Fig. 3: Experimental demonstration of topological transport in hyperbolic networks.
From: Anomalous and Chern topological waves in hyperbolic networks
a Photograph of the experimental prototype (top layer), consisting of 200 circulators with n = 3 layers. The circulators are connected by coplanar waveguides (CPWs). b Schematic for measuring the topological invariant of the hyperbolic lattice. The magnetic flux Φ in the topological pump (left panel) is synthetically realized by applying twisted boundary conditions with a tunable non-reciprocal phase delay ± Φ (right panel). The topological invariant W counts the winding of the reflection coefficient at a probe on the edge during a cycle of the non-reciprocal phase delay from 0 to 2π (from 0 to −2π in the opposite direction). c Experimental setup for measuring the topological invariant in the hyperbolic scattering network. Three designed phase shifters provide phase delays +Φ and −Φ in two opposite directions by tuning the bias voltages V1 and V2, respectively. The inset depicts the phase delay as a function of bias voltage. d Measured topological invariant W in the frequency spectrum. The darker blue and grey areas (split by dashed lines) respectively feature edge modes and bulk modes, according to the predicted bandgap map (see Supplementary Fig. 12d). e, f Measured field maps (e) and measured windings of reflection coefficient (f). The frequencies are 5.8 GHz (W = 1, edge mode), 5.9 GHz (W = 0, bulk mode), 6.0 GHz (W = 1, edge mode), and 6.1 GHz (W = 0, bulk mode).
