Classical and Quantum chaos in a spin-1 atomic Bose–Einstein condensate via Floquet driving

Abstract

We investigate both the classical and quantum dynamics of a spin-1 Bose–Einstein condensate (BEC) system subject to periodic driving of quadratic Zeeman splitting. Without driving, the system is integrable. Here, we found that increasing the driving strength will drive the system to chaos. Classically, we demonstrate chaotic dynamics by examining the Poincaré section and Lyapunov exponent. While in the quantum regime, the level statistic and Husimi distribution are studied, and they also clearly indicate the onset of quantum chaos. The dynamics of atom number and out-of-time-ordered correlator (OTOC) are also studied. In the integrable region, the variance of atom number and OTOC both remain very small during the time evolution; while in the chaos region, a quick increase is observed in the early time. This work presents a quantum many-body system showing chaotic behavior and can be readily realized in experiment.