Figure 3
(a) Color map of maximum deviation parameter, \(\epsilon \), of the final spin direction from the fixed points \({z}_{A,B}\) after encircling protocols \({P}_{\mathrm{1,2}}\), as a function of initial protocol phase \({\varphi }_{0}\) (deviation from the line of \({\mathscr{P}}{\mathscr{T}}\)-symmetry, \({h}_{y}=0\)) and protocol frequency \(\omega \), plotted in logarithmic scale. The deviation \(\epsilon \) is a measure of effectiveness of the non-reciprocal spin-filter effect. (b) Dependence of the deviation parameter on the initial phase for a range of protocol frequencies, showing that slower encircling protocols yield higher non-reciprocal efficiency. The plot corresponds to encircling protocols starting and ending on the black dashed line in panel (a). (c) The deviation parameter as a function of protocol radius R0. A sharp jump in deviation from perfect non-reciprocity is observed for large radii within the considered range, corresponding to the boundary of the high-efficiency region in panel (a), shown in blue. The size of the region with small deviation parameter \(\epsilon \) shrinks with increasing frequency. The plot corresponds to encircling protocols starting and ending on the white dashed line in panel (a).
