Fig. 1

Artificial gauge fields engineering via periodically modulated driving. By tailoring the temporal dependence of the driving parameters—either the amplitude \({\cal K}(t)\) or the phase a(t)—we are able to create an artificial gauge field which controls the time-reversal symmetry properties of a periodically driven (Floquet) system. For example, for a time-symmetric kick sequence a the system belongs to the orthogonal symmetry class, whereas a kick sequence without any particular symmetry axes b puts the system in the unitary symmetry class (broken T-symmetry). c, d Our kicked-rotor system with periodic amplitude (or phase) modulations (1) maps on a disordered synthetic nanotube in momentum space threaded by an artificial Aharonov–Bohm flux Φ₂. For the symmetric sequence a this flux is zero, whereas a non-symmetric sequence b corresponds to the presence of a non-zero Aharonov–Bohm flux Φ₂ (sketched as the light blue area). Experimentally, two distinct interference signatures can be used to characterize symmetry and localization: the disappearance of the CBS peak is a clear-cut signature of the symmetry breaking, while the emergence of a CFS peak is a direct interference signature of the onset of Anderson localization, in both symmetry classes