  A field, which mediates entanglement between two quantum systems, must be of
quantum nature. Attempts to witness this way quantumlike features of the
gravitational field with tabletop experiments are actively studied recently, in
particular by considering to look at two masses in a superposition in two
locations, each in one interferometer. Entanglement intervention is probed when
the interferometers are put side by side. If the masses interact only via
Newtonian attraction, and still some degree of entanglement is found, than the
gravitational field must be quantum like, or at least non-classical. The masses
considered are mesoscopic, 10-14 Kg to 10-12 Kg, and in one proposal
Mach-Zehnder interferometry is considered. Liquid He4 is superfluid below 2.17
K, and shows macroscopic quantum behaviour, in particular matter
interferometry, as in the Superfluid He Quantum Inteference Device - SHeQUID.
With its Josephson junctions as slits, the SHeQUID parallels a Mach-Zehnder. In
this case the matter quantities involved are macroscopic, 10-8 Kg. We propose
and analize the feasibility of a scheme on the lines of the above, where the
matter field is given by superfluid He4, and the Mach-Zehnder's are two
SHeQUID, put side by side. We find that the proposed experiment is feasible,
using only well demonstrated methods and technologies, with no need to
extensions beyond the current frontiers.
