  We study entanglement dynamics in the nearest-neighbour fermionic chain that
is subjected to both DC and AC electric fields. The dynamics gives the well
known Bloch oscillations in the DC field case provided that the system size is
larger than the Bloch length whereas in the AC field case the entropy is
bounded and oscillates with the driving frequency at the points of dynamical
localization, and has a logarithmic growth at other points. A combined AC + DC
field yields super Bloch oscillations for the system size larger than the super
Bloch length which puts a constraint on the device size in a typical
non-equilibrium set-up to observe super Bloch oscillations where the device is
connected to the leads. Entanglement entropy provides useful signatures for all
of these phenomena, and an alternate way to capture the various length scales
involved.
