Anti-crossing phenomena in a resonator with 2D electrons on liquid helium

We have investigated the details of the eigenmode for a resonator containing a two-dimensional electron system (2DES), formed on the surface of liquid helium. We show that anti-crossing phenomena occur near the crossing point $\omega_0 = \omega_c$, where $\omega_0$ is the eigenmode of the resonator and $\omega_c$ is the cyclotron frequency. The structure of the coupling constant is established. It is a flexible parameter, i.e., sensitive especially to magnetic field and electron density. A finite coupling leads to a perturbation, $\delta\omega$, of the eigenmode of the resonator in presence of the 2DES. Corresponding calculations and measurements of $\delta\omega$ are presented. The theory fits the experimental data. The influence of anti-crossing on the cyclotron resonance absorption line-shape is demonstrated.