Quantum signatures of chaos in a kicked top

Chaotic behaviour is ubiquitous and plays an important part in most fields of science. In classical physics, chaos is characterized by hypersensitivity of the time evolution of a system to initial conditions. Quantum mechanics does not permit a similar definition owing in part to the uncertainty principle, and in part to the Schrodinger equation, which preserves the overlap between quantum states. This fundamental disconnect poses a challenge to quantum-classical correspondence(1), and has motivated a long-standing search for quantum signatures of classical chaos(2,3). Here we present the experimental realization of a common paradigm for quantum chaos-the quantum kicked top(2,4)- and the observation directly in quantum phase space of dynamics that have a chaotic classical counterpart. Our system is based on the combined electronic and nuclear spin of a single atom and is therefore deep in the quantum regime; nevertheless, we find good correspondence between the quantum dynamics and classical phase space structures. Because chaos is inherently a dynamical phenomenon, special significance attaches to dynamical signatures such as sensitivity to perturbation(1,5) or the generation of entropy(6) and entanglement(7,8), for which only indirect evidence has been available(9- 11). We observe clear differences in the sensitivity to perturbation in chaotic versus regular, non-chaotic regimes, and present experimental evidence for dynamical entanglement as a signature of chaos.