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Freely falling point-like objects converge towards the center of the
Earth. Hence the gravitational eld of the Earth is inhomogeneous, and
possesses a tidal component. The free fall of an extended quantum object
such as a hydrogen atom prepared in a high principal-quantum-number
stretch state, i.e., a circular Rydberg atom, is predicted to fall more slowly
that a classical point-like object, when both objects are dropped from
the same height from above the Earth. This indicates that, apart from
\quantum jumps," the atom exhibits a kind of \quantum incompressibility" during free fall in inhomogeneous, tidal gravitational elds 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 incompressible." The ions of the ionic lattice
of the superconductor, however, are not \quantum 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 elds
is predicted to lead to a charge separation eect, which in turn leads to
a large repulsive Coulomb force that opposes the convergence caused by
the tidal, attractive gravitational force on the superconducting system.
A \Cavendish-like" experiment is proposed for observing the charge
separation eect induced by inhomogeneous gravitational elds in a superconducting circuit. This experiment would demonstrate the existence
of a novel coupling between gravity and electricity via macroscopically
coherent quantum matter