Transferring Rydberg wave packets between islands across the chaotic sea

A protocol to take a Rydberg wave packet that is trapped in a period-1 island, i.e., that is synchronized with the period of the driving field, and transfer it to a period-2 island such that the wave packet evolves with twice the period is theoretically analyzed and experimentally demonstrated. Such period-doubling transitions are realized using two superposed trains of half-cycle pulses whose relative time delay is varied adiabatically. It is shown that this protocol provides a tool to manipulate the angle variable of a Rydberg wave packet while its conjugate principal action is maintained constant.