  We consider a class of states in an ensemble of two-level atoms: a
superposition of two distinct atomic coherent states, which can be regarded as
atomic analogues of the states usually called Schrodinger cat states in quantum
optics. According to the relation of the constituents we define polar and
nonpolar cat states. The properties of these are investigated by the aid of the
spherical Wigner function. We show that nonpolar cat states generally exhibit
squeezing, the measure of which depends on the separation of the components of
the cat, and also on the number of the constituent atoms. By solving the master
equation for the polar cat state embedded in an external environment, we
determine the characteristic times of decoherence, dissipation and also the
characteristic time of a new parameter, the non-classicality of the state. This
latter one is introduced by the help of the Wigner function, which is used also
to visualize the process. The dependence of the characteristic times on the
number of atoms of the cat and on the temperature of the environment shows that
the decoherence of polar cat states is surprisingly slow.
