A Gravity of Earth Measurement with a qBOUNCE Experiment

We report a measurement of the local acceleration $g$ with ultracold neutrons based on quantum states in the gravity potential of the Earth. The new method uses resonant transitions between the states $|1u003e -u003e |3u003e$ and for the first time between $|1u003e -u003e |4u003e$. The measurements demonstrate that Newtonu0027s Inverse Square Law of Gravity is understood at micron distances at an energy level of $10^{-14}$ eV with $frac{Delta g}{g}=4times10^{-3}$. The results provide constraints on any possible gravity-like interaction at a micrometer interaction range. In particular, a dark energy candidate, the chameleon field is restricted to $betau003c6.9times10^{6}$ for $n=2$ (95% C.L.).