One-dimensional density waves of ultracold bosons in an optical lattice

TL;DR

This paper studies the dynamics of density waves in ultracold bosons within an optical lattice using advanced numerical methods, revealing how wave properties depend on interactions and perturbation parameters, and exploring regimes of fermionic behavior.

Contribution

It provides a comprehensive, numerically exact analysis of density wave propagation in the Bose-Hubbard model, including decay, velocity dependence, and experimental detection strategies.

Findings

Decay of wave amplitude over time

Velocity depends on density, interaction, and perturbation height

Identification of regimes with fermionic behavior

Abstract

We investigate the propagation of density-wave packets in a Bose-Hubbard model using the adaptive time-dependent density-matrix renormalization group method. We discuss the decay of the amplitude with time and the dependence of the velocity on density, interaction strength and the height of the perturbation in a numerically exact way, covering arbitrary interactions and amplitudes of the perturbation. In addition, we investigate the effect of self-steepening due to the amplitude dependence of the velocity and discuss the possibilities for an experimental detection of the moving wave packet in time of flight pictures. By comparing the sound velocity to theoretical predictions, we determine the limits of a Gross-Pitaevskii or Bogoliubov type description and the regime where repulsive one-dimensional Bose gases exhibit fermionic behaviour.