Fig. 3: Experimental observation of evolution trajectories in the phase space.
From: Nonlinear Chiral-like State Transfer realized with a minimal set of parameters
a The circuit used in the experiment, showing the inductors (L), capacitors (C), resistors (R), diodes (D), and an amplifier (A). The left black dashed rectangular marks the negative resistor \(-{{{\rm{R}}}}_{A}\) \(\left(\left|{{{\rm{V}}}}_{A}\right|\right)\), while the right one marks the inductive element \({L}_{A}\), the value of which is selected by the triple-throw switch. b A photo of the experimental setup. c The relative phase difference \({\theta }_{B-A}={{\rm{arg }}}\left({V}_{B}\right)-{{\rm{arg }}}\left({V}_{A}\right)\) versus the perturbation \(\delta y\) by varying \({L}_{A}\). Here, the perturbation \(\delta y\) is defined as \(\delta y\equiv ({\omega }_{A}-{\omega }_{A0})/2\pi\), where \({\omega }_{A0}\) represents the resonance frequency of resonator A when \({L}_{0}\) is connected in series with \({L}_{i}\) (the effective inductance marks LA0). The measured values are averaged over 8 independent measurements. The experimental errors (standard deviation over these 8 measurements) are smaller than the marker size. For demonstration purposes, we exaggerate the error bars by a factor of five. d The measured evolution trajectories in the phase space with different initial states (marked by the colored squares). In (c), \({S}_{i}\) = 0, \({S}_{1}\) = 2.66 and \({S}_{2}\) = −2.76. In (d), \(\delta y={S}_{i}=0\). Parameters used in the experiments are LA0 = 229.1 μH, C0 = 18.3 nF, Cc = 4 nF, RB = 945.1 Ω, and LB = 226.9 μH. The detail property of \({{{\rm{R}}}}_{{{\rm{A}}}}\) is calibrated in S.M. Sec. 4 of ref. 32.
