Geometric gauge potentials and forces in low-dimensional scattering systems

Abstract

We introduce and analyze several low-dimensional scattering systems that exhibit geometric phase phenomena. The systems are fully solvable and we compare exact solutions of them with those obtained in a Born-Oppenheimer projection approximation. We illustrate how geometric magnetism manifests in them, and explore the relationship between solutions obtained in the diabatic and adiabatic pictures. We provide an example, involving a neutral atom dressed by an external field, in which the system mimics the behavior of a charged particle that interacts with, and is scattered by, a ferromagnetic material. We also introduce a similar system that exhibits Aharonov-Bohm scattering. We propose some practical applications. We provide a theoretical approach that underscores universality in the appearance of geometric gauge forces. We do not insist on degeneracies in the adiabatic Hamiltonian, and we posit that the emergence of geometric gauge forces is a consequence of symmetry breaking in the latter.

(Final version, published in Phy. Rev. A. 86, 042704 (2012)

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• Artificial gauge potentials for neutral atoms
• Synthetic magnetic fields for ultracold neutral atoms
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• A Bose-Einstein Condensate in a Uniform Light-induced Vector Potential
• Generalized Rashba spin-orbit coupling for cold atoms
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Cited by in corpus (9)

• Light-induced gauge fields for ultracold atoms
• Is the molecular Berry phase an artifact of the Born-Oppenheimer approximation?
• Molecular geometric phase from the exact electron-nuclear factorization
• Three-body bound states in dipole-dipole interacting Rydberg atoms
• Few-Body Bound States of Dipole-Dipole Interacting Rydberg Atoms
• The Molecular Aharonov-Bohm effect Redux
• Geometric Phase Atom Optics and Interferometry
• Topological spin models in Rydberg lattices
• Abelian and non-Abelian topological behavior of a neutral spin-1/2 particle in a background magnetic field