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The preparation of mesoscopic states of the radiation and matter fieldsthrough atom-field interactions has been achieved in recent years and employedfor a range of striking applications in quantum optics. Here we present atechnique for the preparation and control of a cavity mode which, besidesinteracting with a two-level atom, is simultaneously submitted to linear andparametric amplification processes. The role of the amplification-controllingfields in the achievement of real mesoscopic states, is to producehighly-squeezed field states and, consequently, to increase both: i) thedistance in phase space between the components of the prepared superpositionsand ii) the mean photon number of such superpositions. When submitting thesqueezed superposition states to the action of similarly squeezed reservoirs,we demonstrate that under specific conditions the decoherence time of thestates becomes independent of both the distance in phase space between theircomponents and their mean photon number. An explanation is presented to supportthis remarkable result, together with a discussion on the experimentalimplementation of our proposal. We also show how to produce number states withfidelities higher than those derived as circular states

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