Quantum control modeling beyond semiclassical approximation

Semiclassical approximation is broadly used for modeling coherent control of quantum systems, which considers only the mean value but not the quantum fluctuation in the field for control. When nonclassical fields (e.g., weak coherent or single-photon lights) are applied, the fluctuation induced dynamics has to be considered. In this paper, we study, from a general open systems point of view, how to describe quantum control dynamics with nonclassical fields in frequency-domain via Laplace transform. Both nonstationary and stationary noises brought by field interaction are considered, and a two-level system example is given for demonstration.