  We propose using ultracold fermionic atoms trapped in a periodically shaken
optical lattice as a quantum simulator of the t-J Hamiltonian, which describes
the dynamics in doped antiferromagnets and is thought to be relevant to the
problem of high-temperature superconductivity in the cuprates. We show
analytically that the effective Hamiltonian describing this system for
off-resonant driving is the t-J model with additional pair hopping terms, whose
parameters can all be controlled by the drive. We then demonstrate numerically
using tensor network methods for a 1D lattice that a slow modification of the
driving strength allows near-adiabatic transfer of the system from the ground
state of the underlying Hubbard model to the ground state of the effective t-J
Hamiltonian. Finally, we report exact diagonalization calculations illustrating
the control achievable on the dynamics of spin-singlet pairs in 2D lattices
utilising this technique with current cold-atom quantum-simulation technology.
These results open new routes to explore the interplay between density and spin
in strongly-correlated fermionic systems through their out-of-equilibrium
dynamics.
