  We demonstrate that the static structure factor, momentum distribution and
density distribution provide clear signatures of the emergence of Wigner
crystal for the fermionic dipolar gas with strongly repulsive dipole-dipole
interactions trapped in one-dimensional optical lattices. Our numerical
evidences are based on the exact diagonalization of the microscopic effective
lattice Hamiltonian of few particles interacting with long-range interactions.
As a comparison, we also study the system with only nearest-neighbor
interactions, which displays quite different behaviors from the dipolar system
in the regime of strong repulsion.
