Floquet analysis of time-averaged trapping potentials

TL;DR

This paper uses Floquet theory to analyze the conditions under which time-averaged trapping potentials in ultracold atoms can be considered effective, focusing on the transition from localized to delocalized states and the influence of driving parameters.

Contribution

It provides a comprehensive Floquet analysis of time-averaged trapping potentials, characterizing the transition and quantifying the degree of time-averaging in simple systems.

Findings

Transition from localized to delocalized states identified

Quantitative measures of time-averaging provided

Effects of driving parameters on Floquet ground state analyzed

Abstract

Time-averaged trapping potentials have played an important role in the development of the field of ultracold atoms. Despite their widespread application, there is not yet a complete understanding of when a system can be considered time-averaged. Here we use Floquet theory to analyse the lowest energy state of time-periodic trapping potentials, and characterise the transition from a localised state in a slowly moving trap to a delocalised state in a rapidly oscillating time-averaged potential. We investigate how the driving parameters affect the density and phase of the Floquet ground state, and provide a quantitative measure of the degree to which they can be considered time-averaged. We study a number of simple representative systems, and comment on the features affecting the experimental realisation of time-averaged trapping potentials.