Quantum materials are unique in their long-range interactions and competing phases tunable by external stimuli. Due to the incommensuracy of the quantum order or competing phases, the volume of quantum materials is partitioned into multiple domains. Light-matter interaction in quantum materials presents a new paradigm as light can tip the balance between many competing quantum many-body phases and give rise to new phenomena.

In the field of light probing quantum materials, most studies focus on ultrashort high-energy probing; rarely has anyone tried to use low-energy light to probe the material in the linear response regime and still get interesting results. In this dissertation, I will present the results of low-intensity light probing of quantum materials. Firstly, I present a nonlocal model of the dielectric function and show it can accurately describe the angle-resolved spectrum of TaS2 in the visible. The competing stacking configurations of the charge domains in this layered material result in significant optical inhomogeneity that necessitates a nonlocal dielectric function. I performed intensity-sweep characterizations and used our model to predict the domain size dependence on light intensity. The non-local parameter extracted from our measurements sheds light on the competition between the two stacking orders.

Next, seeking direct microscopic evidence of light-induced stacking reconfigurations, I present our experimental results from the Laser-STM system probing the surface charge density under stable laser illumination. Despite the noise at room temperature and laser power instability, which prevent an accurate determination of stacking order configurations, the TaS2 topography images uniquely exhibit a clear low-frequency charge-density oscillation on the order of 0.2 Hz. To investigate the dynamics of this light-matter interaction, an optical chopper is used to modulate the laser illumination. I demonstrate the emergence of a breathing charge density wave modulated by the chopping frequency. Furthermore, I propose our conjectures and hypotheses regarding the physics underlying this novel phenomenon. Finally, I will present simulations results that utilize quantum materials to realize advanced phase control and to design an anomalous diffraction grating.