  We analyze a Bose-Einstein condensate (BEC) - based free oscillation atom
Michelson interferometer in a weakly confining harmonic magnetic trap. A BEC at
the center of the trap is split into two harmonics by a laser standing wave.
The harmonics move in opposite directions with equal speeds and turn back under
the influence of the trapping potential at their classical turning points. The
harmonics are allowed to pass through each other and a recombination pulse is
applied when they overlap at the end of a cycle after they return for the
second time. We derive an expression for the contrast of the interferometric
fringes and obtain the fundamental limit of performance of the interferometer
in the parameter space.
