  Engineering topological quantum order has become a major field of physics.
Many advances have been made by synthesizing gauge fields in cold atomic
systems. Here, we carry over these developments to other platforms which are
extremely well suited for quantum engineering, namely trapped ions and
nano-trapped atoms. Since these systems are typically one-dimensional, the
action of artificial magnetic fields has so far received little attention.
However, exploiting the long-range nature of interactions, loops with
non-vanishing magnetic fluxes become possible even in one-dimensional settings.
This gives rise to intriguing phenomena, such as fractal energy spectra, flat
bands with localized edge states, and topological many-body states. We
elaborate on a simple scheme for generating the required artificial fluxes by
periodically driving an XY spin chain. Concrete estimates demonstrating the
experimental feasibility for trapped ions and atoms in waveguides are given.
