Abstract
Emergence of fundamental forces from gauge symmetry is among our most profound insights about the physical universe. In nature, such symmetries remain hidden in the space of internal degrees of freedom of subatomic particles. Here we propose a way to realize and study gauge structures in real space, manifest in external degrees of freedom of quantum states. We present a model based on a ring-shaped lattice potential, which allows for both Abelian and non-Abelian constructs. Non trivial Wilson loops are shown possible via physical motion of the system. The underlying physics is based on the close analogy of geometric phase with gauge potentials that has been utilized to create synthetic gauge fields with internal states of ultracold atoms. By scaling up to an array with spatially varying parameters, a discrete gauge field can be realized in position space, and its dynamics mapped over macroscopic size and time scales.
Highlights
Gauge theories originated as an attempt by H
Gauge structures were found to appear naturally in the adiabatic evolution of quantum systems, as definitively shown by Berry[6], anticipated in an earlier work on effective nuclear Hamiltonians in the Born-Oppenheimer approximation[7]. This discovery led to multiple studies, both theoretical and experimental, that identified such structures in diverse phenomena such as nuclear magnetic resonance[8], nuclear quadrupole resonance[9,10], effective nuclear Hamiltonians in diatoms[11] and in the context of molecular Kramers degeneracy[12] and in atomic collisions[13]
The same principle has been applied extensively to generate numerous phenomena based on synthetic gauge structures in neutral ultracold atoms[14,15,16,17]
Summary
Emergence of fundamental forces from gauge symmetry is among our most profound insights about the physical universe. Gauge structures were found to appear naturally in the adiabatic evolution of quantum systems, as definitively shown by Berry[6], anticipated in an earlier work on effective nuclear Hamiltonians in the Born-Oppenheimer approximation[7]. This discovery led to multiple studies, both theoretical and experimental, that identified such structures in diverse phenomena such as nuclear magnetic resonance[8], nuclear quadrupole resonance[9,10], effective nuclear Hamiltonians in diatoms[11] and in the context of molecular Kramers degeneracy[12] and in atomic collisions[13]. Gauge structures remain typically associated with some internal degrees of freedom, in the latter case, the electronic and nuclear states of atoms, even when the parameters inducing the adiabatic changes could be external or even classical in nature. Since gravity is associated with general co-ordinate transformations[19] but the other fundamental forces are tied to gauge transformations, the construction of gauge structures in macroscopic co-ordinate space may help to diminish that persistent gulf, with experiments that can probe both kinds of transformations in a shared space
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