  We measured the relative phase of two Bose-Einstein condensates confined in
an radio frequency induced double well potential on an atom chip. We observed
phase coherence between the separated condensates for times up to 200 ms after
splitting, a factor of 10 beyond the phase diffusion limit expected for a
coherent state in our experimental conditions (20 ms). The enhanced coherence
time is attributed to number squeezing of the initial state by a factor of 10.
In addition, we demonstrated a rotationally sensitive (Sagnac) geometry for a
guided atom interferometer by propagating the split condensates.
