Expansion velocity of a one-dimensional, two-component Fermi gas during the sudden expansion in the ballistic regime

We show that in the sudden expansion of a spin-balanced, two-component Fermi gas into an empty optical lattice induced by releasing particles from a trap, over a wide parameter regime, the radius Rₙ of the particle cloud grows linearly in time. This allow us to define the expansion velocity Vₑₓ from Rₙ=Vₑₓt. The goal of this work is to clarify the dependence of the expansion velocity on the initial conditions which we establish from time-dependent density matrix renormalization group simulations, both for a box trap and a harmonic trap. As a prominent result, the presence of a Mott-insulating region leaves clear fingerprints in the expansion velocity. Our predictions can be verified in experiments with ultracold atoms.