  Ultra strong coupling is studied in a modulation-doped parabolic potential
well coupled to an inductance-capacitance resonant circuit. In this system, in
accordance to Kohn's theorem, strong reduction of the energy level separation
caused by the electron-electron interaction compensates the depolarization
shift. As a result, a very large ratio of 27% of the Rabi frequency to the
center resonance frequency as well as a polariton gap of width 2? ? 670GHz are
observed, suggesting parabolic quantum wells as the system of choice in order
to explore the ultra-strong coupling regime.
