= Gravitational phase shift in matter-wave interferometry
{title2=$\Delta\varphi=mgA/(\hbar v)$}
For equal-speed nonrelativistic matter waves in an interferometer with signed enclosed vertical area $A$, a uniform <gravitational acceleration> gives the displayed leading-order phase difference. In a rectangular device, the horizontal paths differ in <gravitational potential energy> by $mg h$ for a time $\ell/v$, so their phase difference has magnitude $mg h\ell/(\hbar v)$. Assumptions include negligible fractional changes of speed, matched unperturbed optical paths and a consistent treatment of the beam splitters. The <Colella–Overhauser–Werner experiment> uses neutron interference to test this gravitational phase.
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