  Motivated by recent interests in exploring excitonic condensate as the ground
state of some narrow-bandgap semiconductors such as transition metal
dichalcogenides and layered chalcogenide material Ta$_2$NiSe$_5$, in this work
we theoretically study the dynamics of condensate in response to periodically
driven laser fields with different polarizations and intensities. In
particular, we consider laser light beams with bicircular and circular
polarizations breaking the time-revesal symmetry, and linear polarization. We
show that the amplitude of the condensate oscillates in time during irradiating
by light with a magnitude depending on the light intensity. The dynamics
survives even after the light is switched off. The phase mode however changes
linearly with time for a condensate originating from purely electronic
correlations. We further show that in the presence of electron-phonon coupling
the linear-in-time behavior is replaced by a harmonically oscillating behavior,
a manifestation of gapped phase modes due to relative band charge symmetry
breaking. Furthermore, we show that the primarily electronic and primarily
lattice cases corresponding to strong and weak electron-phonon coupling,
respectively, reveal distinct dynamics of the condensate, an observation which
can modify the optical response of an excitonic insulator by stimulating
amplitude and phase modes in the former case.
