Cancellation of the collision shift in caesium fountains

Collisions contributing to the shift of the clock transition frequency in a caesium fountain take place during the Ramsey interaction time, i.e. between the two passages through the Ramsey microwave cavity. Collision energies derived simply from the initial temperature T₀ do not provide an adequate description of the collision processes during this time. This is due to the expansion of the atomic cloud and correlations between position and velocity, which develop in the course of the ballistic flight. As the cloud expands, collisions are only possible for atoms with small relative velocities. As a result, for T₀ = 1 μK and initial cloud size less than 1 mm, above the microwave cavity the collision energies divided by the Boltzmann constant are less than 300 nK.

For these collision energies the rate coefficients λ₃₀ and λ₄₀, which describe the collision shift contribution from atoms in a given state, differ in sign. This gives rise to a strong variation of the collisional shift of the clock transition frequency as the composition of the clock states after the first Ramsey interaction is varied. The collision shift is expected to vary linearly with clock state composition, which can be changed conveniently by adjusting the amplitude of the microwave field in the Ramsey cavity. These predictions have been experimentally verified at NPL and PTB.

These findings open up the possibility of cancelling the collisional shift, leading to an improvement in the performance of caesium fountain primary frequency standards.

Firstly we note that in a fountain working at cancellation point (fraction of the atoms in the |4, 0> state ρ₄₀ = 0.4) the fringe contrast (hence the signal to noise ratio and the short-term stability) is only reduced by 3.5 %. If the launch parameters and the microwave field amplitude in the cavity are sufficiently stable, uncertainty of the collisional shift at the parts in 10¹⁶ level should be achievable without any need for extrapolation, which would shorten the averaging time required. Alternatively, one could operate a fountain in the vicinity of the zero-shift point and extrapolate the residual shift to zero density. Assuming that the deviation in linearity between the number of atoms and the density causes an error in the collisional shift evaluation of less than 10 % of the shift itself, the uncertainty of the shift may be reduced to parts in 10¹⁷, if one can neglect collisions with atoms residually populating the |F = 3, m_F ≠ 0> state.