Abstract
Gauge fields, typified by the electromagnetic field, often appear as emergent phenomena due to geometrical properties of a curved Hilbert subspace, and provide a key mechanism for understanding such exotic phenomena as the anomalous and topological Hall effects. Non-abelian gauge potentials serve as a source of non-singular magnetic monopoles. Here we show that unlike conventional solid materials, the non-abelianness of emergent gauge potentials in spinor Bose-Fermi atomic mixtures can be continuously varied by changing the relative particle-number densities of bosons and fermions. The non-abelian feature is captured by an explicit dependence of the measurable spin current density of fermions in the mixture on the variable coupling constant. Spinor mixtures also provide us with a method to coherently and spontaneously generate a pure spin current without relying on the spin Hall effect. Such a spin current is expected to have potential applications in the new generation of atomtronic devices.
Highlights
Gauge fields, typified by the electromagnetic field, often appear as emergent phenomena due to geometrical properties of a curved Hilbert subspace, and provide a key mechanism for understanding such exotic phenomena as the anomalous and topological Hall effects
If a particle with spin degrees of freedom moves in a spatially varying magnetic field and its spin adiabatically follows the field’s direction, the particle accumulates a quantum-mechanical phase known as the Berry phase[3]. This phase arises from geometric properties of the Hilbert subspace composed of the spin and motional degrees of freedom, and it serves as an emergent gauge potential in the Hamiltonian description[4]
Examples include the anomalous Hall effect in magnetic materials due to non-coplanar spin configurations[6,7] and the topological Hall effect, which has been observed in both chiral magnets[8,9,10] and atomic Bose–Einstein condensates (BECs)[11] with skyrmion spin textures
Summary
Gauge fields, typified by the electromagnetic field, often appear as emergent phenomena due to geometrical properties of a curved Hilbert subspace, and provide a key mechanism for understanding such exotic phenomena as the anomalous and topological Hall effects. The non-abelianness of the emergent gauge potential is characterized by an explicit dependence of the spin current density in the Fermi gas on the variable coupling constant.
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