  We analyze the formation of squeezed states in a condensate of ultracold
bosonic atoms confined by a double-well potential. The emphasis is set on the
dynamical formation of such states from initially coherent many-body quantum
states. Two cases are described: the squeezing formation in the evolution of
the system around the stable point, and in the short time evolution in the
vicinity of an unstable point. The latter is shown to produce highly squeezed
states on very short times. On the basis of a semiclassical approximation to
the Bose-Hubbard Hamiltonian, we are able to predict the amount of squeezing,
its scaling with $N$ and the speed of coherent spin formation with simple
analytical formulas which successfully describe the numerical Bose-Hubbard
results. This new method of producing highly squeezed spin states in systems of
ultracold atoms is compared to other standard methods in the literature.
