  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.
