We develop and utilize time-resolved and nonlinear optical techniques in both the terahertz (THz) and optical frequency regimes to study and control properties of materials broadly known as ''quantum materials’’, which are topological and correlated materials. In this class of matter, collective phases and properties defy a classical description, often leading to an exotically rich range of emergent phenomena. We are particular interested in topological materials and quantum magnets. Our ultimate goals are to understand/discover new physics of these materials and to control them by light or strain or electrical gating to apply them to the next generation of quantum computers, solar cells and memory devices.