Cancellation of the Collisional Frequency Shift in Caesium Fountain Clocks

We have observed that the collisional frequency shift in primary caesium fountain clocks varies with the clock state population composition and, in particular, is zero for a given fraction of the $|F=4,m_F=0⟩$ atoms, depending on the initial cloud parameters. We present a theoretical model explaining our observations. The possibility of the collisional shift cancellation implies an improvement in the performance of caesium fountain standards and a simplification in their operation.