Magnetic field fluctuations analysis for the ion trap implementation of the quantum Rabi model in the the deep strong coupling regime

The dynamics of the quantum Rabi model in the deep strong coupling regime is theoretically analyzed in a trapped-ion setup. Recognizably, the main hallmark of this regime is the emergence of collapses and revivals, whose faithful observation is hindered under realistic magnetic dephasing noise. Here we discuss how to attain a faithful implementation of the quantum Rabi model in the deep strong coupling regime which is robust against magnetic field fluctuations and at the same time provides a large tunability of the simulated parameters. This is achieved by combining standing wave laser configuration with continuous dynamical decoupling. In addition, we study the role that amplitude fluctuations play to correctly attain the quantum Rabi model using the proposed method. In this manner the present work further supports the suitability of continuous dynamical decoupling techniques in trapped-ion settings to faithfully realize different interacting dynamics.