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

TL;DR

This paper investigates the non-equilibrium dynamics of bosons in a two-leg ladder with an effective magnetic field, revealing a slowing down of collective modes near a quantum phase transition, observable through real-time imaging.

Contribution

It provides the first analysis of quench dynamics in a Bose-Hubbard ladder with complex hopping and magnetic field, highlighting the slowing down near the phase transition.

Findings

Slowing down of collective mode dynamics near the quantum phase transition.

Experimental visualization of dynamics through atomic cloud imaging.

Dynamics influenced by quenches of trapping potential and rung hopping.

Abstract

Motivated by a recent experiment with optical lattices that has realized a ladder geometry with an effective magnetic field (Atala et al., Nature Physics \textbf{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 non-equilibrium 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.