  Most classical dynamical systems are chaotic. The trajectories of two
identical systems prepared in infinitesimally different initial conditions
diverge exponentially with time. Quantum systems, instead, exhibit
quasi-periodicity due to their discrete spectrum. Nonetheless, the dynamics of
quantum systems whose classical counterparts are chaotic are expected to show
some features that resemble chaotic motion. Among the many controversial
aspects of the quantum-classical boundary, the emergence of chaos remains among
the least experimentally verified. Time-resolved observations of quantum
chaotic dynamics are particularly rare, and as yet unachieved in a single
particle, where the subtle interplay between chaos and quantum measurement
could be explored at its deepest levels. We present here a realistic proposal
to construct a chaotic driven top from the nuclear spin of a single donor atom
in silicon, in the presence of a nuclear quadrupole interaction. This system is
exquisitely measurable and controllable, and possesses extremely long intrinsic
quantum coherence times, allowing for the observation of subtle dynamical
behavior over extended periods. We show that signatures of chaos are expected
to arise for experimentally realizable parameters of the system, allowing the
study of the relation between quantum decoherence and classical chaos, and the
observation of dynamical tunneling.
