  We study superflow decay via quantum phase slips in trapped one-dimensional
(1D) quantum gases through dipole oscillations induced by sudden displacement
of the trapping potential. We find the relation between the damping rate of the
dipole oscillation $G$ and the phase-slip nucleation rate $\Gamma$ as $G\propto
\Gamma/v$, where $v$ is the flow velocity. This relation allows us to show that
damping of 1D Bose gases in optical lattices, which has been extensively
studied in experiment, is due to quantum phase slips. It is also found that the
damping rate versus the flow velocity obeys the scaling formula for an impurity
potential even in the absence of an explicit impurity. We suggest that the
damping rate at a finite temperature exhibits a universal crossover behavior
upon changing the flow velocity.
