  We study the dynamics of excitonic insulators coupled to phonons. Without
phonon couplings, the linear response is given by the damped amplitude
oscillations of the order parameter with frequency equal to the minimum band
gap. A phonon coupling to the interband transfer integral induces two types of
long-lived collective oscillations of the amplitude, one originating from the
phonon dynamics and the other from the phase mode, which becomes massive. We
show that even for small phonon coupling, a photo-induced enhancement of the
exciton condensation and the gap can be realized. Using the Anderson
pseudo-spin picture, we argue that the origin of the enhancement is a
cooperative effect of the massive phase mode and the Hartree shift induced by
the photo excitation. We also discuss how the enhancement of the order and the
collective modes can be observed with time-resolved photo-emission
spectroscopy.
