  Engineering quantum phases using light is a novel route to designing
functional materials, where light-induced superconductivity is a successful
example. Although this phenomenon has been realized experimentally, especially
for the high-$T_c$ cuprates, the underlying mechanism remains mysterious. Using
the recently developed variational non-Gaussian exact diagonalization method,
we investigate a particular type of photoenhanced superconductivity by
suppressing a competing charge order in a strongly correlated electron-electron
and electron-phonon system. We find that the $d$-wave superconductivity pairing
correlation can be enhanced by a pulsed laser, consistent with recent
experiments based on gap characterizations. However, we also find that the
pairing correlation length is heavily suppressed by the pump pulse, indicating
that light-enhanced superconductivity may be of fluctuating nature. Our
findings also imply a general behavior of nonequilibrium states with competing
orders, beyond the description of a mean-field framework.
