  We address the problem of finding a system in which there would be measurable
quantum gravitational effects. Following standard quantum-field methods, we
have calculated the first-order radiative correction of graviton exchange on
the binding energy of an electron with an ultra cold superfluid droplet of
$^4$He with mass about the Planck mass. For two $^4$He droplets with a mass
difference of about one microgram, we show that the relative difference in the
binding energies is about one percent.
