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Iterated dynamical maps offer an ideal setting to investigate quantumdynamical bifurcations and are well adapted to few-qubit quantum computerrealisations. We show that a single trapped ion, subject to periodic impulsiveforces, exhibits a rich structure of dynamical bifurcations derived from theJahn-Teller Hamiltonian flow model. We show that the entanglement between theoscillator and electronic degrees of freedom reflects the underlying dynamicalbifurcation in a Floquet eigenstate.

Iterated dynamical maps in an ion trap