  We demonstrate Floquet engineering in a basic yet scalable 2D architecture of
individually trapped and controlled ions. Local parametric modulations of
detuned trapping potentials steer the strength of long-range inter-ion
couplings and the related Peierls phase of the motional state. In our
proof-of-principle, we initialize large coherent states and tune modulation
parameters to control trajectories, directions and interferences of the phonon
flow. Our findings open a new pathway for future Floquet-based trapped-ion
quantum simulators targeting correlated topological phenomena and dynamical
gauge fields.
