  We demonstrate how to realize an optical clock with neutral atoms that is
competitive to the currently best single ion optical clocks in accuracy and
superior in stability. Using ultracold atoms in a Ca optical frequency standard
we show how to reduce the relative uncertainty to below 1E-15. We observed atom
interferences for stabilization of the laser to the clock transition with a
visibility of 0.36, which is 70 % of the ultimate limit achievable with atoms
at rest. A novel scheme was applied to detect these atom interferences with the
prospect to reach the quantum projection noise limit at an exceptional low
instability of 4E-17 in 1 s.
