Universal damping behavior of dipole oscillations of one-dimensional ultracold gases induced by quantum phase slips

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 $\mathrm{\Gamma }$ 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.