This work proposes a method for constructing a relative atomic gravimeter based on the use of an atomic fountain on ultracold atoms. The method is based on measuring the shift of the Ramsey spectrum line in an atomic fountain in a gravitational field. For a fountain-type microwave frequency standard on Cs atoms, the accuracy of the gravitational field measurement is $\delta g=2\times10^{-6}g/\sqrt{\tau_a}$. With integration time $\tau_a=10000 s$, the achievable accuracy is $\delta g\approx2\times10^{-8}\approx20\,\mu$Gal.

Schematic of an atomic fountain gravimeter using a microwave clock transition. The time of flight of atoms through a microwave gravimeter T depends on the acceleration of gravity g. This leads to a shift in the frequency corresponding to Ramsey resonances at frequencies other than the exact resonance when the acceleration of gravity changes.

A.Afanasiev et al.,
JETP Letters 119, issue 2 (2024)