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In quantum logic spectroscopy (QLS), one species of trapped ion is used as a sensor to detect the state of an otherwise inaccessible ion species. This extends precision measurements to a broader class of atomic and molecular systems for applications like atomic clocks and tests of fundamental physics. Here, we develop a new technique based on a Schr\"{o}dinger cat interferometer to address the problem of scaling QLS to larger ion numbers. We demonstrate the basic features of this method using various combinations of $^{25}\text{Mg}^+$ logic ions and $^{27}\text{Al}^+$ spectroscopy ions. We observe higher detection efficiency by increasing the number of $^{25}\text{Mg}^+$ ions. Applied to multiple $^{27}\text{Al}^+$, this method will improve the stability of high-accuracy optical clocks and could enable Heisenberg-limited QLS., Comment: 6 pages, 4 figures + supplemental material 8 pages, 4 figures

Laser decoherence limits the stability of optical clocks by broadening the observable resonance linewidths and adding noise during the dead time between clock probes. Correlation spectroscopy avoids these limitations by measuring correlated atomic transitions between two ensembles, which provides a frequency difference measurement independent of laser noise. Here, we apply this technique to perform stability measurements between two independent clocks based on the ^{1}S_{0}↔^{3}P_{0} transition in ^{27}Al^{+}. By stabilizing the dominant sources of differential phase noise between the two clocks, we observe coherence between them during synchronous Ramsey interrogations as long as 8 s at a frequency of 1.12×10^{15} Hz. The observed contrast in the correlation spectroscopy signal is consistent with the 20.6 s ^{3}P_{0} state lifetime and represents a measurement instability of (1.8±0.5)×10^{-16}/sqrt[τ/s] for averaging periods longer than the probe duration when dead time is negligible.