摘要： Recently [F. Krumm and W. Vogel, Phys. Rev. A 97, 043806 (2018)], the detuned and nonlinear Jaynes-Cummings model describing the quantized motion of a trapped ion was introduced and its corresponding dynamics was solved via considering the driving laser in a quantized manner. For the dynamics with a classical driving laser an approximation in terms of neglected time ordering was considered to obtain analytical expressions and compared to numerically obtained exact dynamics, which revealed the insufficiency of this approximation. In the present work we reconsider this model and show that it can likewise be solved analytically, i.e., including time ordering, with a classical driving laser field. Using the analytical solution, we investigate the quantum time-ordering effects of the system with respect to nonclassicality and nonsimulatability of the motional states of the ion. Furthermore, we use the Magnus expansion to analyze the impact of certain orders of the time ordering. We derive an exact radius of convergence for these time-ordering corrections beyond the established and only sufficient criterion. Finally, the differences between the solution derived here and the previously found one using a quantized pump are discussed.