  Many-body entanglement in condensed matter systems can be diagnosed from
equilibrium response functions through the use of entanglement witnesses and
operator-specific quantum bounds. Here, we investigate the applicability of
this approach for detecting entangled states in quantum systems driven out of
equilibrium. We use a multipartite entanglement witness, the quantum Fisher
information, to study the dynamics of a paradigmatic fermion chain undergoing a
time-dependent change of the Coulomb interaction. Our results show that the
quantum Fisher information is able to witness distinct signatures of
multipartite entanglement both near and far from equilibrium that are robust
against decoherence. We discuss implications of these findings for probing
entanglement in light-driven quantum materials with time-resolved optical and
x-ray scattering methods.
