Mode-multiplexing deep-strong light-matter coupling

Dressing electronic quantum states with virtual photons creates exotic effects ranging from vacuum-field modified transport to polaritonic chemistry, and squeezing or entanglement of modes. The established paradigm of cavity quantum electrodynamics maximizes the light-matter coupling strength omega R/omega c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varOmega }_{{{{{{\rm{R}}}}}}}/{\omega }_{{{{{{\rm{c}}}}}}}$$\end{document}, defined as the ratio of the vacuum Rabi frequency and the frequency of light, by resonant interactions. Yet, the finite oscillator strength of a single electronic excitation sets a natural limit to omega R/omega c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varOmega }_{{{{{{\rm{R}}}}}}}/{\omega }_{{{{{{\rm{c}}}}}}}$$\end{document}. Here, we enter a regime of record-strong light-matter interaction which exploits the cooperative dipole moments of multiple, highly non-resonant magnetoplasmon modes tailored by our metasurface. This creates an ultrabroadband spectrum of 20 polaritons spanning 6 optical octaves, calculated vacuum ground state populations exceeding 1 virtual excitation quantum, and coupling strengths equivalent to omega R/omega c=3.19\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varOmega }_{{{{{{\rm{R}}}}}}}/{\omega }_{{{{{{\rm{c}}}}}}}=3.19$$\end{document}. The extreme interaction drives strongly subcycle energy exchange between multiple bosonic vacuum modes akin to high-order nonlinearities, and entangles previously orthogonal electronic excitations solely via vacuum fluctuations. The authors show an original approach to achieve strong light-matter interaction harnessing the coupling between plasmonic resonators and the Landau resonances of an underlying quantum well, demonstrating remarkably high coupling strengths.