  We study the survival of super-currents in a system of impenetrable bosons
subject to a quantum quench from its critical superfluid phase to an insulating
phase. We show that the evolution of the current when the quench follows a
Rosen-Zener profile is exactly solvable. This allows us to analyze a quench of
arbitrary rate, from a sudden destruction of the superfluid to a slow opening
of a gap. The decay and oscillations of the current are analytically derived,
and studied numerically along with the momentum distribution after the quench.
In the case of small supercurrent boosts $\nu$, we find that the current
surviving at long times is proportional to $\nu^3$.
