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Freely falling point-like objects converge toward 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 mechanical object such asa hydrogen atom prepared in a high principal-quantum-number state, i.e. acircular Rydberg atom, is predicted to fall more slowly than a classicalpoint-like object, when both objects are dropped from the same height above theEarth's surface. This indicates that, apart from transitions between quantumstates, the atom exhibits a kind of quantum mechanical incompressibility duringfree fall in inhomogeneous, tidal gravitational fields like those of the Earth.  A superconducting ring-like system with a persistent current circulatingaround it behaves like the circular Rydberg atom during free fall. Like theelectronic wavefunction of the freely falling atom, the Cooper-pairwavefunction is quantum mechanically incompressible. The ions in the lattice ofthe superconductor, however, are not incompressible, since they do not possessa globally coherent quantum phase. The resulting difference during free fall inthe response of the nonlocalizable Cooper pairs of electrons and thelocalizable ions to inhomogeneous gravitational fields is predicted to lead toa charge separation effect, which in turn leads to a large Coulomb force thatopposes the convergence caused by the tidal gravitational force on thesuperconducting system.  A "Cavendish-like" experiment is proposed for observing the charge separationeffect induced by inhomogeneous gravitational fields in a superconductingcircuit. The charge separation effect is determined to be limited by apair-breaking process that occurs when low frequency gravitationalperturbations are present.

Quantum Incompressibility of a Freely Falling Hydrogen Atom in a  Circular Rydberg State, and a Gravitationally-Induced Charge Separation  Effect in Superconducting Systems