Maximizing gravitational acceleration measurement accuracy by tuning the interaction time between atoms and gravity

Abstract

We propose a technique using an atom interferometer to obtain the most accurate measurement of gravitational acceleration by changing the interaction time between the atoms and gravity in a harmonic trap. The analytical calculation procedure is based on the Feynman path integral method. The first Kapitza–Dirac (KD) scattering pulse splits the initial state into several modes with different momenta. Before adding the second KD pulse, the interaction time between the atoms and gravity is changed. These modes have a position shift as a result of the gravitational field and are coherently recombined by the harmonic potential. The second KD pulse splits the evolved modes a second time and separates them along different paths again. At the measurement time, we obtain the greatest accuracy from the quantum Fisher information. For the variation of gravitational acceleration on the surface of earth, an accuracy of $$10^{-9}$$ can be achieved at any value of gravity acceleration by tuning the interaction time between the atoms and gravity.