Figure 3
From: Synthetic Gauge Structures in Real Space in a Ring lattice
The degenerate eigenstates and their time evolution. (Line Plots) The real (blue) and imaginary (red) components of the dark states, \({\Phi }_{1}\) on the left and \({\Phi }_{2}\) on the right panels, are shown for three cases that differ in regards to which of the parameters \(\varphi \), and α are allowed to vary in time. The solid lines represent the states at the halfway point of the evolution, and the dashed lines at completion. The potential barriers are measured along the right axis, and share the label (A, B, C, D) of each right adjacent well. The last case, \(\varphi \ne 0\), \(\alpha \ne 0\) is the only one with non-vanishing imaginary component which still vanishes at completion. (Surface Plots) Time evolutions of the population in the wells for case (I) Abelian (upper) and case (II) quasi-Abelian (lower) which is similar to that of case (III) non-Abelian. Red bars mark the barrier positions.
