Bloch dynamics in lattices with long range hoppings

TL;DR

This paper investigates how long-range hopping influences Bloch dynamics in lattices, providing analytical expressions and numerical validation, with implications for ultracold atom experiments.

Contribution

It offers a closed-form propagator for long-range hopping lattices and analyzes the resulting complex Bloch oscillations, extending understanding beyond nearest-neighbor models.

Findings

Capture of anharmonic oscillations in zigzag lattices

Quantitative description of crossover in wave packet dynamics

Agreement between analytical results and numerical simulations

Abstract

We study a discrete Schr\"odinger equation with arbitrary long range hopping terms under the influence of an external force. The impact of long range hoppings on the single particle Bloch dynamics in the lattice is investigated. A closed expression for the propagator is given, based on which we analyze the dynamics of initially Gaussian wave packets. Our findings capture the anharmonic oscillations recently observed in zigzag lattices and furthermore provide a detailed quantitative description of the crossover between center of mass Bloch oscillations for wide wave packets and left-right symmetric width oscillations for narrow single site excitations. The analytical results are shown to be in agreement with numerical simulations. A helix lattice setup for ultracold atoms is proposed where such hopping terms to far neighbors can be experimentally tuned to sizable values.