Two-photon processes have so far been considered only as resulting from frequency-matched second-order expansions of light-matter interaction, with consequently small coupling strengths. However, a variety of novel physical phenomena arises when such coupling values become comparable with the system characteristic frequencies. Here, we propose a realistic implementation of two-photon quantum Rabi and Dicke models in trapped-ion technologies. In this case, effective two-phonon processes can be explored in all relevant parameter regimes. In particular, we show that an ion chain under bichromatic laser drivings exhibits a rich dynamics and highly counterintuitive spectral features, such as interaction-induced spectral collapse.
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