Nonlinear Optics in Magnetic Quantum Materials and Axion Electrodynamics

<br/>Parametric optical nonlinearities are critical to a wide spectrum of photonic technologies, from optical parametric oscillators to frequency combs to quantum information processing. Optical nonlinearities also serve as a powerful method for mapping material properties including the symmetries of electronic structure. Optical nonlinearities are generally very small in conventional materials as they depend on higher order effects. Parallel to these technical needs, the field of topological materials has seen the prediction and discovery of a large number of massless, three-dimensional linear dispersion systems known as Dirac and Weyl semimetals. It was soon realized that these materials may offer a rich new material phase space for extending the nonlinear effects of graphene including the role of topology and Berry connection. In this context, I will present our recent work on predicting the optoelectronic and nonlinear properties of Dirac and Weyl semimetals with an emphasis on figures of merit (FoMs) that we will evaluate for these new Weyl and Dirac semimetals that capture the confinement and nonlinearity to describe the second and third order susceptibilities and electro-optic coefficients of the materials. Next, I will discuss our recent results on the multiphoton spectroscopy of a dynamical axion insulator. Here, the axion receives contributions from the collective motion of electrons, leading to a nonlinear topological magnetoelectric effect. Identifying this collective axion response faces a number of major experimental difficulties, which necessitate a theory-predicted smoking gun signature. We demonstrate a two-step protocol for the unambiguous optical identification of the collective axion mode in such a system. First, we show how collective oscillations of the axion mode can be induced by two-photon absorption or stimulated Raman spectroscopy, with the magnetoelectric nature of the excitation manifesting in the polarization dependence of the excitation beams. Second, we show how the axion oscillations can be confirmed through their manifestations in the time-resolved Kerr-rotation, which again carries signature polarization dependence due to the magnetoelectric nature of the coupling. Looking ahead, I will discuss how collective responses in topological quantum materials can be unambiguously identified in nonlinear electrodynamical probes, as well as identify potential avenues for intersections with particle physics in axion electrodynamics.