Collective non-perturbative coupling of 2D electrons with high-quality-factor terahertz cavity photons

Nonperturbative coupling of light with condensed matter in an optical cavity is expected to reveal a host of coherent many-body phenomena and states. In addition, strong coherent light-matter interaction in a solid-state environment is of great interest to emerging quantum-based technologies. However, creating a system that combines a long electronic coherence time, a large dipole moment, and a high cavity quality ($Q$) factor has been a challenging goal. Here, we report collective ultrastrong light-matter coupling in an ultrahigh-mobility two-dimensional electron gas in a high-$Q$ terahertz photonic-crystal cavity in a quantizing magnetic field, demonstrating a cooperativity of $\sim$360. The splitting of cyclotron resonance (CR) into the lower and upper polariton branches exhibited a $\sqrt{n_\mathrm{e}}$-dependence on the electron density ($n_\mathrm{e}$), a hallmark of collective vacuum Rabi splitting. Furthermore, a small but definite blue shift was observed for the polariton frequencies due to the normally negligible $A^2$ term in the light-matter interaction Hamiltonian. Finally, the high-$Q$ cavity suppressed the superradiant decay of coherent CR, which resulted in an unprecedentedly narrow intrinsic CR linewidth of 5.6 GHz at 2 K. These results open up a variety of new possibilities to combine the traditional disciplines of many-body condensed matter physics and cavity-based quantum optics.