Detection of Compressible and Incompressible States in Quantum Dots and Antidots by Far-Infrared Spectroscopy

In arrays of ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}-\mathrm{GaAs}$ quantum dots and antidots we observe, with far-infrared spectroscopy for increasing magnetic field, huge (up to 20%) oscillations of the resonance frequency of the edge-magnetoplasmon-like mode. At fully occupied Landau levels the frequency has a maximum for the dots, and the reverse behavior, a minimum, for the antidots. We show that this is caused by the formation of compressible and incompressible stripes at the edges of the dots and antidots.