Nonlinear interaction of radiation with matter

In this work we study quantum mechanically the effect of bistable resonance in microscopic system. Bistable resonance is one manifestation of nonlinear interaction of radiation with matter, which may occur when a nonlinear system is irradiated by an external electromagnetic field. The microscopic systems that we analyze are intrinsically nonlinear, due to a first-order relativistic correction of the electron velocity of the system. When the external electromagnetic field is near resonance with the natural frequency of the microscopic system, we resort to non-perturbative methods in analyzing the interplay between the constituents of the interacting system. We investigate the interaction of a single atomic system with an external Electromagnetic field, describing the atom by a one electron Hamiltonian with a weak relativistic correction. Next, we consider as the microscopic system a single one-dimensional nonlinear oscillator, that models an individual electron trapped in a magnetic field. In this case, the master equation approach and the Quantum Classical Correspondence are invoked in order to analyze the interplay between the relativistic nonlinearity, the electromagnetic wave and the heat bath. This result contributes to the debate concerning the validity of the bistable resonance in the quantum regime, when single particles are considered. Finally, an additional scheme that exploits the effect of bistable resonance, is studied. We consider the interaction of the weakly relativistic oscillator that is subjected to a weak probe field, in the presence of a strong pump field, and analyze the power absorbed by the nonlinear oscillator from the probe field. The absorption from the probe field exhibits strong dependence upon the pump field regime, thus offering new schemes for studying the nonlinear interaction of radiation with matter