Topological behavior of a neutrals spin-1/2 particle in a background magnetic field

Following a suggestion in [J. March-Russell, J. Preskill, and F. Wilczek, Phys. Rev. Lett. 68, 2567 (1992)] we present results of a numerical experiment in which a neutral spin-1/2 particle is subjected to a static magnetic vortex field as passes through a double slit barrier. We demonstrate that the resulting interference pattern on a detection screen exhibits fringes that are identical to that produced by a charged particle undergoing Aharonov-Bohm (AB) scattering. We provide analytic solutions to systems that exhbit synthetic gauge fields that allow an SU(2) generalization of AB scattering. We provide an expression for the partition function in which the dependence of the Wilson loop integral of the synthetic gauge potential is explicit and demonstrates a topological phase transition. We explore the interference between fundamental gauge fields (i.e. electromagnetism) with effective synthetic gauge potentials. We propose a possible laboratory demonstration for the latter in an ion trap setting. We illustrate how effective gauge potentials influence wave-packet revivals in the said ion trap.