  We study the nonequilibrium dynamics of photoinduced phase transitions in
charge ordered (CO) systems with a strong electron-lattice interaction and
analyze the interplay between electrons, periodic lattice distortions, and a
phonon thermal reservoir. Simulations based on a tight-binding Hamiltonian and
Boltzmann equations reveal partially decoupled oscillations of the electronic
order parameter and the periodic lattice distortion during CO melting, which
becomes more energy efficient with lower photon energy. The cooling rate of the
electron system correlates with the CO gap dynamics, responsible for an order
of magnitude decrease in the cooling rate upon the gap reopening. We also find
that the time-dependent frequency of coherent oscillation reflects the dynamics
of the energy landscape, such as transition between single-well and
double-well, which sensitively depends on the photon energy and the pump
fluence. The results demonstrate the intricate nonequilibrium dynamics in CO
materials.
