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To date, no framework combining quantum field theory and general relativityand hence unifying all four fundamental interactions, exists. Violations of theEinstein's equivalence principle (EEP), being the foundation of generalrelativity, may hold the key to a theory of quantum gravity. The universalityof free fall (UFF), which is one of the three pillars of the EEP, has beenextensively tested with classical bodies. Quantum tests of the UFF, e.g. byexploiting matter wave interferometry, allow for complementary sets of testmasses, orders of magnitude larger test mass coherence lengths andinvestigation of spin-gravity coupling. We review our recent work towardshighly sensitive matter wave tests of the UFF on ground. In this scope, thefirst quantum test of the UFF utilizing two different chemical elements, Rb-87and K-39, yielding an E\"otv\"os ratio $\eta_{\,\text{Rb,K}}=(0.3\pm 5.4)\times10^{-7}$ has been performed. We assess systematic effects currently limitingthe measurement at a level of parts in $10^8$ and finally present ourstrategies to improve the current state-of-the-art with a test comparing thefree fall of rubidium and ytterbium in a very long baseline atom interferometrysetup. Here, a 10 m baseline combined with a precise control of systematiceffects will enable a determination of the E\"otv\"os ratio at a level of partsin $10^{13}$ and beyond, thus reaching and overcoming the performance limit ofthe best classical tests.

Ground Tests of Einstein's Equivalence Principle: From Lab-based to 10-m Atomic Fountains