Quantum effects of operator time ordering in the nonlinear Jaynes-Cummings model

TL;DR

This paper revisits the nonlinear Jaynes-Cummings model for a trapped ion, demonstrating it can be solved with a classical laser field and analyzing quantum time-ordering effects on motional state nonclassicality.

Contribution

It shows the model can be solved with a classical laser, analyzes quantum time-ordering effects, and derives an exact convergence radius for the Magnus expansion.

Findings

Quantum time-ordering affects motional state nonclassicality.

Exact solution with classical laser field is possible.

Derived an exact radius of convergence for the Magnus expansion.

Abstract

Recently, in [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. In this work we reconsider this model and show that it can likewise be solved with a classical driving laser field. Using the exact solution we investigate the quantum time-ordering effects of the system with respect to nonclassicality of the motional states of the ion. Furthermore, we use the Magnus expansion to analyze the impact of certain orders of the time ordering and derive and exact radius of convergence beyond the established and only sufficient criterion. Finally, the differences of the solution derived here and the previously found one using a quantized pump, are discussed.