  We propose a robust realization of the two-photon quantum Rabi model in a
trapped-ion setting based on a continuous dynamical decoupling scheme. In this
manner the magnetic dephasing noise, which is identified as the main obstacle
to achieve long time coherent dynamics in ion-trap simulators, can be safely
eliminated. More specifically, we investigate the ultrastrong coupling regime
of the two-photon quantum Rabi model whose realization in trapped ions involves
second-order sideband processes. Hence, the resulting dynamics becomes
unavoidably slow and more exposed to magnetic noise requiring an appropriate
scheme for its elimination. Furthermore, we discuss how dynamical decoupling
methods take a dual role in our protocol, namely they remove the main source of
decoherence from the dynamics while actively define the parameter regime of the
simulated model.
