# Bloch oscillations sustained by nonlinearity

## TL;DR

This paper shows that nonlinearity can sustain long-lived Bloch oscillations in a hybrid discrete-continuous model, with potential experimental realizations in optics and Bose-Einstein condensates.

## Contribution

It introduces a model where nonlinearity supports persistent Bloch oscillations and provides an optimal relation between nonlinearity and linear gradient for robustness.

## Key findings

- Long-lived Bloch oscillations achieved with optimal nonlinearity-gradient relation.
- Robust oscillations observed over broad parameter ranges.
- Analytical wave packet evolution matches numerical simulations.

## Abstract

We demonstrate that nonlinearity may play a constructive role in supporting Bloch oscillations in a model which is discrete, in one dimension and continuous in the orthogonal one. The model can be experimentally realized in several fields of physics such as optics and Bose-Einstein condensates. We demonstrate that designing an optimal relation between the nonlinearity and the linear gradient strength provides extremely long-lived Bloch oscillations with little degradation. Such robust oscillations can be observed for a broad range of parameters and even for moderate nonlinearities and large enough values of linear potential. We also present an approximate analytical description of the wave packet's evolution featuring a hybrid Bloch oscillating wave-soliton behavior that excellently corresponds to the direct numerical simulations.