Floquet engineering of binding in doped and photo-doped Mott insulators

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.