  We study the time-evolution of an optically trapped spinor Bose-Einstein
condensate under the influence of a dominating magnetic bias field in the
z-direction, and a perpendicular smaller field that couples the spinor states.
We show that if the bias field depends quadratically on time, the relative
phases of the spinor components affect the populations of the final state. This
allows one to measure the differences in the time-evolution of the relative
phases, thereby realizing a multi-arm interferometer in a spinor Bose-Einstein
condensate.
