Status and plans of the Gravitational Behaviour of Antihydrogen at Rest experiment

The GBAR experiment aims to directly test the Weak Equivalence Principle of ultracold antihydrogen in Earth's gravitational field. The gravitational acceleration $\bar{g}$ will be measured to a precision of $1\,\%$ using a classical free fall of the anti-atoms from a fixed height. Reaching a precision of $10^{-6}$ is planned by performing a "quantum free fall" experiment by detecting quantum interference of $\mathrm{\bar{H}}$ due to quantum gravitational bound states above a reflecting surface. Additionally, a $\mathrm{\bar{H}}$ Lamb shift measurement is being prepared in parallel that will allow to determine the antiproton charge radius at the level of $10\,\%$.