Study of Quantum Dynamics in the Transition from Classical Stability to Chaos

We report an experimental and theoretical study of momentum transfer from a modulated standing wave of light to a sample of ultracold atoms. This system is a quantum realization of the periodically driven rotor where the underlying classical phase space goes from stable to chaotic as a control parameter is varied. Our experimental results are in good absolute agreement with a quantum Floquet analysis and with a quantum simulation. We relate the quantum evolution to the underlying classical dynamics in this mixed phase space regime.