Limitations to the short term frequency stability in a compact cold atom clock

The HORACE device is a compact cold atom clock where about 10/sup 8/ cesium atoms are laser cooled at a few /spl mu/K, then interrogated and detected directly in a 20 cm/sup 3/ spherical microwave cavity. The optimization of the short term stability with the cooling and interrogation durations is presented, leading to an estimation of the Allan deviation of /spl sigma//sub y/(/spl tau/) -1 10/sup -13/ /spl tau/ /sup - 1/2 /on earth and /spl sigma//sub y/(/spl tau/) = 7 10/sup -14/ /spl tau//sup -frac12;/ in space. The quantum projection noise, the Dick effect and the detection laser noises are taken into account. The calculations are based on a preliminary model for the recapture of cold atoms, in reasonable agreement with measurements.