Werner Vogel

In a previous paper (Krumm and Vogel 2018 Phys. Rev. A 97, 043806) we presented a method to solve the nonlinear Jaynes-Cummings dynamics, describing the quantized motion of a trapped ion exactly, including detuning. Here we investigate this model with respect to nonclassical effects, such as squeezing and sub-Poisson statistics. We show that for the versatile model under study there exist quantum phenomena beyond squeezing and sub-Poisson statistics, such as anomalous quantum correlations of two non-commuting observables. In particular, it is shown that for the excitation of the zeroth sideband neither squeezing nor sub-Poisson statistics do occur, but anomalous correlations can be verified. Furthermore, it is shown how these anomalous correlation functions can be derived from measured data.

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.

In quantum interaction problems with explicitly time-dependent interaction Hamiltonians, the time ordering plays a crucial role for describing the quantum evolution of the system under consideration. In such complex scenarios, exact solutions of the dynamics are rarely available. Here we study the nonlinear vibronic dynamics of a trapped ion, driven in the resolved sideband regime with some small frequency mismatch. By describing the pump field in a quantized manner, we are able to derive exact solutions for the dynamics of the system. This eventually allows us to provide analytical solutions for various types of time-dependent quantities. In particular, we study in some detail the electronic and the motional quantum dynamics of the ion, as well as the time evolution of the nonclassicality of the motional quantum state.