  We consider a dynamical phase transition induced by a short optical pulse in
a system prone to thermodynamical instability. We address the case of pumping
to excitons whose density contributes directly to the order parameter. To
describe both thermodynamic and dynamic effects on equal footing, we adopt a
view of the excitonic insulator for the phase transition and suggest a
formation of the Bose condensate for the pumped excitons. The work is motivated
by experiments in donor-acceptor organic compounds with a neutral-ionic phase
transition coupled to the spontaneous lattice dimerization and to charge
transfer excitons. The double nature of the ensemble of excitons leads to an
intricate time evolution, in particular to macroscopic quantum oscillations
from the interference between the Bose condensate of excitons and the ground
state of the excitonic insulator. The coupling of excitons and the order
parameter also leads to self-trapping of their wave function, akin to
self-focusing in optics. The locally enhanced density of excitons can surpass a
critical value to trigger the phase transformation, even if the mean density is
below the required threshold. The system is stratified in domains that evolve
through dynamical phase transitions and sequences of merging.
