We study the nonlinear dynamics of trapped-ion models far away from the Lamb-Dicke regime. This nonlinearity induces a sideband cooling blockade, stopping the propagation of quantum information along the Hilbert space of the Jaynes-Cummings and quantum Rabi models. We compare the linear and nonlinear cases of these models in the ultrastrong and deep strong coupling regimes. Moreover, we propose a scheme that simulates the nonlinear quantum Rabi model in all coupling regimes. This can be done via off-resonant nonlinear red and blue sideband interactions, yielding applications as a dynamical quantum filter.
@article{arxiv.1709.07378,
title = {Nonlinear Quantum Rabi Model in Trapped Ions},
author = {Xiao-Hang Cheng and Iñigo Arrazola and Julen S. Pedernales and Lucas Lamata and Xi Chen and Enrique Solano},
journal= {arXiv preprint arXiv:1709.07378},
year = {2018}
}