Stability and decay of Bloch oscillations in presence of time-dependent nonlinearity

TL;DR

This paper investigates how time-dependent nonlinear interactions affect the stability and decay of Bloch oscillations in Bose-Einstein condensates, revealing conditions for sustained periodic behavior.

Contribution

It introduces a cyclic-time approach to identify modulation schemes that preserve Bloch oscillations despite nonlinear interactions.

Findings

Identification of modulation schemes leading to periodic wave packet evolution

Demonstration of robustness of certain modulations against perturbations

Quantitative analysis of Bloch oscillation decay and stability

Abstract

We consider Bloch oscillations of Bose-Einstein condensates in presence of a time-modulated s-wave scattering length. Generically, interaction leads to dephasing and decay of the wave packet. Based on a cyclic-time argument, we find---additionally to the linear Bloch oscillation and a rigid soliton solution---an infinite family of modulations that lead to a periodic time evolution of the wave packet. In order to quantitatively describe the dynamics of Bloch oscillations in presence of time-modulated interactions, we employ two complementary methods: collective-coordinates and the linear stability analysis of an extended wave packet. We provide instructive examples and address the question of robustness against external perturbations.