The confinement of elementary excitations induces distinctive features in the
non-equilibrium quench dynamics. One of the most remarkable is the suppression
of entanglement entropy which in several instances turns out to oscillate
rather than grow indefinitely. While the qualitative physical origin of this
behavior is clear, till now no quantitative understanding away from the field
theory limit was available. Here we investigate this problem in the weak quench
limit, when mesons are excited at rest, hindering entropy growth and exhibiting
persistent oscillations. We provide analytical predictions of the entire
entanglement dynamics based on a Gaussian approximation of the many-body state,
which captures numerical data with great accuracy and is further simplified to
a semiclassical quasiparticle picture in the regime of weak confinement. Our
methods are valid in general and we apply explicitly to two prototypical
models: the Ising chain in a tilted field and the experimentally relevant
long-range Ising model.
