  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 $10\,\%$.
