We demonstrate terahertz chiral sub-wavelength cavities that break time-reversal symmetry by coupling the degenerate linearly polarized modes of two orthogonal sets of nano-antenna arrays using the inter-Landau level transition of a two-dimensional electron gas in a perpendicular magnetic field, realizing normalized light-matter coupling rates up to with a dispersion that is modified by the parasitic capacitive coupling between the orthogonal antennas. The deep sub-wavelength confinement of the nano-antennas means that the ultra-strong coupling regime can be reached even with a small number of carriers compared to Fabry-Perot cavities, making it viable to be used with a variety of 2D materials. The non-degenerate circularly polarized ground state was only obtained after carefully optimizing the optical design to minimize the parasitic coupling to linearly polarized light.

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