  We study dynamics of quantum entanglement in smooth global quenches with a
finite rate, by computing the time evolution of entanglement entropy in 1 + 1
dimensional free scalar theory with time-dependent masses which start from a
nonzero value at early time and either crosses or approaches zero. The
time-dependence is chosen so that the quantum dynamics is exactly solvable. If
the quenches asymptotically approach a critical point at late time, the
early-time and late-time entropies are proportional to the time and subsystem
size respectively. Their proportionality coefficients are determined by scales:
in a fast limit, an initial correlation length; in a slow limit, an effective
scale defined when adiabaticity breaks down. If the quenches cross a critical
point, the time evolution of entropy is characterized by the scales: the
initial correlation length in the fast limit and the effective correlation
length in the slow limit. The entropy oscillates, and the entanglement
oscillation comes from a coherence between right-moving and left-moving waves
if we measure the entropy after time characterized by the quench rate. The
periodicity of the late-time oscillation is consistent with the periodicity of
the oscillation of zero modes which are zero-momentum spectra of two point
functions of a fundamental field and its conjugate momentum.
