  We experimentally demonstrate a multi-mode interferometer comprising a
Bose-Einstein condensate of $^{39}$K atoms trapped in a harmonic potential,
where the interatomic interaction can be cancelled exploiting Feshbach
resonances. Kapitza-Dirac diffraction from an optical lattice coherently splits
the BEC in multiple momentum components equally spaced that form different
interferometric paths, closed by the trapping harmonic potential. We
investigate two different interferometric schemes, where the recombination
pulse is applied after a full or half oscillation in the confining potential.
We find that the relative amplitudes of the momentum components at the
interferometer output are sensitive to external forces, through the induced
displacement of the harmonic potential with respect to the optical lattice. We
show how to calibrate the interferometer, fully characterize its output and
discuss perspective improvements.
