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We investigate theoretically the coupling between a cavity resonator and thecyclotron transition of a two dimensional electron gas under an appliedperpendicular magnetic field. We derive and diagonalize an effective quantumHamiltonian describing the magnetopolariton excitations of the two dimensionalelectron gas for the case of integer filling factors. The limits of validity ofthe present approach are critically discussed. The dimensionless vacuum Rabifrequency $\Omega_0/\omega_0$ (i.e., normalized to the cyclotron frequency$\omega_0$) is shown to scale as $\sqrt{\alpha\: n_{QW} \nu}$, where $\alpha$is the fine structure constant, $n_{QW}$ is the number of quantum wells and$\nu$ is the filling factor in each well. We show that with realisticparameters of a high-mobility semiconductor two dimensional electron gas, thedimensionless coupling $\Omega_0/\omega_0$ can be much larger than 1 in thecase of $\nu \gg 1$, the latter condition being typically realized forcyclotron transitions in the microwave range. Implications of such ultrastrongcoupling regime are discussed.

Ultrastrong coupling between a cavity resonator and the cyclotron transition of a 2D electron gas in the case of integer filling factor