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Bistability and Hysteresis of Intersubband Absorption in Strongly Interacting Electrons on Liquid Helium

We study nonlinear inter-subband microwave absorption of electrons bound to the liquid helium surface. Already for a comparatively low radiation intensity, resonant absorption due to transitions between the two lowest subbands is accompanied by electron overheating. The overheating results in a significant population of higher subbands. The Coulomb interaction between electrons causes a shift of the resonant frequency, which depends on the population of the excited states and thus on the electron temperature $T_e$. The latter is determined experimentally from the electron photoconductivity. The experimentally established relationship between the frequency shift and $T_e$ is in reasonable agreement with the theory. The dependence of the shift on the radiation intensity introduces nonlinearity into the rate of the inter-subband absorption resulting in bistability and hysteresis of the resonant response. The hysteresis of the response explains the behavior in the regime of frequency modulation, which we observe for electrons on liquid $^3$He and which was previously seen for electrons on liquid $^4$He.