Characterization and critical behavior of a periodically driven interacting three-dimensional quantum gas

Quantum many-body systems are generally fragile under external perturbations. Periodic driving often induces heating and decoherence, pushing the dynamics toward effectively classical behavior. Yet in certain driven systems, heating can be strongly suppressed and long-lived nonthermal dynamics can emerge. A paradigmatic example is the many-body quantum kicked rotor (QKR), in which an interacting quantum gas is subjected to a sequence of short pulses of a sinusoidal potential. While dynamical localization is well established in the single-particle QKR, and interaction effects have been explored in limited regimes, a systematic experimental characterization of the quantum-to-classical crossover in a driven interacting gas remains incomplete. Here we experimentally map the boundary between quantum and classical behavior in a periodically kicked, interacting three-dimensional quantum gas. Over a broad parameter range we observe persistent quantum behavior, evidenced by momentum-space localization accompanied by arrested real-space expansion. By varying both the kick strength and the interaction strength, we construct a localization-delocalization phase diagram and identify the critical point using a one-parameter scaling analysis at finite time. These results provide a unified experimental characterization of many-body dynamical localization (MBDL) in a driven interacting quantum gas beyond near integrable system and clarify how classical heating emerges as interactions and drive parameters are tuned.