  We study a production of spin-squeezed states with ultra-cold atomic fermions
described by the Fermi-Hubbard model in the Mott insulating phase. We show
activation of two twisting mechanisms by a position-dependent laser coupling
between internal degrees of freedom of atoms. A single laser coupling simulates
the one-axis twisting model with the orientation of the twisting axis
determined by the coupling phase. Adding a second laser beam with a properly
chosen phase paves the way to simulate the two-axis counter-twisting model,
enabling to approach the Heisenberg-limited level of squeezing.
