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Freely falling point-like objects converge towards the center of the Earth.Hence the gravitational field of the Earth is inhomogeneous, and possesses atidal component. The free fall of an extended quantum object such as a hydrogenatom prepared in a high principal-quantum-number stretch state, i.e., acircular Rydberg atom, is predicted to fall more slowly that a classicalpoint-like object, when both objects are dropped from the same height fromabove the Earth. This indicates that, apart from "quantum jumps," the atomexhibits a kind of "quantum incompressibility" during free fall ininhomogeneous, tidal gravitational fields like those of the Earth. Asuperconducting ring-like system with a persistent current circulating aroundit behaves like the circular Rydberg atom during free fall. Like the electronicwavefunction of the freely falling atom, the Cooper-pair wavefunction is"quantum incompressible." The ions of the ionic lattice of the superconductor,however, are not "quantum incompressible," since they do not possess a globallycoherent quantum phase. The resulting difference during free fall in theresponse of the nonlocalizable Cooper pairs of electrons and the localizableions to inhomogeneous gravitational fields is predicted to lead to a chargeseparation effect, which in turn leads to a large repulsive Coulomb force thatopposes the convergence caused by the tidal, attractive gravitational force onthe superconducting system. A "Cavendish-like" experiment is proposed forobserving the charge separation effect induced by inhomogeneous gravitationalfields in a superconducting circuit. This experiment would demonstrate theexistence of a novel coupling between gravity and electricity viamacroscopically coherent quantum matter.

Quantum incompressibility of a falling Rydberg atom, and a gravitationally-induced charge separation effect in superconducting systems