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

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.