  We study the driven critical dynamics of the quantum link model, whose
Hamiltonian describes the one-dimensional $U(1)$ lattice gauge theory. We find
that combined topological defects emerge after the quench and they consist of
both gauge field and matter field excitations. Furthermore, the ratio of gauge
field and matter field excitation is $1/2$ due to the constraint of the Gauss'
law. We show that the scaling of these combined topological defects satisfies
the usual Kibble-Zurek mechanism. We verify that both the electric flux and the
entanglement entropy satisfy the finite-time scaling theory in the whole driven
process. Possible experimental realizations are discussed.
