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### Abstract

The understanding of quantum many-body physics is the key to develop new quantum technologies including novel quantum materials, high-precision sensors, and quantum computers. However, understanding the general quantum many-body physics is extremely difficult, particularly when such systems are driven far from an equilibrium state. Ultracold atoms, a clean, fully controllable, and coherent quantum many-body systems can provide useful insights into the fundamental properties of quantum matter. This thesis discusses experiments on studying nonequilibrium dynamics in driven ultracold bosonic atoms with fantastic static and dynamical controls of the inter-particle interactions through Feshbach resonances and external trapping potentials using optical lattices and digital micromirror device (DMD). With this versatile apparatus, we first study the critical dynamics across a quantum phase transition in shaken optical lattices. Across a ferromagnetic transition where the $\mathbb{Z}_2$ inversion symmetry is broken, we are interested in how the system evolves toward the new ground states generally with a different symmetry. Utilizing the phase imprinting technique with DMD, we show that the macroscopic coherence is maintained across the phase transition, the system undergoes a coherent population transfer of particles toward lower energy states and quantum fluctuations determine the domain structure but do not destroy the macroscopic coherence. We then present the complex correlations rising from the matter-wave version of a high-harmonic generation with oscillating interaction. This high-harmonic generation of matterwave is a result of stimulated secondary collisions. The stimulated primary collisions, two condensate atoms collide absorbing one energy quantum from the oscillating field, give rise to the first observation of Bose fireworks. The scattered atoms from the primary collisions can further collide with each other or the ground-state atoms from the condensate and such secondary collisions promote atoms to higher momentum modes. Moreover, we show the density-wave dynamics prior to the jets emission within the condensate with oscillating interactions and explain the asymmetry in the jets emission pattern based on near-field interference. Besides, we further demonstrate the spatial and temporal phase coherence of the emitted jets using matter-wave interference and connect our matter-wave jets emission to the famous Unruh radiation in relativistic physics.