  Dressing quantum states of matter with virtual photons can create exotic
effects ranging from vacuum-field modified transport to polaritonic chemistry,
and may drive strong squeezing or entanglement of light and matter modes. The
established paradigm of cavity quantum electrodynamics focuses on resonant
light-matter interaction to maximize the coupling strength
$\Omega_\mathrm{R}/\omega_\mathrm{c}$, defined as the ratio of the vacuum Rabi
frequency and the carrier frequency of light. Yet, the finite oscillator
strength of a single electronic excitation sets a natural limit to
$\Omega_\mathrm{R}/\omega_\mathrm{c}$. Here, we demonstrate a new regime of
record-strong light-matter interaction which exploits the cooperative dipole
moments of multiple, highly non-resonant magnetoplasmon modes specifically
tailored by our metasurface. This multi-mode coupling creates an ultrabroadband
spectrum of over 20 polaritons spanning 6 optical octaves, vacuum ground state
populations exceeding 1 virtual excitation quantum for electronic and optical
modes, and record coupling strengths equivalent to
$\Omega_\mathrm{R}/\omega_\mathrm{c}=3.19$. The extreme interaction drives
strongly subcycle exchange of vacuum energy between multiple bosonic modes akin
to high-order nonlinearities otherwise reserved to strong-field physics, and
entangles previously orthogonal electronic excitations solely via vacuum
fluctuations of the common cavity mode. This offers avenues towards tailoring
phase transitions by coupling otherwise non-interacting modes, merely by
shaping the dielectric environment.
