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Traditionally, strong-field physics explores phenomena in laser-driven matter (atoms, molecules, and solids) that cannot be understood by treating the laser field as a small perturbation. Therefore, the presence of an extremely strong external field is usually a prerequisite for observing strong-field phenomena. However, even in the complete absence of an external electromagnetic field, strong-field phenomena can arise when matter strongly couples with the zero-point field of the quantum vacuum state, i.e., fluctuating electromagnetic waves whose expectation value is zero. This can occur in free space where the matter strongly interacts with a continuum of photon modes, but some of the most striking examples of strong-field physics without an external field occur in a cavity setting, in which an ensemble of two-level atoms resonantly interacts with a single photonic mode of vacuum fields, producing vacuum Rabi splitting. In particular, the nature of the matter-vacuum-field coupled system fundamentally changes when the coupling rate (equal to one half of the vacuum Rabi splitting) becomes comparable to, or larger than, the resonance frequency. In this so-called ultrastrong coupling regime, a non-negligible number of photons exist in the ground state of the coupled system. Furthermore, the coupling rate can be cooperatively enhanced (via so-called Dicke cooperativity) when the matter is comprised of a large number of identical two-level particles, and a quantum phase transition is predicted to occur as the coupling rate reaches a critical value. Low-energy electronic or magnetic transitions in many-body condensed matter systems with large dipole moments are ideally suited for searching for these predicted phenomena. Here, we discuss two condensed matter systems that have shown cooperative ultrastrong interactions in the terahertz frequency range: a Landau-quantized two-dimensional electron gas interacting with high-quality-factor cavity photons, and an Er3+ spin ensemble interacting with Fe3+ magnons in ErFeO3.
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