  Competition and cooperation among orders is at the heart of many-body physics
in strongly correlated materials and leads to their rich physical properties.
It is crucial to investigate what impact many-body physics has on extreme
nonlinear optical phenomena, with the possibility of controlling material
properties by light. However, the effect of competing orders and
electron-electron correlations on highly nonlinear optical phenomena has not
yet been experimentally clarified. Here, we investigated high-order harmonic
generation from the Mott-insulating phase of Ca2RuO4. Changing the gap energy
in Ca2RuO4 as a function of temperature, we observed a strong enhancement of
high order harmonic generation at 50 K, increasing up to several hundred times
compared to room temperature. We discovered that this enhancement can be
well-reproduced by an empirical scaling law that depends only on the material
gap energy and photon emission energy. Such scaling law cannot be explained by
a simple two-band model under the single electron approximation. Our results
suggest that the highly nonlinear optical response of strongly correlated
materials is deeply coupled to their electron-electron correlations and
resultant many-body electronic structure.
