectroscopy signal is consistent with the20.6 s $^3P_0$ state lifetime and supports a measurement instability of$(1.8\pm0.5)\times 10^{-16}/\sqrt{\tau/\textrm{s}}$ for averaging periodslonger than the probe duration when deadtime is negligible.

Lifetime-Limited Interrogation of Two Independent ${}^{27}\textrm{Al}^{+}$ Clocks Using Correlation Spectroscopy