  The ultra-strong light-matter coupling regime has been demonstrated in a
novel three-dimensional inductor-capacitor (LC) circuit resonator, embedding a
semiconductor two-dimensional electron gas in the capacitive part. The
fundamental resonance of the LC circuit interacts with the intersubband plasmon
excitation of the electron gas at $\omega_c = 3.3$~THz with a normalized
coupling strength $2\Omega_R/\omega_c = 0.27$. Light matter interaction is
driven by the quasi-static electric field in the capacitors, and takes place in
a 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 be
applied to the integration of a semiconductor region into arbitrary
nano-engineered three dimensional meta-atoms. This circuit architecture can be
considered the building block of metamaterials for ultra-low dark current
detectors.
