Parametric Instabilities in Resonantly-Driven Bose-Einstein Condensates

TL;DR

This paper investigates the early-stage parametric instabilities in resonantly-driven Bose-Einstein condensates within optical lattices, providing theoretical insights to help experimentalists achieve stable conditions for exploring topological quantum states.

Contribution

It extends Bogoliubov theory to analyze stability in various resonantly-driven band models, offering predictions to guide experimental efforts in stabilizing these systems.

Findings

Identifies conditions for stability in driven Bose-Einstein condensates

Provides analytical and numerical predictions for instability thresholds

Offers insights to prevent heating and enable topological states

Abstract

Shaking optical lattices in a resonant manner offers an efficient and versatile method to devise artificial gauge fields and topological band structures for ultracold atomic gases. This was recently demonstrated through the experimental realization of the Harper-Hofstadter model, which combined optical superlattices and resonant time-modulations. Adding inter-particle interactions to these engineered band systems is expected to lead to strongly-correlated states with topological features, such as fractional Chern insulators. However, the interplay between interactions and external time-periodic drives typically triggers violent instabilities and uncontrollable heating, hence potentially ruling out the possibility of accessing such intriguing states of matter in experiments. In this work, we study the early-stage parametric instabilities that occur in systems of resonantly-driven Bose-Einstein condensates in optical lattices. We apply and extend an approach based on Bogoliubov theory [PRX 7, 021015 (2017)] to a variety of resonantly-driven band models, from a simple shaken Wannier-Stark ladder to the more intriguing driven-induced Harper-Hofstadter model. In particular, we provide ab initio numerical and analytical predictions for the stability properties of these topical models. This work sheds light on general features that could guide current experiments to stable regimes of operation.