  We investigate the emergence of bound states in chemically and photo-doped
Mott insulators, mediated by spin and $\eta$-pairing fluctuations within both
2-leg ladder and 2D systems. To effectively describe the photo and chemically
doped state on the same footings, we employ the Schrieffer-Wolff
transformation, resulting in a generalized $t$-$J$ model. Our results
demonstrate that the binding energies and localization length in the chemically
and photo-doped regimes are comparable, with $\eta$-pairing fluctuations not
playing a crucial role. Furthermore, we show that manipulating the binding is
possible through external periodic driving, a technique known as Floquet
engineering, leading to significantly enhanced binding energies. We also
roughly estimate the lifetime of photo-doped states under periodic driving
conditions based on the Fermi golden rule. Lastly, we propose experimental
protocols for realizing Hubbard excitons in cold-atom experiments.
