We demonstrate that circular wave packets in high Rydberg states generated by a pulsed electric field applied to extreme Stark states are characterized by a position-dependent energy gradient that leads to a correlation between the principal quantum number n and the spatial coordinate. This correlation is rather insensitive to the initial state and can be seen even in an incoherent mix of states such as is generated experimentally allowing information to be placed into, and extracted from, such wave packets. We show that detailed information on the spatial distribution of a circular wave packet can be extracted by analyzing the complex phase of its expansion coefficients.
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