  Diffusion wake is an unambiguous part of the jet-induced medium response in
high-energy heavy-ion collisions that leads to a depletion of soft hadrons in
the opposite direction of the jet propagation. New experimental data on
$Z$-hadron correlation in Pb+Pb collisions at the Large Hadron Collider show,
however, an enhancement of soft hadrons in the direction of both the $Z$ and
the jet. Using a coupled linear Boltzmann transport and hydro model, we
demonstrate that medium modification of partons from the initial multiple
parton interaction (MPI) gives rise to a soft hadron enhancement that is
uniform in azimuthal angle while jet-induced medium response and soft gluon
radiation dominate the enhancement in the jet direction. After subtraction of
the contributions from MPI with a mixed-event procedure, the diffusion wake
becomes visible in the near-side $Z$-hadron correlation. We further employ the
longitudinal and transverse gradient jet tomography for the first time to
localize the initial jet production positions in $Z/\gamma$-jet events in which
the effect of the diffusion wake is apparent in $Z/\gamma$-hadron correlation
even without the subtraction of MPI.
