Bose-Hubbard ladder subject to effective magnetic field: Quench dynamics in a harmonic trap

Motivated by a recent experiment with optical lattices that has realized a ladder geometry with an effective magnetic field [Atala et al., Nat. Phys. 10, 588 (2014)], we study the dynamics of bosons on a tight-binding two-leg ladder with complex hopping amplitudes. This system displays a quantum phase transition even without interactions. We study the nonequilibrium dynamics without and with interactions, in the presence of a harmonic trapping potential. In particular we consider dynamics induced by quenches of the trapping potential and of the magnitude of the rung hopping. We present a striking "slowing down" effect in the collective mode dynamics near the phase transition. This manifestation of a slowing down phenomenon near a quantum phase transition can be visualized unusually directly: The collective mode dynamics can be followed experimentally in real time and real space by imaging the atomic cloud.