Dressing matter excitations with cavity photons can create novel, exotic quantum states. Ultrastrong coupling, where the ratio of vacuum Rabi frequency and carrier frequency of light, ΩR/ωc, approaches unity, has enabled vacuum-field modified transport, polaritonic chemistry, or strong mode squeezing and entanglement. Past investigations of this regime of cavity quantum electrodynamics (c-QED) focused on coupling of a single pair of light and matter modes, in equilibrium. Here, we discuss conceptually new extremes of c-QED. We demonstrate subcycle control of deep-strong coupling, where ΩR/ωc is collapsed from 1.3 to zero within 5% of the optical cycle duration, leading to characteristic trailing oscillations of the extinguished polariton states. Moreover, we investigate coherent subcycle nonlinearities of multiple cavity polaritons and observe dynamical mixing between otherwise orthogonal modes. Our most recent structures demonstrate extremely strong, multi-mode coupling of 20 matter resonances and multiple cavity modes over 6 optical octaves, boosting the number of virtual cavity photons beyond unity for the first time while achieving a record coupling strength of ΩR/ωc = 3.19.
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