Nonlinear Response Theory of Fermionic Layers

For both, fundamental physics and novel applications, nonlinear effects are crucial. Powerful laser fields require to treat mobile electrons beyond linear response theory. Phenomena familiar from nonlinear optics are manifest in ultracold Rydberg systems, which have a high potential for ad- vancing the understanding of many-body physics via quantum simulations and promote progress in quantum computation and -information. Various devices and plasmonics systems are based on thin, nearly two dimensional (2D) layers, such as quantum wells, graphene-like structures or tran- sition metal dichalcogenides. We here derive an expression for nonlinear response functions in ar- bitrary order, and evaluate it explicitly in 2D for the quadratic and the cubic density response of non-interacting fermions. As correlations are of enhanced importance in low dimensions, we next incorporate screened interactions. This results in the generation of 2nd and 3rd harmonics of the col- lective modes (zero sound and plasmons), damped by multiple particle-hole continua.