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We investigate the possibility to form high fidelity atomic Fock states bygradual reduction of a quasi one dimensional trap containing spin polarizedfermions or strongly interacting bosons in the Tonk-Girardeau regime. Makingthe trap shallower and simultaneously squeezing it can lead to the preparationof an ideal atomic Fock state as one approaches either the sudden or theadiabatic limits. Nonetheless, the fidelity of the resulting state is shown toexhibit a non-monotonic behaviour with the time scale in which the trappingpotential is changed.

Atomic Fock states by gradual trap reduction: from sudden to adiabatic limits