Processos Paramétricos em eletrodinâmica quântica de cavidades

Abstract

In this thesis we study the interaction between an atom and a cavity mode submitted to linear and parametric amplifications. The evolution operator of the system was derived through the technique of time-dependent invariants of Lewis and Riesenfeld. We show how to prepare several squeezed states of the cavity field and, particularly, the truly mesoscopic "Schrödinger cat"-like state. When submitting such a mesoscopic superposition to the action of a likewise squeezed reservoir, we demonstrate that under specific conditions the decoherence time of the state is about the relaxation time of the cavity field. Next, the amplification process was engineered through the interaction of a single driven three-level atom with two cavity modes. Depending on the configuration of the atomic levels we obtain the parametric up- or down-conversion process between the cavity modes. With these processes we show how to generate one-mode mesoscopic squeezed superpositions (such as squeezed "Schrödinger cat"-like states), two-mode squeezed vacuum states (such as the original Eisntein-Podolsky-Rosen state (EPR)), and two-mode entanglements (such as the even and odd EPR states). The degree of squeezing achieved is up to 95% with currently feasible experimental parameters in cavity quantum electrodynamics. For the atom-field interaction time required in our technique, related to the high coupling parameter, the dissipative mechanism becomes practically negligible.