Fig. 2: Loop dynamics and topological transitions in interacting hysteretic scatterers with asymmetric dual modulation.
From: Topological hysteretic winding for temporal anti-lasing
a Experimental setup for dynamic topological transitions. Two circulators interact through a bidirectional transmission line and are modulated at different periods Tm1,m2 or amplitudes Vm1,m2. Two of the ports are used for scattering measurements, while all other ports are left unexcited and matched. Multiple periods of winding loops are recorded over time, leading to the accumulated charge Q over time, and we observe two types of topological transitions. b Path switch topological transition, obtained for (1/Tm1, 1/Tm2) = (100, 100.1) Hz and Vm1 = Vm2 = 4 V. The loop crosses zero and collapse, before crossing zero again, flipping the winding direction. c, Loop switch topological transition, obtained for (1/Tm1, 1/Tm2) = (100, 100.1) Hz and (Vm1, Vm2) = (4, 2) V. Two counter-winding loops form an “8”-shaped path, also allowing for a topological transition. Insets show the corresponding winding loop at the arrowhead instant, and the stars mark the singularity of \(\det (S)=0\) in polar coordinates. Topological transitions occur when the color of the line changes.
