Abstract
An atomic coherent state will evolve to an atomic coherent state under a classical driving field. Under a time-periodic driving field the phase space for the dynamics is S2 × S1, so that chaotic motion is possible. We explore the types of motion that can occur for periodically driven atomic coherent states by investigating the properties of the first return map S2 → S2. The sphere map that we introduce is a generalization of the Kolmogorov–Arnold circle map that is based on the Gauss sphere map. We find mixtures of mode-locking, quasiperiodicity, forward and reverse period-doubling cascades and chaos.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.
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