Microwave Realization of the Gaussian Symplectic Ensemble

Area of Science:

• Quantum chaos
• Condensed matter physics
• Microwave network theory

Background:

• Antiunitary symmetry (T^2 = -1) is crucial in quantum mechanics, particularly in systems exhibiting Kramers degeneracy.
• Previous theoretical work suggested the realization of such symmetries in engineered systems like microwave graphs.
• Understanding spectral properties in chaotic systems with antiunitary symmetry is key to exploring quantum chaos phenomena.

Purpose of the Study:

• To experimentally realize a microwave graph exhibiting antiunitary symmetry (T^2 = -1).
• To identify and analyze Kramers doublets in the realized system.
• To investigate the effect of symmetry-breaking perturbations on the spectral properties and compare with theoretical predictions.

Main Methods:

• Construction of a microwave graph designed to possess antiunitary symmetry.
• Experimental measurement of the system's spectral properties.
• Analysis of spectral level spacings distribution and comparison with theoretical models like the Gaussian Symplectic Ensemble.

Main Results:

• Successful realization of a microwave graph with the targeted antiunitary symmetry.
• Clear identification of Kramers doublets in the experimental spectrum.
• Observation that Kramers doublets can be lifted by perturbations that break the antiunitary symmetry.
• The spectral level spacings distribution of the Kramers doublets aligns with predictions from the Gaussian Symplectic Ensemble for chaotic systems.

Conclusions:

• The experimental realization confirms the feasibility of engineering antiunitary symmetries in microwave graphs.
• The study validates the existence and behavior of Kramers doublets in such systems.
• The findings support the application of random matrix theory, specifically the Gaussian Symplectic Ensemble, to describe spectral statistics in chaotic systems with antiunitary symmetry.