  We determine the exact time-resolved photoemission spectroscopy for a nesting
driven charge-density-wave (described by the spinless Falicov-Kimball model
within dynamical mean-field theory). The pump-probe experiment involves two
light pulses: the first is an ultrashort intense pump pulse that excites the
system into nonequilibrium, and the second is a lower amplitude higher
frequency probe pulse that photoexcites electrons. We examine three different
cases: the strongly correlated metal, the quantum-critical charge density wave
and the critical Mott insulator. Our results show that the quantum critical
charge density wave has an ultra efficient relaxation channel that allows
electrons to be de-excited during the pump pulse, resulting in little net
excitation. In contrast, the metal and the Mott insulator show excitations that
are closer to what one expects from these systems. In addition, the pump field
produces spectral band narrowing, peak sharpening, and a spectral gap
reduction, all of which rapidly return to their field free values after the
pump is over.
