From weather phenomena, to population dynamics, to the orbits of Jupiter's moons, chaos appears everywhere around us. All chaotic systems exhibit an extreme sensitivity to tiny changes in initial conditions that has come to be popularly illustrated by the butterfly effect: The flapping of a butterfly's wings can trigger the eventual development of a tornado half a world away. A majority of real-world phenomena, natural or human-made, are governed by nonlinear equations of motion that can lead to chaos, and this circumstance has inspired a systematic study of nonlinear dynamics and chaos theory over many decades.

Recent advances in optics, solid-state physics, and nanoscience are now making it possible to control systems at the level of individual atoms and photons. At this microscopic level governed by the laws of quantum mechanics, the concept of nonlinear dynamics and chaos becomes ambiguous and difficult to characterize. The problem arises from the uncertainty principle, which forbids exact knowledge of initial conditions, and from the Schrödinger equation, which appears to forbid nonlinear dynamics. The study of how chaos manifests itself at the quantum level is therefore crucial for understanding the fundamental connections between the quantum world and our macroscopic classical world, and also for developing a toolbox of useful quantum control techniques.

Quantum control of nonlinear systems is important for a variety of future applications, including control of molecular processes for chemical and biological purposes, controlling electron transport in solid-state devices, and performing high-precision measurements. Furthermore, due to the ever-increasing miniaturization of transistors on a computer chip, quantum chaos has gained new relevance in the field of quantum computation.