The Harper-Hofstadter model describes particles in two-dimensional (2D) lattices subjected to a uniform magnetic field. Ultracold atomic gases in optical lattices are an ideal platform to study this model, thanks to their capability for realizing large and tunable magnetic fluxes per lattice plaquette. We experimentally assembled such a 2D lattice rolled into a long tube, just 3-site around, thereby realizing periodic boundary conditions. These three sites were constructed from a synthetic dimension built from the atoms’ internal degrees of freedom. We inserted an additional longitudinal flux through the long axis of the cylinder, a process which has no analogy in a planar geometry. We observe a time-domain order-by-disorder transition: When the transverse flux is a simple rational number (2/3 in our experiments), the system’s unitary evolution is exquisitely sensitive to the longitudinal flux and becomes incoherent when all values of the longitudinal flux are sampled. Remarkably, away from simple rational fractions, the temporal order is restored. We explain that this transition can be understood equivalently in terms of a spatial self-averaging effect or interference between different matter-wave momentum states.
(pizza and drinks served 10 min. before talk)
