Processos Paramétricos em eletrodinâmica quântica de cavidades.
Resumen
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.