Thermally activated phase slips of one-dimensional Bose gases in shallow optical lattices

We study the decay of superflow via thermally activated phase slips in one-dimensional Bose gases in a shallow optical lattice. By using the Kramers formula, we numerically calculate the nucleation rate of a thermally activated phase slip for various values of the filling factor and flow velocity in the absence of a harmonic trapping potential. Within the local density approximation, we derive a formula connecting the phase-slip nucleation rate with the damping rate of a dipole oscillation of the Bose gas in the presence of a harmonic trap. We use the derived formula to directly compare our theory with the recent experiment done by the LENS group [L. Tanzi, et al., Sci. Rep. {\bf 6}, 25965 (2016)]. From the comparison, the observed damping of dipole oscillations in a weakly correlated and small velocity regime is attributed dominantly to thermally activated phase slips rather than quantum phase slips.