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Exceptional points in a microwave billiard with time-reversal invariance violation
B Dietz1, H L Harney, O N Kirillov
1Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany.
Physical Review Letters
|May 17, 2011
Summary
This study experimentally investigates exceptional points (EPs) in a microwave billiard, revealing how time-reversal (T) violation influences system behavior. The findings show T violation magnitude depends on eigenvector phases at the EP.
Area of Science:
- Physics
- Quantum Mechanics
- Electromagnetism
Background:
- Exceptional points (EPs) are singularities in non-Hermitian systems.
- Time-reversal (T) invariance violation is crucial in various physical phenomena.
- Dissipative systems exhibit unique behaviors near EPs.
Purpose of the Study:
- To experimentally study an exceptional point (EP) in a dissipative microwave billiard.
- To investigate the impact of induced time-reversal (T) violation on the system.
- To characterize the non-Hermitian and nonsymmetric Hamiltonian associated with the EP.
Main Methods:
- Experimental realization of a dissipative microwave billiard.
- Inducing time-reversal (T) violation within the system.
- Determining the two-state Hamiltonian experimentally around the EP.
- Analyzing eigenvector components and their relative phases at the EP.
Main Results:
- The size of T violation at the EP is determined by the relative phase of eigenvector components.
- Eigenvectors exhibit geometric phases when adiabatically transported around the EP.
- Geometric amplitudes of eigenvectors deviate from unity near the EP.
Conclusions:
- The study provides experimental evidence of EP behavior in dissipative systems with T violation.
- The findings elucidate the role of eigenvector phases in quantifying T violation.
- Adiabatic transport around the EP leads to non-trivial geometric phases and amplitudes.
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