Matter-wave propagation in optical lattices: geometrical and flat-band effects

TL;DR

This paper explores how the geometry of optical lattices influences matter-wave propagation velocities and reveals how flat bands induce unique dynamical effects, providing insights for designing controllable quantum transport systems.

Contribution

The study systematically analyzes matter-wave propagation in various 2D optical lattice geometries, highlighting the impact of lattice structure and flat bands on quantum transport.

Findings

Triangular lattices support faster propagation than square lattices.

Body-centered square lattices exhibit even higher propagation velocities.

Flat bands cause dynamical density discontinuities in quantum transport.

Abstract

The geometry of optical lattices can be engineered allowing the study of atomic transport along paths arranged in patterns that are otherwise difficult to probe in the solid state. A question readily accessible to atomic systems is related to the speed of propagation of matter-waves as a function of the lattice geometry. To address this issue, we have investigated theoretically the quantum transport of non-interacting and weakly-interacting ultracold fermionic atoms in several 2D optical lattice geometries. We find that the triangular lattice has a higher propagation velocity compared to the square lattice, despite supporting longer paths. The body-centered square lattice has even longer paths, nonetheless the propagation velocity is yet faster. This apparent paradox arises from the mixing of the momentum states which leads to different group velocities in quantum systems. Standard band theory provides an explanation and allows for a systematic way to search and design systems with controllable matter-wave propagation. Moreover, the presence of a flat band such as in a two-leg ladder geometry leads to a dynamical density discontinuity, which contrasts the behavior of mobile and localized atoms in quantum transport. Our predictions are realizable with present experimental capability.