Excitação paramétrica em modos acoplados: casos fechado e aberto

Abstract

The optical cavities investigation in quantum mechanics is well estabilished in the literature, however in the last few decades the insertion of parametric excitation in cavities frequencies presented interesting results for different system arrangements. In this work we aim at the dynamics analysis and the extraction of some properties of interest in two cases of the same system, composed by two weakly coupled parametrically excited optical cavities, but in free and dissipative mediums respectively. The differentiation between these cases requires use of two perspectives in the study of quantum mechanical dynamics, one of them uses the quadrature variables of the electromagnetic fields ^𝑥 and ^𝑝 in the quantum invariants method, in which the proprerties of a system described by a quadratic hamiltonian are extracted from a propagator’s algebra, that in the present case used the multiple scales method for the construction of the propagator components explicit forms. The other uses the transfomation of the these quadrature variables to the creation and annihilation operators ^𝑎 and ^𝑎† along with the new variables from the considered thermal reservoir, so they are used in the master equation derived from the Neumann-Liouville equations whose solution seeks to describe the system dynamics through the density operator. The extraction of properties of interest was done through operations on the covariance matrices considering initial Gaussian states, properties such as fluctuation energy, purity, squeezing and entanglement for example. Through the qualitative analysis of these properties it was possible to ascertain the action of parametric excitation in both cavities for both cases, along with differentiation of free and dissipative cases.