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We consider an interacting, one-dimensional Bose gas confined in a splittrap, obtained by an harmonic potential with a localized barrier at its center.We address its quantum-transport properties through the study of dipolaroscillations, which are induced by a sudden quench of the position of thecenter of the trap. We find that the dipole-mode frequency strongly depends onthe interaction strength between the particles, yielding information on theclassical screening of the barrier and on its renormalization due to quantumfluctuations. Furthermore, we predict a parity effect which becomes mostprominent in the strongly correlated regime.

Dipole mode of a strongly correlated one-dimensional Bose gas in a split trap: parity effect and barrier renormalization