  Freely falling point-like objects converge toward the center of the Earth.
Hence the gravitational field of the Earth is inhomogeneous, and possesses a
tidal component. The free fall of an extended quantum mechanical object such as
a hydrogen atom prepared in a high principal-quantum-number state, i.e. a
circular Rydberg atom, is predicted to fall more slowly than a classical
point-like object, when both objects are dropped from the same height above the
Earth's surface. This indicates that, apart from transitions between quantum
states, the atom exhibits a kind of quantum mechanical incompressibility during
free fall in inhomogeneous, tidal gravitational fields like those of the Earth.
  A superconducting ring-like system with a persistent current circulating
around it behaves like the circular Rydberg atom during free fall. Like the
electronic wavefunction of the freely falling atom, the Cooper-pair
wavefunction is quantum mechanically incompressible. The ions in the lattice of
the superconductor, however, are not incompressible, since they do not possess
a globally coherent quantum phase. The resulting difference during free fall in
the response of the nonlocalizable Cooper pairs of electrons and the
localizable ions to inhomogeneous gravitational fields is predicted to lead to
a charge separation effect, which in turn leads to a large Coulomb force that
opposes the convergence caused by the tidal gravitational force on the
superconducting system.
  A "Cavendish-like" experiment is proposed for observing the charge separation
effect induced by inhomogeneous gravitational fields in a superconducting
circuit. The charge separation effect is determined to be limited by a
pair-breaking process that occurs when low frequency gravitational
perturbations are present.
