Experimental Study of Quantum Graphs With Symplectic Symmetry*

Quantum graphs had been introduced as a powerful tool to study quantum chaos. Graphs with time-reversal symmetry (TRS) and broken time-reversal symmetry (BTRS), which correspond to the Gaussian orthogonal ensemble (GOE) and Gaussian unitary ensemble (GUE) respectfully, had been previously explored experimentally. We are introducing a microwave network with special design to study the Gaussian symplectic ensemble (GSE) statistics, which may be useful for research in quantum dots with strong spin-orbit scattering and other quantum chaotic systems. Two geometrically identical subgraphs with GUE symmetry are constructed from coaxial cables connected by T junctions. BTRS properties are realized by making nodes with circulators. The two subgraphs are connected with two bonds, along which one has phase shift of π, and the other one has zero phase shift. The phase shift π and 0 are achieved by putting short and open circuit connector caps into the bonds respectfully. This trick ensures the graph has an antiunitary symmetry T which squares to -1. Statistical analysis of both experimental data and simulations based on the Random Coupling Model (RCM) for this GSE graph will be presented.