Gravity-induced geometric spin Hall effect of freely falling quantum particle

We discuss a new gravitational effect that the wave packet of a free-fall quantum particle undergoes a spin-dependent transverse shift in Earth's gravitational field. This effect is similar to the geometric spin Hall effect (GSHE) (Aiello 2009 et al Phys. Rev. Lett. 103 100401 ), and can be called gravity-induced GSHE. This effect suggests that the free-fall wave packets of opposite spin-polarized quantum particles can be split in the direction perpendicular to spin and gravity.