Complex oxides present a fertile ground states of spin, lattice, orbital, and charge degree of freedom. The competition and interaction among different degrees of freedom provide a fascinating playground for fundamental scientific research as well as exploring applications in modern technologies. The scope of materials research has gone beyond understanding materials behaviors in ground states, and has extended to engineering new properties into materials and exploring possible hidden phases. There are static and dynamic approaches can be utilized to drive a material away from its ground state. Statically, by engineering complex oxides into heterostructures, the strain epitaxy effect can significantly alter the properties of the epitaxially grown films. In addition, tilt epitaxy promises an even more powerful route to directly control materials properties through a ubiquitous distortion in complex oxides. However, the characterization of tilt epitaxy is still challenging. The dynamic approach based on the idea of mode-selective pumping using ultrafast optical pulses, which can transiently drive a material away from its ground state by exciting a particular degree of freedom. Combining with delayed probe pulses, the dynamic trajectories of materials can be mapped out at femtosecond temporal resolution. Chapter 2 adopts the static approach following the scheme of tilt epitaxy. This chapter explores the paradigm of tilt epitaxy in thin films and demonstrates the non-destructively characterizing such epitaxy in three-dimensions for low symmetry complex tilt systems composed of light anions. More specifically, this chapter demonstrates that the interfacial tilt epitaxy can transform ultrathin calcium titanate, a non-polar earth-abundant mineral, into high-temperature polar oxides that last above 900 K. The comprehensive picture of octahedral tilts and polar distortions is revealed by reconstructing the three-dimensional electron density maps across film-substrate interfaces with atomic resolution using coherent Bragg rod analysis. The results are complemented with aberration-corrected transmission electron microscopy, film superstructure reflections, and are in excellent agreement with density functional theory. The study could serve as a broader template for non-destructive, three-dimensional atomic resolution probing of complex low symmetry functional interfaces. Chapter 3 turns to dynamic modulation the ground state of Ca3Ru2O7, which exhibits a rich phase diagram including two magnetic transitions (TN=56 K and TC=48 K) with the appearance of an insulating-like pseudogap (at TC). In addition, there is a crossover back to metallic behavior at T*=30 K, the origin of which is still under debate. This chapter applies ultrafast optical pump optical probe spectroscopy to investigate quasi-particle dynamics as a function of temperature in this enigmatic quantum material. Two dynamical processes are identified, both of which are influenced by the onset of the pseudogap. This includes electron-phonon relaxation and, below TC, the onset of a phonon bottleneck hindering the relaxation of quasiparticles across the pseudogap. A gap-modified two-temperature model is introduced to describe the temperature dependence of electron-phonon thermalization, and use the Rothwarf-Taylor to model the phonon bottleneck. In conjunction with density functional theory, the experimental results synergistically reveal the origin of the T-dependent pseudogap. Further, the data and analysis indicate that T* emerges as a natural consequence of T-dependent gapping out of carriers, and does not correspond to a separate electronic transition. The results highlight the value of low fluence ultrafast optics as a sensitive probe of low energy electronic structure, thermodynamic parameters, and transport properties of quantum materials. Chapter 4 serves as a comprehensive technical review of coherent Bragg rods analysis. This chapter starts with a mathematical description of the COBRA method and related iteration algorithms. Technical details being discussed includes: experimental data processing, symmetry application, convergence discussion, choice of boundary condition, sample thickness, and error analysis. The newly developed MATLAB routines for COBRA is introduced in appendix. Chapter 5 is a summary of the thesis and contains possible future directions.