  We study the quench dynamics of a one-dimensional ultracold Fermi gas in an
optical lattice potential with synthetic spin-orbit coupling. At equilibrium,
the ground state of the system can undergo a topological phase transition and
become a topological superfluid with Majorana edge states. As the interaction
is quenched near the topological phase boundary, we identify an interesting
dynamical phase transition of the quenched state in the long-time limit,
characterized by an abrupt change of the pairing gap at a critical quenched
interaction strength. We further demonstrate the topological nature of this
dynamical phase transition from edge-state analysis of the quenched states. Our
findings provide interesting clues for the understanding of topological phase
transitions in dynamical processes, and can be useful for the dynamical
detection of Majorana edge states in corresponding systems.
