Strain control of correlated electron phenomena has been a theme of condensed matter research in recent years. Two primary areas of investigation have been controllable symmetry breaking and measurements of susceptibility with respect to elastic deformation and in this thesis we present an example of each. In 2H-NbSe₂ explore the effect of lattice anisotropy on the charge-ordered superconductor. Using a novel strain apparatus, we measure the superconducting transition temperature 𝑇_{sc} as a function of uniaxial strain. It is found that 𝑇_{sc} is independent of tensile(compressive) strain below a threshold of 0.2% (0.1%), but decreases strongly with larger strains with an average rate of 1.3𝐊/% (2.5𝐊/%). Transport signatures of charge order are largely unaffected as a function of strain. We employ theoretical considerations to show that the change in the behavior of 𝑇_{sc} with strain coincides with a phase transition from 3𝐐 to 1𝐐 charge order in the material. The spectral weight on one of the Fermi surface bands is found to change strongly as a consequence of this phase transition, providing a pathway to tune superconducting order. In the bilayer ruthenate Ca₃(Ru₁₋ₓTiₓ)₂O₇ a material that is unique among correlated insulators for its hybrid improper ferroelectricity and, at elevated temperatures, transitioning to a polar metallic phase, we investigate phase textures and their susceptibility to strain. Through multi-messenger low-temperature infrared and Kelvin probe nano-imaging, we reveal a spontaneous striped texture of coexisting insulating and metallic domains in single crystals across their insulator-metal phase transition at T=50-100K. Under in situ uniaxial strain, we image anisotropic nucleation and growth of these domains, rationalized through on-demand control of a spontaneous Jahn-Teller distortion. Through spatially correlative transmission electron microscopy and nano-scale strain mapping, we also reveal the selective interplay between this textured phase coexistence and domain boundaries between polar twins in these crystals. We study the strain susceptibility of the striped phase mixture and explain our results in terms of homogeneous phase susceptibilities and the strain susceptibility of domains. We study the anisotropy in bulk response functions (resistivity and elastosusceptibility) and we find that the results are consistent with a network model of the phase texture. We also perform low-temperature infrared nanoimaging and elastosusceptibility of the nonequilibrium current-driven metal-insulator transition in Ca₃(Ru₁₋ₓTiₓ)₂O₇. Our results are consistent with the emerging consensus explanation in terms of Joule heating.

Indiana University-Purdue University Indianapolis (IUPUI) / The tight-binding model that has been used for many years in condensed matter physics, due to its analytic and numerical tractability, has recently been used to describe light propagating through an array of evanescently coupled waveguides. This dissertation presents analytic and numerical simulation results of light propagating in a waveguide array. The first result presented is that photonic transport can be achieved in an array where the propagation constant is linearly increasing across the array. For an input at the center waveguide, the breathing modes of the system are observed, while for a phase displaced, asymmetric input, phase-controlled photonic transport is predicted. For an array with a waveguide-dependent, parity-symmetric coupling constant, the wave packet dynamics are predicted to be tunable. In addition to modifying the propagation constant, the coupling between waveguides can also be modified, and the quantum correlations are sensitive to the form of the tunneling function. In addition to modifying the waveguide array parameters in a structured manner, they can be randomized as to mimic the insertion of impurities during the fabrication process. When the refractive indices are randomized and real, the amount of light that localizes to the initial waveguide is found to be dependent on the initial waveguide when the waveguide coupling is non-uniform. In addition, when the variance of the refractive indices is small, light localizes in the initial waveguide as well as the parity-symmetric waveguide. In addition to real valued disorder, complex valued disorder can be introduced into the array through the imaginary component of the refractive index. It is shown that the two-particle correlation function is qualitatively similar to the case when the waveguide coupling is real and random, as both cases preserve the symmetry of the eigenvalues. Lastly, different input fields have been used to investigate the quantum statistical aspects of Anderson localization. It is found that the fluctuations in the output intensity are enhanced and the entropy of the system is reduced when disorder is present in the waveguides.