  In the presence of electron-phonon coupling, an excitonic insulator harbors
two degenerate ground states described by an Ising-type order parameter.
Starting from a microscopic Hamiltonian, we derive the equations of motion for
the Ising order parameter in the phonon coupled excitonic insulator
Ta$_2$NiSe$_5$ and show that it can be controllably reversed on ultrashort
timescales using appropriate laser pulse sequences. Using a combination of
theory and time-resolved optical reflectivity measurements, we report evidence
of such order parameter reversal in Ta$_2$NiSe$_5$ based on the anomalous
behavior of its coherently excited order-parameter-coupled phonons. Our work
expands the field of ultrafast order parameter control beyond spin and charge
ordered materials.
