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The equivalence principle of gravity is examined at the quantum level usingthe diffraction in time of matter waves in two ways. First, we consider aquasi-monochromatic beam of particles incident on a shutter which is removed attime $t = 0$ and fall due to the gravitational field. The probability densityexhibits a set of mass-dependent oscillations which are genuinely quantum innature, thereby reflecting quantum violations to the weak equivalenceprinciple, although the strong equivalence principle remains valid. We estimatethe degree of violation in terms of the width of the diffraction-in-timeeffect. Second, motivated by the recent advances in the manipulation ofultracold atoms and neutrons as well as the experimental observation of quantumstates of ultracold neutrons in the gravitational field above a flat mirror, westudy the diffraction in time of a suddenly released beam of particlesinitially prepared in gravitational quantum bound states. In this case, wequantify the degree of violation by comparing the time of flight from the meanposition of the initial wave packet versus the time of flight as measured fromthe mirror. We show that, in this case both the weak and strong versions of theequivalence principle are violated. We demonstrate that compatibility betweenequivalence principle and quantum mechanics is recovered in the macroscopic(large-mass) limit. Possible realizations with ultracold neutrons, cesium atomsand large molecules are discussed.

Testing the equivalence principle with time-diffracted free-falling quantum particles