Time-dependent nonlinear Jaynes-Cummings dynamics of a trapped ion

TL;DR

This paper derives exact analytical solutions for the nonlinear, time-dependent quantum dynamics of a trapped ion, including electronic and motional states, highlighting the role of time ordering and nonclassicality evolution.

Contribution

It introduces a method to obtain exact solutions for the complex, time-dependent vibronic dynamics of a trapped ion with a quantized pump field, advancing understanding of quantum evolution.

Findings

Exact solutions for time-dependent ion dynamics derived

Analysis of nonclassicality evolution in motional states

Insights into time ordering effects in quantum systems

Abstract

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.