  Understanding phase transitions in quantum matters constitutes a significant
part of present day condensed matter physics. Quantum phase transitions concern
ground state properties of many-body systems, and hence their signatures are
expected to be pronounced in low-energy states. Here we report signature of a
quantum critical point manifested in strongly out-of-equilibrium states with
finite energy density with respect to the ground state and extensive
(subsystem) entanglement entropy, generated by an external pulse. These
non-equilibrium states are evidently completely disordered (e.g., paramagnetic
in case of a magnetic ordering transition). The pulse is applied by switching a
coupling of the Hamiltonian from an initial value ($\lambda_{I}$) to a final
value ($\lambda_{F}$) for sufficiently long time and back again. The signature
appears as non-analyticities (kinks) in the energy absorbed by the system from
the pulse as a function of $\lambda_{F}$ at critical-points (i.e., at values of
$\lambda_{F}$ corresponding to static critical-points of the system). As one
excites higher and higher eigenstates of the final Hamiltonian $H(\lambda_{F})$
by increasing the pulse height ($|\lambda_{I} - \lambda_{F}|$), the
non-analyticity grows stronger monotonically with it. This implies adding
contributions from higher eigenstates help magnifying the non-analyticity,
indicating strong imprint of the critical-point on them. Our findings are
grounded on exact analytical results derived for Ising and XY chains in
transverse field.
