Sudden expansion and domain-wall melting of strongly interacting bosons in two-dimensional optical lattices and on multileg ladders

TL;DR

This study uses numerical methods to explore how strongly interacting bosons expand in two-dimensional optical lattices and multi-leg ladders, revealing a crossover from fast to slow expansion as the system transitions from 1D to 2D.

Contribution

It introduces a detailed numerical analysis of boson expansion dynamics across different lattice geometries and anisotropies, connecting 1D and 2D behaviors with new insights into domain-wall melting.

Findings

Expansion slows from ballistic to diffusive as the system becomes more two-dimensional.

Two-leg ladders expand slower than wider ladders, approaching 2D behavior.

The expansion velocity depends on anisotropy and number of ladder legs.

Abstract

We numerically investigate the expansion of clouds of hard-core bosons in the two-dimensional square lattice using a matrix-product-state based method. This nonequilibrium set-up is induced by quenching the trapping potential to zero and our work is specifically motivated by a recent experiment with interacting bosons in an optical lattice [Ronzheimer et al., Phys. Rev. Lett. 110, 205301 (2013)]. As the anisotropy of the amplitudes $J_x$ and $J_y$ for hopping in different spatial directions is varied from the one- to the two-dimensional case, we observe a crossover from a fast ballistic expansion in the one-dimensional limit $J_x \gg J_y$ to much slower dynamics in the isotropic two-dimensional limit $J_x=J_y$. We further study the dynamics on multi-leg ladders and long cylinders. For these geometries we compare the expansion of a cloud to the melting of a domain wall, which helps us to identify several different regimes of the expansion as a function of time. By studying the dependence of expansion velocities on both the anisotropy $J_y/J_x$ and the number of legs, we observe that the expansion on two-leg ladders, while similar to the two-dimensional case, is slower than on wider ladders. We provide a qualitative explanation for this observation based on an analysis of the rung spectrum.