Sub-cycle high-order nonlinearities in a terahertz quantum cascade laser

Ultrafast electron dynamics in quantum cascade lasers hold enormous potential for the implementation of intense, compact mode-locked terahertz sources, squeezed terahertz light, frequency mixers, and comb-based metrology systems. Yet the important sub-cycle dynamics have been notoriously difficult to access in operational terahertz quantum cascade lasers. Here we show the first field-resolved two-dimensional terahertz spectroscopy of a free-running quantum cascade laser, revealing its sub-cycle gain dynamics and disentangling resonantly enhanced high-order nonlinearities up to eight-wave mixing in a regime of negative absorption.