Abelian and non-Abelian topological behavior of a neutral spin-1/2 particle in a background magnetic field

Abstract

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 non-Abelian Aharonov-Bohm effect due to the emergence of an effective 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 Wilzcek-Zee (WZ) mechanism in a full quantum setting. We show how degeneracy can be lifted by higher order gauge corrections that alter the semi-classical, non-Abelian, WZ phase. Models that allow analytic description offer 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 study concerns the emergence of gauge structure in neutral systems, the theory is also applicable to systems that posses 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.

References in corpus (21)

• Topological Insulators
• A Delayed Choice Quantum Eraser
• Quantum wave packet revivals
• Geometric phase from Aharonov-Bohm to Pancharatnam-Berry and beyond
• A quantum delayed choice experiment
• The Peierls substitution in an engineered lattice potential
• Consequences of Time-reversal-symmetry Breaking in the Light-Matter Interaction: Berry Curvature, Quantum Metric and Diabatic Motion
• Synthesis and Observation of Non-Abelian Gauge Fields in Real Space
• Is the molecular Berry phase an artifact of the Born-Oppenheimer approximation?
• Non-Abelian gauge field optics
• Internal Frame Dragging and a Global Analog of the Aharonov-Bohm Effect
• Classical and quantum dynamics of a particle constrained on a circle
• Coherent Control of the Rotational Degree of Freedom of a Two-Ion Coulomb Crystal
• A Brief Introduction to Wilson Loops and Large N
• Non-Abelian Berry phase for open quantum systems: Topological protection vs geometric dephasing
• Non-Abelian Geometric Dephasing
• Geometric gauge potentials and forces in low-dimensional scattering systems
• The Molecular Aharonov-Bohm effect Redux
• Geometric Phase Atom Optics and Interferometry
• Analytical evaluation and asymptotic evaluation of Dawson's integral and related functions in mathematical physics
• Synthetic Gauge Structures in Real Space in a Ring lattice

Cited by in corpus (2)

• Three-dimensional non-Abelian generalizations of the Hofstadter model: spin-orbit-coupled butterfly trios
• An exactly solvable model for anyons with non-Abelian flux