  We present a mixed-dimensional atomic gas system to unambiguously detect and
systematically probe mediated interactions. In our scheme, fermionic atoms are
confined in two parallel planes and interact via exchange of elementary
excitations in a three-dimensional background gas. This interaction gives rise
to a frequency shift of the out-of-phase dipole oscillations of the two clouds,
which we calculate using a strong coupling theory taking the two-body
mixed-dimensional scattering into account exactly. The shift is shown to be
easily measurable for strong interactions and can be used as a probe for
mediated interactions.
