Production of two-Fock states superpositions from even circular states andtheir decoherence

We analyze the even circular state (ECS - a superposition of N coherent sta tes \alpha > uniformly distributed with equal amplitudes on a circle) that can be engineered for the center of mass vibrational motion of a trapped io n. As a result of interference effects in phase space this state shows inte resting features: depending on the value of loll it may show up as the vacu um state \0 >, the number state \N > or as two-state superposition, \0 > \N >, \N > + \2N >. Here we discuss the statistics of the ECS, the probabil ity for its production, its evolution under the effects of the environment and decoherence. (C) 2001 Published by Elsevier Science B.V.