Quantum Stern-Gerlach experiment and path entanglement of Bose-Einstein condensate

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.