Quantum Phase Slips of Trapped Superfluid Bose Gases in One Dimension

We discuss transport of trapped one-dimensional superfluids through a single impurity potential, in connection with quantum phase-slip nucleation rate I". We specifically consider damping of dipole oscillations induced by sudden displacement of the trapping potential, which has been investigated in previous experiments. Applying the time-evolving block decimation method to the 1D Bose-Hubbard model with an impurity potential in the hardcore limit, we calculate the dynamics of dipole oscillations and extract the damping rate from the oscillations. We show that there is a broad parameter region in which the damping rate G of the oscillation obeys the formula GaeI"/vaev (2K-2) with the Tomonaga-Luttinger parameter K, regardless of whether the impurity potential is repulsive or attractive. We find that in that parameter region the damping rate is almost symmetric with respect to the change of the sign of the impurity strength.