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The ultra-strong light-matter coupling regime has been demonstrated in anovel three-dimensional inductor-capacitor (LC) circuit resonator, embedding asemiconductor two-dimensional electron gas in the capacitive part. Thefundamental resonance of the LC circuit interacts with the intersubband plasmonexcitation of the electron gas at $\omega_c = 3.3$~THz with a normalizedcoupling strength $2\Omega_R/\omega_c = 0.27$. Light matter interaction isdriven by the quasi-static electric field in the capacitors, and takes place ina highly subwavelength effective volume $V_{\mathrm{eff}} = 10^{-6}\lambda_0^3$. This enables the observation of the ultra-strong light-matter coupling with$2.4\times10^3$ electrons only. Notably, our fabrication protocol can beapplied to the integration of a semiconductor region into arbitrarynano-engineered three dimensional meta-atoms. This circuit architecture can beconsidered the building block of metamaterials for ultra-low dark currentdetectors.

Ultra-Strong Light-Matter Coupling in Deeply Subwavelength THz LC resonators