Preparation and control of a cavity-field state through an atom-driven-field interaction: Towards long-lived mesoscopic states

The preparation of mesoscopic states of radiation and matter fields through atom-field interactions has been achieved in recent years and employed for a range of striking applications in quantum optics. Here we present a technique for the preparation and control of a cavity mode which, in addition to interacting with a two-level atom, is simultaneously submitted to linear and parametric amplification processes. The role of the amplification-controlling fields in the achievement of real mesoscopic states is to produce highly squeezed field states and, consequently, to increase both (i) the distance in phase space between the components of the prepared superpositions and (ii) the mean photon number of such superpositions. When the squeezed superposition states are submitted to the action of similarly squeezed reservoirs, we demonstrate that under specific conditions the decoherence time of the states becomes independent of both the distance in phase space between their components and their mean photon number. An explanation is presented to support this remarkable result, together with a discussion of the experimental implementation of our proposal. We also show how to produce number states with fidelities higher than those derived as circular states.