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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>η</a:mi></a:math>-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 <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>t</b:mi><b:mtext>−</b:mtext><b:mi>J</b:mi></b:mrow></b:math> model. Our results demonstrate that the binding energies and localization length in the chemically and photo-doped regimes are comparable, with <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>η</c:mi></c:math>-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.