  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.
