LAUSR

Time-averaged trapping potentials have played an important role in the development of the field of ultracold atoms. Despite their widespread application, a complete understanding of when a system can be considered time-averaged, and how a system transitions from being localised in an oscillating trap to being delocalised in the time-averaged potential is still to be achieved. Here we use Floquet theory to perform such an analysis of oscillating trapping potentials, and provide a quantitative measure of the degree to which the states in these traps are in the time-averaged limit. We investigate how drive parameters change the density and phase and investigate how each component contributes to the localised to delocalised transition. By studying simple representative systems we demonstrate a number of features of the localised to delocalised transition, and highlight those particularly relevant to the experimental implementation of time-averaged potentials.