  Quantum entanglement provides a novel way to test short-distance quantum
physics in a non-relativistic regime. We provide entanglement-based protocols
to potentially test the magnetically induced dipole-dipole interaction and the
Casimir-Polder potential between the two nano-crystals kept in a Schrodinger
Cat state. Our scheme is based on the Stern-Gerlach (SG) apparatus, where we
can witness the entanglement mediated by these interactions for the
nano-crystal mass m~10^-19 kg with a spatial superposition size of order 0.1
micron in a trap relying on diamagnetic levitation. We show that it is possible
to close the SG interferometer in position and momentum with a modest gradient
in the magnetic field.
