The Aharonov Casher phase of a bipartite entanglement pair traversing a quantum square ring

We propose in this article a quantum square ring that conveniently generates, annihilates and distills the Aharonov Casher phase with the aid of entanglement. The non-Abelian phase is carried by a pair of spin-entangled particles traversing the square ring. At maximal entanglement, dynamic phases are eliminated from the ring and geometric phases are generated in discrete values. By contrast, at partial to no entanglement, both geometric and dynamic phases take on discrete or locally continuous values depending only on the wavelength and the ring size. We have shown that entanglement in a non-Abelian system could greatly simplify future experimental efforts revolving around the studies of geometric phases.