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

Dynamic generation of spin-squeezed states in bosonic Josephson junctions