Ultrafast control of quantum geometry and nonlinear optical response in topological materials

Nonlinear optical responses are central to modern optical technologies and the possibility to tune them on-demand and on ultrafast timescales is highly desirable. We theoretically analyze the possibility of using bicircular light (BCL) irradiation as a way to dynamically control nonlinear optical responses in Dirac semimetals and topological insulators. BCL consists of a superposition of two circularly polarized light beams with frequencies that are integer multiples of each other. The resulting electric field traces a rose curve whose shape and orientation can be controlled by light parameters. A distinctive feature of BCL is its capability of simultaneously breaking time-reversal and spatial inversion symmetry, which has profound implications for the electronic properties of the driven system. We show that periodically driving a centrosymmetric material with BCL results in the emergence of intense second harmonic generation and bulk photovoltaic responses that are absent in equilibrium. We contrast the responses of Dirac semimetal and topological insulators and address their connection with photoinduced quantum geometry changes.