  High temperature cuprate superconductors consist of stacked CuO2 planes, with
primarily two dimensional electronic band structures and magnetic excitations,
while superconducting coherence is three dimensional. This dichotomy highlights
the importance of out-of-plane charge dynamics, believed to be incoherent in
the normal state, yet lacking a comprehensive characterization in
energy-momentum space. Here, we use resonant inelastic x-ray scattering (RIXS)
with polarization analysis to uncover the pure charge character of a recently
discovered collective mode in electron-doped cuprates. This mode disperses
along both the in- and, importantly, out-of-plane directions, revealing its
three dimensional nature. The periodicity of the out-of-plane dispersion
corresponds to the CuO2 plane distance rather than the crystallographic c-axis
lattice constant, suggesting that the interplane Coulomb interaction drives the
coherent out-of-plane charge dynamics. The observed properties are hallmarks of
the long-sought acoustic plasmon, predicted for layered systems and argued to
play a substantial role in mediating high temperature superconductivity.
