  We consider the nonequilibrium dynamics of an interacting spin-1/2 fermion
gas in a one-dimensional optical lattice after switching off the confining
potential. In particular, we study the creation and the time evolution of
spatially separated, spin-entangled fermionic pairs. The time-dependent
density-matrix renormalization group is used to simulate the time evolution and
evaluate the two-site spin correlation functions, from which the concurrence is
calculated. We find that the typical distance between entangled fermions
depends crucially on the onsite interaction strength, and that a time-dependent
modulation of the tunneling amplitude can enhance the production of
spin-entanglement. Moreover, we discuss the prospects of experimentally
observing these phenomena using spin-dependent single-site detection.
