  In a microcavity, light-matter coupling is quantified by the vacuum Rabi
frequency $\Omega_R$. When $\Omega_R$ is larger than radiative and
non-radiative loss rates, the system eigenstates (polaritons) are linear
superposition of photonic and electronic excitations, a condition actively
investigated in diverse physical implementations. Recently, a quantum
electrodynamic regime (ultra-strong coupling) was predicted when $\Omega_R$
becomes comparable to the transition frequency. Here we report unambiguous
signatures of this regime in a quantum-well intersubband microcavity. Measuring
the cavity-polariton dispersion in a room-temperature linear optical
experiment, we directly observe the anti-resonant light-matter coupling and the
photon-energy renormalization of the vacuum field.
