  We experimentally demonstrate that well-designed driven lattices are
versatile tools to simultaneously tune multiple key parameters (namely
spin-dependent interactions, spinor phase, and Zeeman energy) for manipulating
phase diagrams of spinor gases with negligible heating and atom losses. This
opens a new avenue for studying dynamical phase transitions in engineered
Hamiltonians. The driven lattice creates additional separatrices in phase space
at driving-frequency-determined locations, with progressively narrower
separatrices at higher Zeeman energies due to modulation-induced higher
harmonics. The vastly expanded range of magnetic fields at which significant
spin dynamics occur and improved sensitivities at higher harmonics represent a
step towards quantum sensing with ultracold gases.
