  The nonlinear optical response of an excitonic insulator coupled to lattice
degrees of freedom is shown to depend in strong and characteristic ways on
whether the insulating behavior originates primarily from electron-electron or
electron-lattice interactions. Linear response optical signatures of the
massive phase mode and the amplitude (Higgs) mode are identified. Upon
nonlinear excitation resonant to the phase mode, a new in-gap mode at twice the
phase mode frequency is induced, leading to a huge second harmonic response.
Excitation of in-gap phonon modes leads to different and much smaller effects.
A Landau-Ginzburg theory analysis explain these different behavior and reveals
that a parametric resonance of the strongly excited phase mode is the origin of
the photo-induced mode in the electron-dominant case. The difference in the
nonlinear optical response serve as a measure of the dominant mechanism of the
ordered phase.
