Multiphoton Spectroscopy of a Dynamical Axion Insulator

The unusual magnetoelectric transport present in Weyl semimetals and 3D topological insula- tors can be compactly understood as manifestations of a background axion field, which itself is determined by the microscopic band structure. In the presence of correlations, an additional axion quasiparticle may emerge as the collective excitations on top of the mean background field. Such modes couple nonlinearly to electric and magnetic fields, giving rise to a dynamical magnetoelectric response. However, unambiguous identification of this collective axion mode is challenging due to its inherent nonlinear dynamics. Here, we propose an all-optical protocol that utilizes a pump-probe setup for verifying and characterizing the transient dynamics of axion fields in three-dimensional insulator systems. In particular, we show that nonlinear Raman processes induce dynamical oscillations of the axion field that depend on the geometry of the incident electromagnetic fields. These oscillations manifest in the polarization and magnetization of the material, hence, can be subsequently measured using time-resolved Kerr rotation spectroscopy. Our results open a pathway toward using multiphoton and quantum pair spectroscopies to identify new correlated phases of quantum matter.