Strong-field-driven dynamics and high-harmonic generation in interacting one dimensional systems

The observation of high-order harmonic generation (HHG) from bulk crystals is stimulating substantial efforts to understand the involved mechanisms and their analog to the intuitive three-step recollision model of gas-phase HHG. Here we explore the roles of electronic band structure and Coulomb interactions in solid-state HHG by studying the optical response of linear atomic chains and carbon nanotubes to intense ultrashort pulses. Specifically, we simulate electron dynamics by solving the single-particle density matrix equation of motion in the presence of intense ultrafast optical fields, incorporating tight-binding electronic states and a self-consistent electron-electron interaction. At this level of description, linear atomic chains constitute an idealized yet realistic one dimensional (1D) system in which to explore HHG that can advantageously be tuned to describe metals, regular insulators, and topological insulators. Our chain model readily provides insight on the temporal evolution of electronic states in reciprocal space, revealing the important role played by electron interactions in HHG, due in part to the presence of collective optical resonances. This model further predicts that doped semiconductors generate high harmonics more efficiently than their metallic and undoped counterparts. To complement this idealized system we also show results for HHG in more realistic quasi-1D structures such as carbon nanotubes, the behavior of which is found to be in good qualitative agreement with the atomic chains. Our findings apply directly to extreme nonlinear optical phenomena in atoms on surfaces, carbon-based structures, linear arrays of dopant atoms in semiconductors, and linear molecules, such as polycyclic aromatic hydrocarbon chains, and can be straightforwardly extended to optimize existing platforms for HHG or identify new solid-state alternatives in the context of nonlinear plasmonics.