Experimental investigation of distributions of the off-diagonal elements of the scattering and the Wigner's $\hat{K}$ matrices for networks with broken time reversal invariance

Abstract

We present an extensive experimental study of the distributions of the real and imaginary parts of the off-diagonal elements of the scattering matrix $\hat{S}$ and the Wigner's reaction $\hat{K}$-matrix for open microwave networks with broken time ($T$) reversal invariance. Microwave Faraday circulators were applied in order to break $T$-invariance. The experimental distributions of the real and imaginary parts of the off-diagonal entries of the scattering matrix $\hat{S}$ are compared with the theoretical predictions from the supersymmetry random matrix theory [A. Nock, S. Kumar, H.-J. Sommers, and T. Guhr, Annals of Physics {\bf 342}, 103-132 (2014)]. Furthermore, we show that the experimental results are in very good agreement with the recent predictions for the distributions of the real and imaginary parts of the off-diagonal elements of the Wigner's reaction $\hat{K}$-matrix obtained within the framework of the Gaussian unitary ensemble of random matrix theory (RMT) [S. B. Fedeli and Y. V. Fyodorov, J. Phys. A: Math. Theor. {\bf 53}, 165701 (2020)]. Both theories include losses as tunable parameters and are therefore well adapted to the experimental verification.

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• Closed and open superconducting microwave waveguide networks as a model for quantum graphs
• Coupled unidirectional chaotic microwave graphs
• Families of isospectral and isoscattering quantum graphs
• Experimental study of the distributions of off-diagonal scattering-matrix elements of quantum graphs with symplectic symmetry
• Universality Emerging in a Universality: Derivation of the Ericson Transition in Stochastic Quantum Scattering and Experimental Validation