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We present a novel fundamental effect that for the matter waves thespace-averaging free-fall point of quantum particles undergoes a spin-dependenttransverse shift in the gravitational field of Earth. This effect is similar tothe geometric spin Hall effect (GSHE) [Aiello et al., Phys. Rev. Lett. 103,100401 (2009)] and can be called gravity-induced GSHE. This effect suggeststhat there might be violations of the universality of free fall (UFF) or weakequivalence principle (WEP) in the quantum domain.

Gravity-induced geometric spin Hall effect as a probe of universality of free fall of quantum particle