Producing, storing and exploiting correlated many-body quantum states are key goals of future quantum technologies and metrology. Such states can be generated over time from the initial coherent states by the so-called dynamic
protocols. In our work, we consider the generation of highly correlated states in a system composed of ultracold fermionic atoms placed in the periodic potential of optical lattices in the Mott phase.

We show how the coupling of atoms with an external laser beam introduces correlations between single atoms, leading to the formation of highly correlated quantum states, the so-called spin-contracted states. We explain the mechanism of correlation formation over time. We also show that our setup can simulate two different protocols for generating squeezed states and how our predictions can be verified in current cold atom experiments.