  In this paper, a quantum Stern-Gerlach thought experiment is introduced
where, in addition to the intrinsic angular momentum of an atom, the magnetic
field is also treated quantum mechanically. A freely falling spin polarised
Bose-Einstein condensate passes close to a flux-qubit and interacts with the
quantum superimposed magnetic field of the flux-qubit. Such an interaction
results a macroscopic quantum entanglement of the path of a Bose-Einstein
condensate with the magnetic flux quantum state of the flux-qubit. In this
paper, three regimes of coupling between the flux-qubit and a freely falling
Bose-Einstein condensate are discussed. The decoherence time limit required to
achieve a strong coupling regime is also estimated. This paper also explores,
how to produce a path entangled Bose-Einstein condensate where, the condensate
can be located at physically distinct locations simultaneously. Paper provides
new fundamental insights about the foundations of the quantum Stern-Gerlach
experiment.
