Modulational Instability in Bose-Einstein Condensates under Feshbach Resonance Management

TL;DR

This paper analyzes the modulational instability in Bose-Einstein condensates with periodically varying interactions, using a Kronig-Penney model to identify instability regions, supported by numerical simulations.

Contribution

It introduces an analytical reduction of the stability problem to a Kronig-Penney model for Feshbach resonance management in BECs, revealing instability windows.

Findings

Identified instability windows in the parameter space.

Validated analytical results with numerical simulations.

Demonstrated effects of magnetic trapping on stability.

Abstract

We investigate the modulational instability of nonlinear Schr{\"o}dinger equations with periodic variation of their coefficients. In particular, we focus on the case of the recently proposed, experimentally realizable protocol of Feshbach Resonance Management for Bose-Einstein condensates. We derive the corresponding linear stability equation analytically and we show that it can be reduced to a Kronig-Penney model, which allows the determination of the windows of instability. The results are tested numerically in the absence, as well as in the presence of the magnetic trapping potential.