Engenharia de interações e de reservatórios

Abstract

In this work we first present a protocol to build effective interactions between two cavity modes, considering a two-level atom under the action of classical fields. Bilinear Hamiltonians associated with parametric up- and down-conversion processes are derived, apart from nonlinear interactions associated with the degenerate parametric down-conversion process, resulting in the squeezing operation of a cavity mode. We also demonstrate how to construct nonlinear Hamiltonians related with a Kerr-type process for one or two cavity modes. In particular, we show how to implement, in the bimodal cavity, the Hamiltonian describing a two-specieis Bose-Einstein condensate in the two-mode approximation. Next, considering a two-level ion trapped in a cavity, under the action of classical amplification field, we show how to build an artificial reservoir for the electronic states of the ion. This reservoir is suited to protect nonstationary superpositions of the electronic levels, enabling us to measure the geometric phase acquired by these states under nonadiabatic evolutions of the system. Finally, we show how to construct squeezed reservoirs, either for a cavity mode or two-level atoms, by previously engineering an effective interaction between the atom(s) and the cavity mode which comprehends the simultaneous implementation of the Jaynes-Cummings and anti-Jaynes-Cummings Hamiltonians.