Floquet analysis of time-averaged trapping potentials

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.