  The complex coupling between charge carriers and phonons is responsible for
diverse phenomena in condensed matter. We apply ultrafast electron diffuse
scattering to unravel electron-phonon coupling phenomena in 1T-TiSe$_2$ in both
momentum and time. We are able to distinguish effects due to the real part of
the many-body bare electronic susceptibility,
$\Re\left[\chi_0(\mathbf{q})\right]$, from those due to the electron-phonon
coupling vertex, $g_{\mathbf{q}}$, by following the response of semi-metallic
(normal phase) 1T-TiSe$_2$ to the selective photo-doping of carriers into the
electron pocket at the Fermi level. Quasi-impulsive and wavevector-specific
renormalization of soft zone-boundary phonon frequencies (stiffening) is
observed, followed by wavevector-independent electron-phonon equilibration.
These results unravel the underlying mechanisms driving the phonon softening
that is associated with the charge density wave transition at lower
temperatures.

Strongly Correlated Electrons;Materials Science