Neutron-gravity interferometry experiment: testing Earth's rotating frequency fluctuations via neutron Berry's phases due to spin-rotation couplings

Neutron spin can be coupled to the Earth's rotating frequency. Once if the Earth's rotating frequency is time-dependent, then the neutron will acquire a Berry's topological phase (cyclic adiabatic geometric phase). So, a potential method to investigate the Earth's time-varying rotating frequency by measuring the phase difference between geometric phases of neutron spin polarized vertically down and up is proposed.