Accurate temperature measurement of cold atoms in cesium fountain clocks

We introduce a new approach to determine if a cloud of cold atoms has or not a unique, well-defined temperature. In the first case, the temperature can be determined using the width of the velocity distribution. However, the temperature in a cloud of cold atoms may not be well-defined if the velocity distribution does not turn out to be Gaussian. In this case, the width of the velocity distribution cannot be associated to a unique temperature, and additional considerations exposed here should be followed to measure the temperatures of two groups of atoms forming the whole cloud. Also an uncertainty evaluation is presented.