  In quantum metrology, one typically creates correlations among atoms or
photons to enhance measurement precision. Here, we show how one can use other
excitations to perform quantum-enhanced measurements on the example of
center-of-mass excitations of a spin-orbit coupled Bose-Einstein condensate and
a Coulomb crystal. We also present a method to simulate a homodyne detection of
center-of-mass excitations in these systems, which is required for optimal
estimation.
