Onset of Bloch oscillations in the almost-strong-field regime

TL;DR

This paper investigates the transition from conventional nonlinear optics to a regime where electrons explore the Brillouin zone in solids, revealing an abrupt change in nonlinear response linked to Bloch electron motion before ionization dominates.

Contribution

It identifies a new regime in high-order harmonic generation where Bloch electron motion influences nonlinear optical response prior to strong-field ionization effects.

Findings

Abrupt change in nonlinear response before intraband currents dominate

Interference structure observed in third-harmonic generation

Bloch motion affects interband response in near-strong-field regime

Abstract

In the field of high-order harmonic generation from solids, the electron motion typically exceeds the edge of the first Brillouin zone. In conventional nonlinear optics, on the other hand, the excursion of band electrons is negligible. Here, the transition from conventional nonlinear optics to the regime where the crystal electrons begin to explore the first Brillouin zone is investigated. It is found that the nonlinear optical response changes abruptly already before intraband currents due to ionization become dominant. This is observed by an interference structure in the third-order harmonic generation of few-cycle pulses in a non-collinear geometry. Although approaching Keldysh parameter $\gamma = 1$, this is not a strong-field effect in the original sense, because the iterative series still converges and reproduces the interference structure. The change of the nonlinear interband response is attributed to Bloch motion of the reversible (or transient or virtual) population, similar to the Bloch motion of the irreversible (or real) population which affects the intraband currents that have been observed in high-order harmonic generation.