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We study the survival of super-currents in a system of impenetrable bosonssubject to a quantum quench from its critical superfluid phase to an insulatingphase. We show that the evolution of the current when the quench follows aRosen-Zener profile is exactly solvable. This allows us to analyze a quench ofarbitrary rate, from a sudden destruction of the superfluid to a slow openingof 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 currentsurviving at long times is proportional to $\nu^3$.

Supercurrent survival under Rosen-Zener quench of hard core bosons