  In solids, the high density of charged particles makes many-body interactions
a pervasive principle governing optics and electronics[1-12]. However, Walter
Kohn found in 1961 that the cyclotron resonance of Landau-quantized electrons
is independent of the seemingly inescapable Coulomb interaction between
electrons[2]. While this surprising theorem has been exploited in sophisticated
quantum phenomena[13-15] such as ultrastrong light-matter coupling[16],
superradiance[17], and coherent control[18], the complete absence of
nonlinearities excludes many intriguing possibilities, such as quantum-logic
protocols[19]. Here, we use intense terahertz pulses to drive the cyclotron
response of a two-dimensional electron gas beyond the protective limits of
Kohn's theorem. Anharmonic Landau ladder climbing and distinct terahertz four-
and six-wave mixing signatures occur, which our theory links to dynamic Coulomb
effects between electrons and the positively charged ion background. This new
context for Kohn's theorem unveils previously inaccessible internal degrees of
freedom of Landau electrons, opening up new realms of ultrafast quantum control
for electrons.
