Topological Behavior of a Neutral Spin-1/2 Particle in a Background Magnetic Field

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Physical Review A





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We present results of a numerical experiment in which a neutral spin-1/2 particle subjected to a static magnetic vortex field passes through a double slit barrier. We demonstrate that the resulting interference pattern on a detection screen exhibits fringes reminiscent of Aharonov-Bohm scattering by a magnetic flux tube. To gain better understanding of the observed behavior, we provide analytic solutions for a neutral spin-1/2 rigid planar rotor in the aforementioned magnetic field. We demonstrate how that system exhibits a generalized Aharonov-Bohm effect [Wu and Yang, Phys. Rev. D 12, 3845 (1975)0556-282110.1103/PhysRevD.12.3845], due to the emergence of an effective SU(2) Wu-Yang (WY) flux tube. We study the behavior of the gauge invariant partition function and demonstrate a topological phase transition for the spin-1/2 planar rotor. We provide an expression for the partition function in which its dependence on the Wilson loop integral of the WY gauge potential is explicit. We generalize to a spin-1 system in order to explore the Wilczek-Zee (WZ) mechanism in a full quantum setting. We show how degeneracy is lifted by higher-order gauge corrections that alter the semiclassical WZ phase. Models that allow analytic description provide a foil to objections that question the fidelity of predictions based on the generalized Born-Oppenheimer approximation in atomic and molecular systems. Though the primary focus of this paper concerns the emergence of gauge structure in neutral systems, the theory is also applicable to systems that possess electric charge. In that case, we explore interference between fundamental gauge fields (i.e., electromagnetism) with effective 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.


Atomic, Molecular and Optical Physics



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