  Deterministic preparation of an ultracold harmonically trapped
one-dimensional Fermi gas consisting of a few fermions has been realized by the
Heidelberg group. Using Floquet formalism, we study the time dynamics of two-
and three-fermion systems in a harmonic trap under an oscillating magnetic
field. The oscillating magnetic field produces a time-dependent interaction
strength through a Feshbach resonance. We explore the dependence of these
dynamics on the frequency of the oscillating magnetic field for
non-interacting, weakly interacting, and strongly interacting systems. We
identify the regimes where the system can be described by an effective
two-state model and an effective three-state model. We find an unbounded
coupling to all excited states at the infinitely strong interaction limit and
several simple relations that characterize the dynamics. Based on our findings,
we propose a technique for driving transition from the ground state to the
excited states using an oscillating magnetic field.
