Parametric Instability Rates in Periodically-Driven Band Systems

TL;DR

This paper investigates dynamical instabilities in periodically-driven band systems, especially Bose-Einstein condensates, by developing numerical and analytical methods to predict instability rates and understand their physical origins, relevant for ultracold atom experiments.

Contribution

It introduces a generic numerical method and an analytical Bogoliubov theory approach to accurately predict parametric instability rates in driven Bose-Einstein condensates.

Findings

Numerical simulations agree with theoretical predictions of instability rates.

Parametric resonances lead to energy absorption and instabilities.

Transverse modes influence the formation of parametric instabilities.

Abstract

This work analyses the dynamical properties of periodically-driven band models. Focusing on the case of Bose-Einstein condensates, and using a meanfield approach to treat inter-particle collisions, we identify the origin of dynamical instabilities arising due to the interplay between the external drive and interactions. We present a widely-applicable generic numerical method to extract instability rates, and link parametric instabilities to uncontrolled energy absorption at short times. Based on the existence of parametric resonances, we then develop an analytical approach within Bogoliubov theory, which quantitatively captures the instability rates of the system, and provides an intuitive picture of the relevant physical processes, including an understanding of how transverse modes affect the formation of parametric instabilities. Importantly, our calculations demonstrate an agreement between the instability rates determined from numerical simulations, and those predicted by theory. To determine the validity regime of the meanfield analysis, we compare the latter to the weakly-coupled conserving approximation. The tools developed and the results obtained in this work are directly relevant to present-day ultracold-atom experiments based on shaken optical lattices, and are expected to provide an insightful guidance in the quest for Floquet engineering.