In this paper we propose an alternative scheme to generate a supersinglet
state of three three-level atoms via a single-mode of a cavity QED based on the
two-photon transitions described by the 'full microscopical Hamiltonian
approach'. In it, three three-level atoms prepared in suitable initial states
are sequentially sent through the cavity originally prepared in its vacuum
state. After an appropriate choice of the atom-cavity interaction times plus a
field detection the state that describes the whole atom-field system is
projected in the desired supersinglet state. The fidelity and success
probability of the state as well as the practical feasibility of the scheme are
discussed.Comment: 10 pages, 3 figures, 4 table