Analytical Solutions of the Driven Time-Dependent Jaynes-Cummings Model

This study explores the dynamics of a Driven Time-Dependent Jaynes-Cummings (DTDJC) model, in which the atom and the field are influenced by an external classical field with time-varying amplitude modulation. By applying a series of unitary transformations and establishing suitable conditions for the time-dependent parameters of the system, the Hamiltonian operator is transformed into one representing a system not driven by an external field, namely a Free TDJC (FTDJC) system. This mapping allows us to determine, in both the time-independent and time-dependent cases, forms of the pumping modulating the field and the atomic population that are amenable to exact analytical solution. The effects of an off-resonance parameter emerging from the analytical solution of the model and the intensity of the classical pumping field on the dynamics of the atomic population are investigated. The exact solution allows us to reveal a rich dynamics of the system (including long-time super-revivals) that could be of use in future quantum technologies.