Quantum signatures of chaos

Chaos is all around us. From weather changes to population dynamics to stock market volatility to the orbits of Jupiter’s moons, nonlinear and chaotic behaviour is commonly observable in our classical world. The key characteristic of chaos in these systems is extreme sensitivity of the dynamics to small perturbations in initial conditions. At the quantum level, the concept of nonlinear dynamics and chaos is more ambiguous due to the apparent linearity of quantum evolution and due to the uncertainty principle, which does not allow localized trajectories in phase space. We can explore the characterization and control of chaotic dynamics in a deeply quantum regime in the experimental setting of cold atoms or ions. A variety of interesting phenomena can be observed such as dynamical tunneling, signatures of chaos in quantum correlations, hypersensitivity to perturbations and the effect of chaos on quantum measurement. These studies provide a stepping-stone towards the development of a toolbox of quantum control for future applications in quantum information processing.