Probing the quantum limit of a chaotic system.

The study of quantum chaos presents the opportunity to observe new and interesting phenomena. This work focuses on the quantum limit of a classically chaotic system. Our approach involves mapping the dynamics $^{\mathrm{87}}$Rb condensate in a (2J$+$1)-site momentum-space lattice to those of an effective non-linear spin-J model. By performing spin rotations and squeezing operations we implement the quantum kicked top, a paradigmatic model for studying chaotic dynamics. We present linear entropy measurements as a probe of the quantum-classical crossover in our kicked top lattice. We also highlight, for a squeezing Hamiltonian, the first atomic quantum gas measurements of out-of-time ordered correlators, which serve both as signatures of quantum chaos and as a measure of information scrambling in complex quantum systems.